LMFDB - Embedded newform 228.5.l.a.217.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,5,Mod(145,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("228.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	228.l (of order $6$, degree $2$, 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:	$23.5683515831$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2358 x^{12} + 15572 x^{11} + 4050518 x^{10} + 21628620 x^{9} + 2974230644 x^{8} + \cdots + 96\!\cdots\!24 $ x^14 - 2x^13 + 2358x^12 + 15572x^11 + 4050518x^10 + 21628620x^9 + 2974230644x^8 + 5952397856x^7 + 1565987836020x^6 + 2094356466136x^5 + 410050182894688x^4 + 121654699639392x^3 + 75130751452572288x^2 + 84471822440408448*x + 96133502759457024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			217.7
Root			$-15.2075 - 26.3401i$ of defining polynomial
Character	$\chi$	$=$	228.217
Dual form			228.5.l.a.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 2.59808i) q^{3} +(13.2075 - 22.8760i) q^{5} +3.95127 q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 2.59808i) q^{3} +(13.2075 - 22.8760i) q^{5} +3.95127 q^{7} +(13.5000 + 23.3827i) q^{9} -66.0544 q^{11} +(251.823 - 145.390i) q^{13} +(-118.867 + 68.6281i) q^{15} +(203.993 - 353.326i) q^{17} +(-248.401 + 261.951i) q^{19} +(-17.7807 - 10.2657i) q^{21} +(62.6209 + 108.463i) q^{23} +(-36.3749 - 63.0032i) q^{25} -140.296i q^{27} +(-1371.33 + 791.736i) q^{29} -457.962i q^{31} +(297.245 + 171.614i) q^{33} +(52.1863 - 90.3894i) q^{35} -2191.32i q^{37} -1510.94 q^{39} +(-1957.61 - 1130.22i) q^{41} +(1261.53 - 2185.04i) q^{43} +713.204 q^{45} +(-1323.10 - 2291.68i) q^{47} -2385.39 q^{49} +(-1835.93 + 1059.98i) q^{51} +(3853.60 - 2224.88i) q^{53} +(-872.412 + 1511.06i) q^{55} +(1798.37 - 533.415i) q^{57} +(-3689.16 - 2129.93i) q^{59} +(123.741 + 214.326i) q^{61} +(53.3422 + 92.3913i) q^{63} -7680.93i q^{65} +(-6640.45 + 3833.86i) q^{67} -650.775i q^{69} +(2609.52 + 1506.61i) q^{71} +(-1797.57 + 3113.47i) q^{73} +378.019i q^{75} -260.999 q^{77} +(6435.38 + 3715.47i) q^{79} +(-364.500 + 631.333i) q^{81} -1653.76 q^{83} +(-5388.46 - 9333.08i) q^{85} +8227.96 q^{87} +(-1852.60 + 1069.60i) q^{89} +(995.019 - 574.474i) q^{91} +(-1189.82 + 2060.83i) q^{93} +(2711.65 + 9142.12i) q^{95} +(12756.3 + 7364.84i) q^{97} +(-891.734 - 1544.53i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 63 q^{3} - 30 q^{5} + 106 q^{7} + 189 q^{9}+O(q^{10}) $ 14 * q - 63 * q^3 - 30 * q^5 + 106 * q^7 + 189 * q^9	$ 14 q - 63 q^{3} - 30 q^{5} + 106 q^{7} + 189 q^{9} - 264 q^{11} + 57 q^{13} + 270 q^{15} + 282 q^{17} + 2 q^{19} - 477 q^{21} + 96 q^{23} - 465 q^{25} - 630 q^{29} + 1188 q^{33} + 1434 q^{35} - 342 q^{39} - 228 q^{41} - 2093 q^{43} - 1620 q^{45} - 4710 q^{47} + 4440 q^{49} - 2538 q^{51} + 2364 q^{53} + 6368 q^{55} + 1143 q^{57} + 11838 q^{59} - 1661 q^{61} + 1431 q^{63} - 20319 q^{67} + 624 q^{71} + 5851 q^{73} - 1080 q^{77} - 13299 q^{79} - 5103 q^{81} + 12252 q^{83} - 5740 q^{85} + 3780 q^{87} - 20010 q^{89} + 15951 q^{91} + 855 q^{93} + 7770 q^{95} + 44904 q^{97} - 3564 q^{99}+O(q^{100}) $ 14 * q - 63 * q^3 - 30 * q^5 + 106 * q^7 + 189 * q^9 - 264 * q^11 + 57 * q^13 + 270 * q^15 + 282 * q^17 + 2 * q^19 - 477 * q^21 + 96 * q^23 - 465 * q^25 - 630 * q^29 + 1188 * q^33 + 1434 * q^35 - 342 * q^39 - 228 * q^41 - 2093 * q^43 - 1620 * q^45 - 4710 * q^47 + 4440 * q^49 - 2538 * q^51 + 2364 * q^53 + 6368 * q^55 + 1143 * q^57 + 11838 * q^59 - 1661 * q^61 + 1431 * q^63 - 20319 * q^67 + 624 * q^71 + 5851 * q^73 - 1080 * q^77 - 13299 * q^79 - 5103 * q^81 + 12252 * q^83 - 5740 * q^85 + 3780 * q^87 - 20010 * q^89 + 15951 * q^91 + 855 * q^93 + 7770 * q^95 + 44904 * q^97 - 3564 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$4$		0			0
$5$	13.2075	−	22.8760i	0.528299	−	0.915041i	−0.471157	−	0.882050i	$-0.656163\pi$
$5$	13.2075	−	22.8760i	0.528299	−	0.915041i	0.999456	−	0.0329913i	$-0.0105034\pi$
$6$		0			0
$7$	3.95127			0.0806382			0.0403191	−	0.999187i	$-0.487163\pi$
$7$	3.95127			0.0806382			0.0403191	+	0.999187i	$0.487163\pi$
$8$		0			0
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$		0			0
$11$	−66.0544			−0.545904			−0.272952	−	0.962028i	$-0.588000\pi$
$11$	−66.0544			−0.545904			−0.272952	+	0.962028i	$0.588000\pi$
$12$		0			0
$13$	251.823	−	145.390i	1.49007	−	0.860295i	0.490139	−	0.871645i	$-0.336946\pi$
$13$	251.823	−	145.390i	1.49007	−	0.860295i	0.999936	+	0.0113498i	$0.00361285\pi$
$14$		0			0
$15$	−118.867	+	68.6281i	−0.528299	+	0.305014i
$16$		0			0
$17$	203.993	−	353.326i	0.705857	−	1.22258i	−0.260524	−	0.965467i	$-0.583895\pi$
$17$	203.993	−	353.326i	0.705857	−	1.22258i	0.966381	−	0.257113i	$-0.0827713\pi$
$18$		0			0
$19$	−248.401	+	261.951i	−0.688090	+	0.725625i
$19$	−248.401	+	261.951i	−0.688090	+	0.725625i
$20$		0			0
$21$	−17.7807	−	10.2657i	−0.0403191	−	0.0232782i
$22$		0			0
$23$	62.6209	+	108.463i	0.118376	+	0.205033i	0.919124	−	0.393968i	$-0.128898\pi$
$23$	62.6209	+	108.463i	0.118376	+	0.205033i	−0.800748	+	0.599001i	$0.795565\pi$
$24$		0			0
$25$	−36.3749	−	63.0032i	−0.0581999	−	0.100805i
$26$		0			0
$27$		−	140.296i		−	0.192450i
$28$		0			0
$29$	−1371.33	+	791.736i	−1.63059	+	0.941422i	−0.646681	+	0.762761i	$0.723843\pi$
$29$	−1371.33	+	791.736i	−1.63059	+	0.941422i	−0.983911	+	0.178661i	$0.942823\pi$
$30$		0			0
$31$		−	457.962i		−	0.476548i	−0.971198	−	0.238274i	$-0.923418\pi$
$31$		−	457.962i		−	0.476548i	0.971198	−	0.238274i	$-0.0765816\pi$
$32$		0			0
$33$	297.245	+	171.614i	0.272952	+	0.157589i
$34$		0			0
$35$	52.1863	−	90.3894i	0.0426011	−	0.0737872i
$36$		0			0
$37$		−	2191.32i		−	1.60068i	−0.599550	−	0.800338i	$-0.704654\pi$
$37$		−	2191.32i		−	1.60068i	0.599550	−	0.800338i	$-0.295346\pi$
$38$		0			0
$39$	−1510.94			−0.993383
$40$		0			0
$41$	−1957.61	−	1130.22i	−1.16455	−	0.672352i	−0.212159	−	0.977235i	$-0.568049\pi$
$41$	−1957.61	−	1130.22i	−1.16455	−	0.672352i	−0.952390	+	0.304883i	$0.901383\pi$
$42$		0			0
$43$	1261.53	−	2185.04i	0.682278	−	1.18174i	−0.292006	−	0.956417i	$-0.594323\pi$
$43$	1261.53	−	2185.04i	0.682278	−	1.18174i	0.974284	−	0.225324i	$-0.0723441\pi$
$44$		0			0
$45$	713.204			0.352199
$46$		0			0
$47$	−1323.10	−	2291.68i	−0.598960	−	1.03743i	−0.992975	−	0.118325i	$-0.962247\pi$
$47$	−1323.10	−	2291.68i	−0.598960	−	1.03743i	0.394015	−	0.919104i	$-0.371086\pi$
$48$		0			0
$49$	−2385.39			−0.993497
$50$		0			0
$51$	−1835.93	+	1059.98i	−0.705857	+	0.407527i
$52$		0			0
$53$	3853.60	−	2224.88i	1.37188	−	0.792053i	0.380712	−	0.924694i	$-0.375679\pi$
$53$	3853.60	−	2224.88i	1.37188	−	0.792053i	0.991164	+	0.132640i	$0.0423455\pi$
$54$		0			0
$55$	−872.412	+	1511.06i	−0.288401	+	0.499525i
$56$		0			0
$57$	1798.37	−	533.415i	0.553515	−	0.164178i
$58$		0			0
$59$	−3689.16	−	2129.93i	−1.05980	−	0.611874i	−0.134421	−	0.990924i	$-0.542918\pi$
$59$	−3689.16	−	2129.93i	−1.05980	−	0.611874i	−0.925376	+	0.379050i	$0.876251\pi$
$60$		0			0
$61$	123.741	+	214.326i	0.0332548	+	0.0575989i	0.882174	−	0.470924i	$-0.156079\pi$
$61$	123.741	+	214.326i	0.0332548	+	0.0575989i	−0.848919	+	0.528523i	$0.822746\pi$
$62$		0			0
$63$	53.3422	+	92.3913i	0.0134397	+	0.0232782i
$64$		0			0
$65$		−	7680.93i		−	1.81797i
$66$		0			0
$67$	−6640.45	+	3833.86i	−1.47927	+	0.854057i	−0.999725	−	0.0234595i	$-0.992532\pi$
$67$	−6640.45	+	3833.86i	−1.47927	+	0.854057i	−0.479546	+	0.877517i	$0.659199\pi$
$68$		0			0
$69$		−	650.775i		−	0.136689i
$70$		0			0
$71$	2609.52	+	1506.61i	0.517660	+	0.298871i	0.735977	−	0.677007i	$-0.236723\pi$
$71$	2609.52	+	1506.61i	0.517660	+	0.298871i	−0.218317	+	0.975878i	$0.570057\pi$
$72$		0			0
$73$	−1797.57	+	3113.47i	−0.337318	+	0.584251i	−0.983927	−	0.178570i	$-0.942853\pi$
$73$	−1797.57	+	3113.47i	−0.337318	+	0.584251i	0.646610	+	0.762821i	$0.276186\pi$
$74$		0			0
$75$			378.019i			0.0672034i
$76$		0			0
$77$	−260.999			−0.0440207
$78$		0			0
$79$	6435.38	+	3715.47i	1.03115	+	0.595332i	0.917312	−	0.398168i	$-0.130354\pi$
$79$	6435.38	+	3715.47i	1.03115	+	0.595332i	0.113833	+	0.993500i	$0.463687\pi$
$80$		0			0
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−1653.76			−0.240059			−0.120029	−	0.992770i	$-0.538299\pi$
$83$	−1653.76			−0.240059			−0.120029	+	0.992770i	$0.538299\pi$
$84$		0			0
$85$	−5388.46	−	9333.08i	−0.745807	−	1.29178i
$86$		0			0
$87$	8227.96			1.08706
$88$		0			0
$89$	−1852.60	+	1069.60i	−0.233884	+	0.135033i	−0.612363	−	0.790577i	$-0.709781\pi$
$89$	−1852.60	+	1069.60i	−0.233884	+	0.135033i	0.378478	+	0.925610i	$0.376447\pi$
$90$		0			0
$91$	995.019	−	574.474i	0.120157	−	0.0693726i
$92$		0			0
$93$	−1189.82	+	2060.83i	−0.137567	+	0.238274i
$94$		0			0
$95$	2711.65	+	9142.12i	0.300459	+	1.01298i
$96$		0			0
$97$	12756.3	+	7364.84i	1.35575	+	0.782744i	0.989048	−	0.147594i	$-0.0471529\pi$
$97$	12756.3	+	7364.84i	1.35575	+	0.782744i	0.366704	+	0.930338i	$0.380486\pi$
$98$		0			0
$99$	−891.734	−	1544.53i	−0.0909840	−	0.157589i
$100$		0			0
$101$	190.130	+	329.315i	0.0186384	+	0.0322826i	0.875194	−	0.483772i	$-0.160734\pi$
$101$	190.130	+	329.315i	0.0186384	+	0.0322826i	−0.856556	+	0.516054i	$0.827400\pi$
$102$		0			0
$103$			15522.1i			1.46310i	0.681787	+	0.731551i	$0.261203\pi$
$103$			15522.1i			1.46310i	−0.681787	+	0.731551i	$0.738797\pi$
$104$		0			0
$105$	−469.677	+	271.168i	−0.0426011	+	0.0245957i
$106$		0			0
$107$		−	19304.7i		−	1.68615i	−0.537796	−	0.843075i	$-0.680743\pi$
$107$		−	19304.7i		−	1.68615i	0.537796	−	0.843075i	$-0.319257\pi$
$108$		0			0
$109$	−5069.64	−	2926.96i	−0.426701	−	0.246356i	0.271239	−	0.962512i	$-0.412567\pi$
$109$	−5069.64	−	2926.96i	−0.426701	−	0.246356i	−0.697940	+	0.716156i	$0.745900\pi$
$110$		0			0
$111$	−5693.23	+	9860.96i	−0.462075	+	0.800338i
$112$		0			0
$113$		−	20207.0i		−	1.58251i	−0.611488	−	0.791254i	$-0.709429\pi$
$113$		−	20207.0i		−	1.58251i	0.611488	−	0.791254i	$-0.290571\pi$
$114$		0			0
$115$	3308.25			0.250152
$116$		0			0
$117$	6799.21	+	3925.52i	0.496691	+	0.286765i
$118$		0			0
$119$	806.030	−	1396.09i	0.0569190	−	0.0985867i
$120$		0			0
$121$	−10277.8			−0.701989
$122$		0			0
$123$	5872.82	+	10172.0i	0.388183	+	0.672352i
$124$		0			0
$125$	14587.7			0.933610
$126$		0			0
$127$	13379.6	−	7724.74i	0.829539	−	0.478935i	−0.0241556	−	0.999708i	$-0.507690\pi$
$127$	13379.6	−	7724.74i	0.829539	−	0.478935i	0.853695	+	0.520773i	$0.174356\pi$
$128$		0			0
$129$	−11353.8	+	6555.12i	−0.682278	+	0.393914i
$130$		0			0
$131$	1431.61	−	2479.63i	0.0834225	−	0.144492i	−0.821295	−	0.570503i	$-0.806748\pi$
$131$	1431.61	−	2479.63i	0.0834225	−	0.144492i	0.904718	+	0.426011i	$0.140082\pi$
$132$		0			0
$133$	−981.498	+	1035.04i	−0.0554863	+	0.0585131i
$134$		0			0
$135$	−3209.42	−	1852.96i	−0.176100	−	0.101671i
$136$		0			0
$137$	1152.70	+	1996.53i	0.0614149	+	0.106374i	0.895098	−	0.445869i	$-0.147105\pi$
$137$	1152.70	+	1996.53i	0.0614149	+	0.106374i	−0.833683	+	0.552243i	$0.813772\pi$
$138$		0			0
$139$	16171.7	+	28010.3i	0.837003	+	1.44973i	0.892389	+	0.451267i	$0.149028\pi$
$139$	16171.7	+	28010.3i	0.837003	+	1.44973i	−0.0553863	+	0.998465i	$0.517639\pi$
$140$		0			0
$141$			13750.1i			0.691620i
$142$		0			0
$143$	−16634.0	+	9603.64i	−0.813438	+	0.469638i
$144$		0			0
$145$			41827.3i			1.98941i
$146$		0			0
$147$	10734.2	+	6197.42i	0.496749	+	0.286798i
$148$		0			0
$149$	6161.61	−	10672.2i	0.277538	−	0.480709i	−0.693235	−	0.720712i	$-0.743815\pi$
$149$	6161.61	−	10672.2i	0.277538	−	0.480709i	0.970772	+	0.240003i	$0.0771483\pi$
$150$		0			0
$151$			26041.0i			1.14210i	0.820916	+	0.571050i	$0.193464\pi$
$151$			26041.0i			1.14210i	−0.820916	+	0.571050i	$0.806536\pi$
$152$		0			0
$153$	11015.6			0.470571
$154$		0			0
$155$	−10476.4	−	6048.53i	−0.436061	−	0.251760i
$156$		0			0
$157$	9055.18	−	15684.0i	0.367365	−	0.636295i	−0.621788	−	0.783186i	$-0.713593\pi$
$157$	9055.18	−	15684.0i	0.367365	−	0.636295i	0.989153	+	0.146891i	$0.0469267\pi$
$158$		0			0
$159$	−23121.6			−0.914584
$160$		0			0
$161$	247.432	+	428.565i	0.00954562	+	0.0165335i
$162$		0			0
$163$	1816.65			0.0683748			0.0341874	−	0.999415i	$-0.489116\pi$
$163$	1816.65			0.0683748			0.0341874	+	0.999415i	$0.489116\pi$
$164$		0			0
$165$	7851.71	−	4533.19i	0.288401	−	0.166508i
$166$		0			0
$167$	−26066.6	+	15049.5i	−0.934655	+	0.539623i	−0.888281	−	0.459301i	$-0.848100\pi$
$167$	−26066.6	+	15049.5i	−0.934655	+	0.539623i	−0.0463740	+	0.998924i	$0.514767\pi$
$168$		0			0
$169$	27995.9	−	48490.3i	0.980214	−	1.69778i
$170$		0			0
$171$	−9478.52	−	2271.94i	−0.324152	−	0.0776970i
$172$		0			0
$173$	27606.0	+	15938.3i	0.922383	+	0.532538i	0.884395	−	0.466740i	$-0.154572\pi$
$173$	27606.0	+	15938.3i	0.922383	+	0.532538i	0.0379886	+	0.999278i	$0.487905\pi$
$174$		0			0
$175$	−143.727	−	248.943i	−0.00469313	−	0.00812874i
$176$		0			0
$177$	11067.5	+	19169.4i	0.353266	+	0.611874i
$178$		0			0
$179$		−	25052.3i		−	0.781884i	−0.920415	−	0.390942i	$-0.872149\pi$
$179$		−	25052.3i		−	0.781884i	0.920415	−	0.390942i	$-0.127851\pi$
$180$		0			0
$181$	30483.9	−	17599.9i	0.930494	−	0.537221i	0.0435262	−	0.999052i	$-0.486141\pi$
$181$	30483.9	−	17599.9i	0.930494	−	0.537221i	0.886968	+	0.461831i	$0.152807\pi$
$182$		0			0
$183$		−	1285.95i		−	0.0383993i
$184$		0			0
$185$	−50128.8	−	28941.9i	−1.46468	−	0.845635i
$186$		0			0
$187$	−13474.6	+	23338.7i	−0.385330	+	0.667412i
$188$		0			0
$189$		−	554.348i		−	0.0155188i
$190$		0			0
$191$	69403.7			1.90246			0.951231	−	0.308479i	$-0.0998201\pi$
$191$	69403.7			1.90246			0.951231	+	0.308479i	$0.0998201\pi$
$192$		0			0
$193$	572.006	+	330.248i	0.0153563	+	0.00886595i	0.507658	−	0.861558i	$-0.330511\pi$
$193$	572.006	+	330.248i	0.0153563	+	0.00886595i	−0.492302	+	0.870424i	$0.663845\pi$
$194$		0			0
$195$	−19955.6	+	34564.2i	−0.524803	+	0.908986i
$196$		0			0
$197$	8731.63			0.224990			0.112495	−	0.993652i	$-0.464116\pi$
$197$	8731.63			0.224990			0.112495	+	0.993652i	$0.464116\pi$
$198$		0			0
$199$	18442.2	+	31942.8i	0.465700	+	0.806616i	0.999233	−	0.0391632i	$-0.0124692\pi$
$199$	18442.2	+	31942.8i	0.465700	+	0.806616i	−0.533533	+	0.845779i	$0.679136\pi$
$200$		0			0
$201$	39842.7			0.986180
$202$		0			0
$203$	−5418.48	+	3128.36i	−0.131488	+	0.0759146i
$204$		0			0
$205$	−51710.1	+	29854.8i	−1.23046	+	0.710406i
$206$		0			0
$207$	−1690.76	+	2928.49i	−0.0394586	+	0.0683444i
$208$		0			0
$209$	16407.9	−	17303.0i	0.375631	−	0.396122i
$210$		0			0
$211$	−28075.1	−	16209.2i	−0.630604	−	0.364079i	0.150382	−	0.988628i	$-0.451950\pi$
$211$	−28075.1	−	16209.2i	−0.630604	−	0.364079i	−0.780986	+	0.624549i	$0.785283\pi$
$212$		0			0
$213$	−7828.57	−	13559.5i	−0.172553	−	0.298871i
$214$		0			0
$215$	−33323.3	−	57717.7i	−0.720894	−	1.24863i
$216$		0			0
$217$		−	1809.53i		−	0.0384279i
$218$		0			0
$219$	16178.1	−	9340.42i	0.337318	−	0.194750i
$220$		0			0
$221$		−	118634.i		−	2.42898i
$222$		0			0
$223$	−73819.4	−	42619.7i	−1.48443	−	0.857039i	−0.484591	−	0.874741i	$-0.661032\pi$
$223$	−73819.4	−	42619.7i	−1.48443	−	0.857039i	−0.999843	+	0.0177024i	$0.994365\pi$
$224$		0			0
$225$	982.123	−	1701.09i	0.0194000	−	0.0336017i
$226$		0			0
$227$		−	27523.0i		−	0.534126i	−0.963679	−	0.267063i	$-0.913947\pi$
$227$		−	27523.0i		−	0.534126i	0.963679	−	0.267063i	$-0.0860532\pi$
$228$		0			0
$229$	53550.6			1.02116			0.510580	−	0.859830i	$-0.329431\pi$
$229$	53550.6			1.02116			0.510580	+	0.859830i	$0.329431\pi$
$230$		0			0
$231$	1174.49	+	678.095i	0.0220104	+	0.0127077i
$232$		0			0
$233$	20198.3	−	34984.4i	0.372051	−	0.644411i	−0.617830	−	0.786312i	$-0.711988\pi$
$233$	20198.3	−	34984.4i	0.372051	−	0.644411i	0.989881	+	0.141901i	$0.0453213\pi$
$234$		0			0
$235$	−69899.4			−1.26572
$236$		0			0
$237$	−19306.1	−	33439.2i	−0.343715	−	0.595332i
$238$		0			0
$239$	−54594.4			−0.955768			−0.477884	−	0.878423i	$-0.658596\pi$
$239$	−54594.4			−0.955768			−0.477884	+	0.878423i	$0.658596\pi$
$240$		0			0
$241$	−41863.1	+	24169.7i	−0.720771	+	0.416137i	−0.815036	−	0.579410i	$-0.803283\pi$
$241$	−41863.1	+	24169.7i	−0.720771	+	0.416137i	0.0942654	+	0.995547i	$0.469950\pi$
$242$		0			0
$243$	3280.50	−	1894.00i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−31505.0	+	54568.2i	−0.524864	+	0.909091i
$246$		0			0
$247$	−24467.9	+	102080.i	−0.401054	+	1.67320i
$248$		0			0
$249$	7441.94	+	4296.61i	0.120029	+	0.0692990i
$250$		0			0
$251$	37943.6	+	65720.3i	0.602270	+	1.04316i	0.992476	+	0.122435i	$0.0390704\pi$
$251$	37943.6	+	65720.3i	0.602270	+	1.04316i	−0.390206	+	0.920728i	$0.627596\pi$
$252$		0			0
$253$	−4136.38	−	7164.43i	−0.0646219	−	0.111928i
$254$		0			0
$255$			55998.5i			0.861184i
$256$		0			0
$257$	−107798.	+	62237.0i	−1.63209	+	0.942286i	−0.648639	+	0.761096i	$0.724661\pi$
$257$	−107798.	+	62237.0i	−1.63209	+	0.942286i	−0.983448	+	0.181189i	$0.942005\pi$
$258$		0			0
$259$		−	8658.52i		−	0.129076i
$260$		0			0
$261$	−37025.8	−	21376.9i	−0.543530	−	0.313807i
$262$		0			0
$263$	34739.9	−	60171.2i	0.502246	−	0.869916i	−0.497750	−	0.867320i	$-0.665840\pi$
$263$	34739.9	−	60171.2i	0.502246	−	0.869916i	0.999997	−	0.00259575i	$-0.000826255\pi$
$264$		0			0
$265$		−	117540.i		−	1.67376i
$266$		0			0
$267$	11115.6			0.155923
$268$		0			0
$269$	−54316.7	−	31359.8i	−0.750635	−	0.433379i	0.0752883	−	0.997162i	$-0.476012\pi$
$269$	−54316.7	−	31359.8i	−0.750635	−	0.433379i	−0.825923	+	0.563782i	$0.809346\pi$
$270$		0			0
$271$	24492.5	−	42422.3i	0.333499	−	0.577638i	−0.649696	−	0.760194i	$-0.725104\pi$
$271$	24492.5	−	42422.3i	0.333499	−	0.577638i	0.983195	+	0.182556i	$0.0584372\pi$
$272$		0			0
$273$	−5970.11			−0.0801046
$274$		0			0
$275$	2402.72	+	4161.64i	0.0317716	+	0.0550299i
$276$		0			0
$277$	83714.4			1.09104			0.545520	−	0.838098i	$-0.316332\pi$
$277$	83714.4			1.09104			0.545520	+	0.838098i	$0.316332\pi$
$278$		0			0
$279$	10708.4	−	6182.49i	0.137567	−	0.0794246i
$280$		0			0
$281$	32897.2	−	18993.2i	0.416626	−	0.240539i	−0.277007	−	0.960868i	$-0.589342\pi$
$281$	32897.2	−	18993.2i	0.416626	−	0.240539i	0.693633	+	0.720329i	$0.256009\pi$
$282$		0			0
$283$	35732.7	−	61890.8i	0.446162	−	0.772775i	−0.551970	−	0.833864i	$-0.686124\pi$
$283$	35732.7	−	61890.8i	0.446162	−	0.772775i	0.998132	+	0.0610884i	$0.0194571\pi$
$284$		0			0
$285$	11549.5	−	48184.6i	0.142192	−	0.593224i
$286$		0			0
$287$	−7735.03	−	4465.82i	−0.0939071	−	0.0542173i
$288$		0			0
$289$	−41465.6	−	71820.4i	−0.496469	−	0.859909i
$290$		0			0
$291$	−38268.8	−	66283.5i	−0.451917	−	0.782744i
$292$		0			0
$293$		−	8987.73i		−	0.104692i	−0.998629	−	0.0523461i	$-0.983330\pi$
$293$		−	8987.73i		−	0.104692i	0.998629	−	0.0523461i	$-0.0166699\pi$
$294$		0			0
$295$	−97448.9	+	56262.1i	−1.11978	+	0.646505i
$296$		0			0
$297$			9267.18i			0.105059i
$298$		0			0
$299$	31538.7	+	18208.9i	0.352778	+	0.203676i
$300$		0			0
$301$	4984.66	−	8633.68i	0.0550177	−	0.0952934i
$302$		0			0
$303$		−	1975.89i		−	0.0215218i
$304$		0			0
$305$	6537.22			0.0702738
$306$		0			0
$307$	7608.34	+	4392.68i	0.0807260	+	0.0466072i	0.539820	−	0.841781i	$-0.318492\pi$
$307$	7608.34	+	4392.68i	0.0807260	+	0.0466072i	−0.459094	+	0.888388i	$0.651826\pi$
$308$		0			0
$309$	40327.5	−	69849.2i	0.422361	−	0.731551i
$310$		0			0
$311$	59943.3			0.619755			0.309878	−	0.950776i	$-0.399712\pi$
$311$	59943.3			0.619755			0.309878	+	0.950776i	$0.399712\pi$
$312$		0			0
$313$	20206.9	+	34999.3i	0.206258	+	0.357249i	0.950533	−	0.310624i	$-0.100538\pi$
$313$	20206.9	+	34999.3i	0.206258	+	0.357249i	−0.744275	+	0.667873i	$0.767205\pi$
$314$		0			0
$315$	2818.06			0.0284007
$316$		0			0
$317$	−43676.0	+	25216.4i	−0.434635	+	0.250937i	−0.701319	−	0.712847i	$-0.747405\pi$
$317$	−43676.0	+	25216.4i	−0.434635	+	0.250937i	0.266684	+	0.963784i	$0.414072\pi$
$318$		0			0
$319$	90582.2	−	52297.7i	0.890147	−	0.513926i
$320$		0			0
$321$	−50155.2	+	86871.3i	−0.486750	+	0.843075i
$322$		0			0
$323$	41882.0	+	141202.i	0.401442	+	1.35343i
$324$		0			0
$325$	−18320.0	−	10577.1i	−0.173444	−	0.100138i
$326$		0			0
$327$	15208.9	+	26342.6i	0.142234	+	0.246356i
$328$		0			0
$329$	−5227.94	−	9055.05i	−0.0482991	−	0.0836564i
$330$		0			0
$331$		−	27515.7i		−	0.251145i	−0.992084	−	0.125573i	$-0.959923\pi$
$331$		−	27515.7i		−	0.251145i	0.992084	−	0.125573i	$-0.0400768\pi$
$332$		0			0
$333$	51239.0	−	29582.9i	0.462075	−	0.266779i
$334$		0			0
$335$			202543.i			1.80479i
$336$		0			0
$337$	108897.	+	62872.0i	0.958866	+	0.553602i	0.895824	−	0.444409i	$-0.146586\pi$
$337$	108897.	+	62872.0i	0.958866	+	0.553602i	0.0630421	+	0.998011i	$0.479920\pi$
$338$		0			0
$339$	−52499.4	+	90931.7i	−0.456830	+	0.791254i
$340$		0			0
$341$			30250.4i			0.260149i
$342$		0			0
$343$	−18912.3			−0.160752
$344$		0			0
$345$	−14887.1	−	8595.10i	−0.125076	−	0.0722125i
$346$		0			0
$347$	−7145.75	+	12376.8i	−0.0593457	+	0.102790i	−0.894172	−	0.447724i	$-0.852235\pi$
$347$	−7145.75	+	12376.8i	−0.0593457	+	0.102790i	0.834826	+	0.550514i	$0.185568\pi$
$348$		0			0
$349$	66467.6			0.545706			0.272853	−	0.962056i	$-0.412033\pi$
$349$	66467.6			0.545706			0.272853	+	0.962056i	$0.412033\pi$
$350$		0			0
$351$	−20397.6	−	35329.7i	−0.165564	−	0.286765i
$352$		0			0
$353$	107847.			0.865487			0.432743	−	0.901517i	$-0.357546\pi$
$353$	107847.			0.865487			0.432743	+	0.901517i	$0.357546\pi$
$354$		0			0
$355$	68930.4	−	39797.0i	0.546959	−	0.315787i
$356$		0			0
$357$	−7254.27	+	4188.26i	−0.0569190	+	0.0328622i
$358$		0			0
$359$	32192.7	−	55759.4i	0.249786	−	0.432643i	−0.713680	−	0.700472i	$-0.752973\pi$
$359$	32192.7	−	55759.4i	0.249786	−	0.432643i	0.963466	+	0.267829i	$0.0863063\pi$
$360$		0			0
$361$	−6915.34	−	130137.i	−0.0530639	−	0.998591i
$362$		0			0
$363$	46250.2	+	26702.5i	0.350994	+	0.202647i
$364$		0			0
$365$	47482.6	+	82242.3i	0.356409	+	0.617319i
$366$		0			0
$367$	−8645.43	−	14974.3i	−0.0641881	−	0.111177i	0.832145	−	0.554557i	$-0.187112\pi$
$367$	−8645.43	−	14974.3i	−0.0641881	−	0.111177i	−0.896334	+	0.443380i	$0.853779\pi$
$368$		0			0
$369$		−	61032.1i		−	0.448235i
$370$		0			0
$371$	15226.6	−	8791.09i	0.110626	−	0.0638697i
$372$		0			0
$373$			83855.1i			0.602715i	0.953511	+	0.301358i	$0.0974398\pi$
$373$			83855.1i			0.602715i	−0.953511	+	0.301358i	$0.902560\pi$
$374$		0			0
$375$	−65644.5	−	37899.9i	−0.466805	−	0.269510i
$376$		0			0
$377$	−230221.	+	398754.i	−1.61980	+	2.80558i
$378$		0			0
$379$			237159.i			1.65105i	0.564363	+	0.825526i	$0.309122\pi$
$379$			237159.i			1.65105i	−0.564363	+	0.825526i	$0.690878\pi$
$380$		0			0
$381$	−80277.8			−0.553026
$382$		0			0
$383$	647.503	+	373.836i	0.00441412	+	0.00254849i	0.502205	−	0.864748i	$-0.332522\pi$
$383$	647.503	+	373.836i	0.00441412	+	0.00254849i	−0.497791	+	0.867297i	$0.665855\pi$
$384$		0			0
$385$	−3447.14	+	5970.61i	−0.0232561	+	0.0402808i
$386$		0			0
$387$	68122.8			0.454852
$388$		0			0
$389$	25400.9	+	43995.7i	0.167861	+	0.290744i	0.937668	−	0.347533i	$-0.112981\pi$
$389$	25400.9	+	43995.7i	0.167861	+	0.290744i	−0.769806	+	0.638277i	$0.779647\pi$
$390$		0			0
$391$	51096.8			0.334226
$392$		0			0
$393$	−12884.5	+	7438.89i	−0.0834225	+	0.0481640i
$394$		0			0
$395$	169990.	−	98143.9i	1.08951	−	0.629027i
$396$		0			0
$397$	58870.5	−	101967.i	0.373522	−	0.646959i	−0.616582	−	0.787290i	$-0.711483\pi$
$397$	58870.5	−	101967.i	0.373522	−	0.646959i	0.990105	+	0.140331i	$0.0448167\pi$
$398$		0			0
$399$	7105.85	−	2107.67i	0.0446344	−	0.0132390i
$400$		0			0
$401$	143708.	+	82970.0i	0.893702	+	0.515979i	0.875152	−	0.483849i	$-0.160762\pi$
$401$	143708.	+	82970.0i	0.893702	+	0.515979i	0.0185504	+	0.999828i	$0.494095\pi$
$402$		0			0
$403$	−66583.0	−	115325.i	−0.409971	−	0.710091i
$404$		0			0
$405$	9628.25	+	16676.6i	0.0586999	+	0.101671i
$406$		0			0
$407$			144747.i			0.873815i
$408$		0			0
$409$	−184594.	+	106575.i	−1.10349	+	0.637103i	−0.937137	−	0.348963i	$-0.886534\pi$
$409$	−184594.	+	106575.i	−1.10349	+	0.637103i	−0.166358	+	0.986066i	$0.553201\pi$
$410$		0			0
$411$		−	11979.2i		−	0.0709158i
$412$		0			0
$413$	−14576.9	−	8415.95i	−0.0854601	−	0.0493404i
$414$		0			0
$415$	−21842.1	+	37831.6i	−0.126823	+	0.219664i
$416$		0			0
$417$		−	168062.i		−	0.966488i
$418$		0			0
$419$	59218.3			0.337309			0.168654	−	0.985675i	$-0.446058\pi$
$419$	59218.3			0.337309			0.168654	+	0.985675i	$0.446058\pi$
$420$		0			0
$421$	57179.4	+	33012.5i	0.322608	+	0.186258i	0.652555	−	0.757742i	$-0.273697\pi$
$421$	57179.4	+	33012.5i	0.322608	+	0.186258i	−0.329946	+	0.944000i	$0.607031\pi$
$422$		0			0
$423$	35723.8	−	61875.4i	0.199653	−	0.345810i
$424$		0			0
$425$	−29680.9			−0.164323
$426$		0			0
$427$	488.934	+	846.859i	0.00268160	+	0.00464467i
$428$		0			0
$429$	99803.9			0.542292
$430$		0			0
$431$	−101448.	+	58570.8i	−0.546119	+	0.315302i	−0.747555	−	0.664200i	$-0.768772\pi$
$431$	−101448.	+	58570.8i	−0.546119	+	0.315302i	0.201436	+	0.979502i	$0.435439\pi$
$432$		0			0
$433$	185685.	−	107205.i	0.990379	−	0.571796i	0.0849918	−	0.996382i	$-0.472914\pi$
$433$	185685.	−	107205.i	0.990379	−	0.571796i	0.905388	+	0.424586i	$0.139580\pi$
$434$		0			0
$435$	108671.	−	188223.i	0.574293	−	0.994705i
$436$		0			0
$437$	−43966.9	−	10538.6i	−0.230230	−	0.0551847i
$438$		0			0
$439$	−228113.	−	131701.i	−1.18364	−	0.683376i	−0.226788	−	0.973944i	$-0.572822\pi$
$439$	−228113.	−	131701.i	−1.18364	−	0.683376i	−0.956854	+	0.290568i	$0.906156\pi$
$440$		0			0
$441$	−32202.7	−	55776.8i	−0.165583	−	0.286798i
$442$		0			0
$443$	−25906.1	−	44870.8i	−0.132006	−	0.228642i	0.792443	−	0.609945i	$-0.208809\pi$
$443$	−25906.1	−	44870.8i	−0.132006	−	0.228642i	−0.924450	+	0.381303i	$0.875475\pi$
$444$		0			0
$445$			56506.8i			0.285352i
$446$		0			0
$447$	−55454.5	+	32016.7i	−0.277538	+	0.160236i
$448$		0			0
$449$			300762.i			1.49187i	0.666019	+	0.745935i	$0.267997\pi$
$449$			300762.i			1.49187i	−0.666019	+	0.745935i	$0.732003\pi$
$450$		0			0
$451$	129308.	+	74656.3i	0.635732	+	0.367040i
$452$		0			0
$453$	67656.5	−	117185.i	0.329696	−	0.571050i
$454$		0			0
$455$		−	30349.4i		−	0.146598i
$456$		0			0
$457$	143035.			0.684872			0.342436	−	0.939541i	$-0.388748\pi$
$457$	143035.			0.684872			0.342436	+	0.939541i	$0.388748\pi$
$458$		0			0
$459$	−49570.2	−	28619.4i	−0.235286	−	0.135842i
$460$		0			0
$461$	−62369.0	+	108026.i	−0.293472	+	0.508309i	−0.974628	−	0.223830i	$-0.928144\pi$
$461$	−62369.0	+	108026.i	−0.293472	+	0.508309i	0.681156	+	0.732138i	$0.261477\pi$
$462$		0			0
$463$	−303815.			−1.41725			−0.708626	−	0.705585i	$-0.750684\pi$
$463$	−303815.			−1.41725			−0.708626	+	0.705585i	$0.750684\pi$
$464$		0			0
$465$	31429.1	+	54436.7i	0.145354	+	0.251760i
$466$		0			0
$467$	407608.			1.86900			0.934499	−	0.355966i	$-0.115848\pi$
$467$	407608.			1.86900			0.934499	+	0.355966i	$0.115848\pi$
$468$		0			0
$469$	−26238.2	+	15148.6i	−0.119286	+	0.0688696i
$470$		0			0
$471$	−81496.6	+	47052.1i	−0.367365	+	0.212098i
$472$		0			0
$473$	−83329.8	+	144331.i	−0.372459	+	0.645117i
$474$		0			0
$475$	25539.3	+	6121.60i	0.113194	+	0.0271317i
$476$		0			0
$477$	104047.	+	60071.7i	0.457292	+	0.264018i
$478$		0			0
$479$	−91751.1	−	158918.i	−0.399890	−	0.692630i	0.593822	−	0.804596i	$-0.297618\pi$
$479$	−91751.1	−	158918.i	−0.399890	−	0.692630i	−0.993712	+	0.111967i	$0.964285\pi$
$480$		0			0
$481$	−318596.	−	551825.i	−1.37705	−	2.38512i
$482$		0			0
$483$		−	2571.39i		−	0.0110223i
$484$		0			0
$485$	336956.	−	194542.i	1.43248	−	0.827046i
$486$		0			0
$487$		−	74156.9i		−	0.312676i	−0.987704	−	0.156338i	$-0.950031\pi$
$487$		−	74156.9i		−	0.312676i	0.987704	−	0.156338i	$-0.0499688\pi$
$488$		0			0
$489$	−8174.93	−	4719.80i	−0.0341874	−	0.0197381i
$490$		0			0
$491$	62825.2	−	108816.i	0.260598	−	0.451369i	−0.705803	−	0.708408i	$-0.749414\pi$
$491$	62825.2	−	108816.i	0.260598	−	0.451369i	0.966401	+	0.257039i	$0.0827470\pi$
$492$		0			0
$493$			646034.i			2.65804i
$494$		0			0
$495$	−47110.3			−0.192267
$496$		0			0
$497$	10310.9	+	5953.02i	0.0417432	+	0.0241004i
$498$		0			0
$499$	−51694.7	+	89537.8i	−0.207608	+	0.359588i	−0.950961	−	0.309312i	$-0.899901\pi$
$499$	−51694.7	+	89537.8i	−0.207608	+	0.359588i	0.743352	+	0.668900i	$0.233235\pi$
$500$		0			0
$501$	156399.			0.623103
$502$		0			0
$503$	−147700.	−	255825.i	−0.583775	−	1.01113i	−0.995027	−	0.0996066i	$-0.968242\pi$
$503$	−147700.	−	255825.i	−0.583775	−	1.01113i	0.411252	−	0.911522i	$-0.365092\pi$
$504$		0			0
$505$	10044.6			0.0393866
$506$		0			0
$507$	−251963.	+	145471.i	−0.980214	+	0.565927i
$508$		0			0
$509$	−311158.	+	179647.i	−1.20101	+	0.693401i	−0.960779	−	0.277316i	$-0.910555\pi$
$509$	−311158.	+	179647.i	−1.20101	+	0.693401i	−0.240227	+	0.970717i	$0.577222\pi$
$510$		0			0
$511$	−7102.67	+	12302.2i	−0.0272007	+	0.0471129i
$512$		0			0
$513$	36750.7	+	34849.6i	0.139647	+	0.132423i
$514$		0			0
$515$	355083.	+	205007.i	1.33880	+	0.772956i
$516$		0			0
$517$	87396.8	+	151376.i	0.326975	+	0.566337i
$518$		0			0
$519$	−82818.0	−	143445.i	−0.307461	−	0.532538i
$520$		0			0
$521$			195107.i			0.718782i	0.933187	+	0.359391i	$0.117016\pi$
$521$			195107.i			0.718782i	−0.933187	+	0.359391i	$0.882984\pi$
$522$		0			0
$523$	259323.	−	149720.i	0.948063	−	0.547364i	0.0555841	−	0.998454i	$-0.482298\pi$
$523$	259323.	−	149720.i	0.948063	−	0.547364i	0.892479	+	0.451090i	$0.148965\pi$
$524$		0			0
$525$			1493.66i			0.00541916i
$526$		0			0
$527$	−161810.	−	93421.0i	−0.582618	−	0.336375i
$528$		0			0
$529$	132078.	−	228765.i	0.471974	−	0.817483i
$530$		0			0
$531$		−	115016.i		−	0.407916i
$532$		0			0
$533$	−657292.			−2.31368
$534$		0			0
$535$	−441616.	−	254967.i	−1.54290	−	0.890792i
$536$		0			0
$537$	−65087.9	+	112736.i	−0.225710	+	0.390942i
$538$		0			0
$539$	157565.			0.542354
$540$		0			0
$541$	83074.6	+	143889.i	0.283840	+	0.491625i	0.972327	−	0.233623i	$-0.0750582\pi$
$541$	83074.6	+	143889.i	0.283840	+	0.491625i	−0.688487	+	0.725249i	$0.741725\pi$
$542$		0			0
$543$	−182903.			−0.620329
$544$		0			0
$545$	−133914.	+	77315.4i	−0.450852	+	0.260299i
$546$		0			0
$547$	345204.	−	199304.i	1.15372	−	0.666102i	0.203931	−	0.978985i	$-0.434628\pi$
$547$	345204.	−	199304.i	1.15372	−	0.666102i	0.949792	+	0.312883i	$0.101295\pi$
$548$		0			0
$549$	−3341.01	+	5786.79i	−0.0110849	+	0.0191996i
$550$		0			0
$551$	133243.	−	555888.i	0.438874	−	1.83098i
$552$		0			0
$553$	25427.9	+	14680.8i	0.0831497	+	0.0480065i
$554$		0			0
$555$	150386.	+	260477.i	0.488228	+	0.845635i
$556$		0			0
$557$	−157159.	−	272208.i	−0.506558	−	0.877384i	−0.999971	−	0.00758920i	$-0.997584\pi$
$557$	−157159.	−	272208.i	−0.506558	−	0.877384i	0.493413	−	0.869795i	$-0.335749\pi$
$558$		0			0
$559$		−	733656.i		−	2.34784i
$560$		0			0
$561$	121272.	−	70016.2i	0.385330	−	0.222471i
$562$		0			0
$563$			39467.4i			0.124515i	0.998060	+	0.0622574i	$0.0198300\pi$
$563$			39467.4i			0.124515i	−0.998060	+	0.0622574i	$0.980170\pi$
$564$		0			0
$565$	−462257.	−	266884.i	−1.44806	−	0.836037i
$566$		0			0
$567$	−1440.24	+	2494.57i	−0.00447990	+	0.00775941i
$568$		0			0
$569$			376002.i			1.16136i	0.814133	+	0.580679i	$0.197213\pi$
$569$			376002.i			1.16136i	−0.814133	+	0.580679i	$0.802787\pi$
$570$		0			0
$571$	452184.			1.38689			0.693446	−	0.720508i	$-0.256091\pi$
$571$	452184.			1.38689			0.693446	+	0.720508i	$0.256091\pi$
$572$		0			0
$573$	−312317.	−	180316.i	−0.951231	−	0.549193i
$574$		0			0
$575$	4555.66	−	7890.63i	0.0137789	−	0.0238658i
$576$		0			0
$577$	−394141.			−1.18386			−0.591929	−	0.805990i	$-0.701633\pi$
$577$	−394141.			−1.18386			−0.591929	+	0.805990i	$0.701633\pi$
$578$		0			0
$579$	−1716.02	−	2972.23i	−0.00511876	−	0.00886595i
$580$		0			0
$581$	−6534.47			−0.0193579
$582$		0			0
$583$	−254547.	+	146963.i	−0.748913	+	0.432385i
$584$		0			0
$585$	179601.	−	103693.i	0.524803	−	0.302995i
$586$		0			0
$587$	248196.	−	429888.i	0.720308	−	1.24761i	−0.240568	−	0.970632i	$-0.577334\pi$
$587$	248196.	−	429888.i	0.720308	−	1.24761i	0.960876	−	0.276978i	$-0.0893330\pi$
$588$		0			0
$589$	119964.	+	113758.i	0.345795	+	0.327908i
$590$		0			0
$591$	−39292.4	−	22685.4i	−0.112495	−	0.0649490i
$592$		0			0
$593$	−89679.7	−	155330.i	−0.255026	−	0.441718i	0.709876	−	0.704326i	$-0.248751\pi$
$593$	−89679.7	−	155330.i	−0.255026	−	0.441718i	−0.964903	+	0.262608i	$0.915417\pi$
$594$		0			0
$595$	−21291.3	−	36877.5i	−0.0601405	−	0.104166i
$596$		0			0
$597$		−	191657.i		−	0.537744i
$598$		0			0
$599$	57674.8	−	33298.5i	0.160743	−	0.0928050i	−0.417471	−	0.908690i	$-0.637083\pi$
$599$	57674.8	−	33298.5i	0.160743	−	0.0928050i	0.578214	+	0.815885i	$0.303750\pi$
$600$		0			0
$601$			117101.i			0.324200i	0.986774	+	0.162100i	$0.0518267\pi$
$601$			117101.i			0.324200i	−0.986774	+	0.162100i	$0.948173\pi$
$602$		0			0
$603$	−179292.	−	103514.i	−0.493090	−	0.284686i
$604$		0			0
$605$	−135744.	+	235116.i	−0.370860	+	0.642348i
$606$		0			0
$607$			480656.i			1.30454i	0.757988	+	0.652269i	$0.226183\pi$
$607$			480656.i			1.30454i	−0.757988	+	0.652269i	$0.773817\pi$
$608$		0			0
$609$	32510.9			0.0876586
$610$		0			0
$611$	−666374.	−	384731.i	−1.78499	−	1.03056i
$612$		0			0
$613$	274075.	−	474712.i	0.729372	−	1.26331i	−0.227777	−	0.973713i	$-0.573146\pi$
$613$	274075.	−	474712.i	0.729372	−	1.26331i	0.957149	−	0.289596i	$-0.0935209\pi$
$614$		0			0
$615$	310260.			0.820306
$616$		0			0
$617$	346802.	+	600678.i	0.910985	+	1.57787i	0.812676	+	0.582716i	$0.198010\pi$
$617$	346802.	+	600678.i	0.910985	+	1.57787i	0.0983085	+	0.995156i	$0.468657\pi$
$618$		0			0
$619$	−89967.6			−0.234804			−0.117402	−	0.993084i	$-0.537457\pi$
$619$	−89967.6			−0.234804			−0.117402	+	0.993084i	$0.537457\pi$
$620$		0			0
$621$	15216.9	−	8785.46i	0.0394586	−	0.0227815i
$622$		0			0
$623$	−7320.11	+	4226.27i	−0.0188600	+	0.0108888i
$624$		0			0
$625$	215401.	−	373085.i	0.551425	−	0.955097i
$626$		0			0
$627$	−118790.	+	35234.4i	−0.302166	+	0.0896255i
$628$		0			0
$629$	−774251.	−	447014.i	−1.95695	−	1.12985i
$630$		0			0
$631$	266143.	+	460974.i	0.668431	+	1.15776i	0.978343	+	0.206991i	$0.0663672\pi$
$631$	266143.	+	460974.i	0.668431	+	1.15776i	−0.309912	+	0.950765i	$0.600299\pi$
$632$		0			0
$633$	84225.3	+	145883.i	0.210201	+	0.364079i
$634$		0			0
$635$		−	408097.i		−	1.01208i
$636$		0			0
$637$	−600694.	+	346811.i	−1.48038	+	0.854701i
$638$		0			0
$639$			81356.9i			0.199247i
$640$		0			0
$641$	−346114.	−	199829.i	−0.842371	−	0.486343i	0.0156986	−	0.999877i	$-0.495003\pi$
$641$	−346114.	−	199829.i	−0.842371	−	0.486343i	−0.858069	+	0.513534i	$0.828336\pi$
$642$		0			0
$643$	59063.7	−	102301.i	0.142856	−	0.247434i	−0.785715	−	0.618589i	$-0.787705\pi$
$643$	59063.7	−	102301.i	0.142856	−	0.247434i	0.928571	+	0.371155i	$0.121038\pi$
$644$		0			0
$645$			346306.i			0.832417i
$646$		0			0
$647$	343903.			0.821538			0.410769	−	0.911740i	$-0.365260\pi$
$647$	343903.			0.821538			0.410769	+	0.911740i	$0.365260\pi$
$648$		0			0
$649$	243685.	+	140692.i	0.578548	+	0.334025i
$650$		0			0
$651$	−4701.30	+	8142.90i	−0.0110932	+	0.0192140i
$652$		0			0
$653$	327275.			0.767515			0.383757	−	0.923434i	$-0.374630\pi$
$653$	327275.			0.767515			0.383757	+	0.923434i	$0.374630\pi$
$654$		0			0
$655$	−37816.0	−	65499.3i	−0.0881441	−	0.152670i
$656$		0			0
$657$	−97068.5			−0.224878
$658$		0			0
$659$	112125.	−	64735.4i	0.258185	−	0.149063i	−0.365321	−	0.930882i	$-0.619041\pi$
$659$	112125.	−	64735.4i	0.258185	−	0.149063i	0.623506	+	0.781818i	$0.285708\pi$
$660$		0			0
$661$	121616.	−	70215.1i	0.278348	−	0.160704i	−0.354327	−	0.935121i	$-0.615290\pi$
$661$	121616.	−	70215.1i	0.278348	−	0.160704i	0.632675	+	0.774417i	$0.281957\pi$
$662$		0			0
$663$	−308220.	+	533852.i	−0.701186	+	1.21449i
$664$		0			0
$665$	10714.4	+	36123.0i	0.0242285	+	0.0816847i
$666$		0			0
$667$	−171747.	−	99158.4i	−0.386045	−	0.222883i
$668$		0			0
$669$	221458.	+	383577.i	0.494811	+	0.857039i
$670$		0			0
$671$	−8173.64	−	14157.2i	−0.0181539	−	0.0314435i
$672$		0			0
$673$			245792.i			0.542673i	0.962485	+	0.271336i	$0.0874656\pi$
$673$			245792.i			0.542673i	−0.962485	+	0.271336i	$0.912534\pi$
$674$		0			0
$675$	−8839.11	+	5103.26i	−0.0194000	+	0.0112006i
$676$		0			0
$677$			429443.i			0.936974i	0.883470	+	0.468487i	$0.155201\pi$
$677$			429443.i			0.936974i	−0.883470	+	0.468487i	$0.844799\pi$
$678$		0			0
$679$	50403.5	+	29100.5i	0.109325	+	0.0631190i
$680$		0			0
$681$	−71506.8	+	123853.i	−0.154189	+	0.267063i
$682$		0			0
$683$		−	110387.i		−	0.236634i	−0.992976	−	0.118317i	$-0.962250\pi$
$683$		−	110387.i		−	0.236634i	0.992976	−	0.118317i	$-0.0377499\pi$
$684$		0			0
$685$	60896.8			0.129782
$686$		0			0
$687$	−240978.	−	139129.i	−0.510580	−	0.294783i
$688$		0			0
$689$	646949.	−	1.12055e6i	1.36280	−	2.36044i
$690$		0			0
$691$	202528.			0.424159			0.212080	−	0.977252i	$-0.431976\pi$
$691$	202528.			0.424159			0.212080	+	0.977252i	$0.431976\pi$
$692$		0			0
$693$	−3523.48	−	6102.85i	−0.00733679	−	0.0127077i
$694$		0			0
$695$	854351.			1.76875
$696$		0			0
$697$	−798675.	+	461115.i	−1.64401	+	0.949169i
$698$		0			0
$699$	−181784.	+	104953.i	−0.372051	+	0.214804i
$700$		0			0
$701$	−121102.	+	209755.i	−0.246443	+	0.426851i	−0.962536	−	0.271153i	$-0.912595\pi$
$701$	−121102.	+	209755.i	−0.246443	+	0.426851i	0.716094	+	0.698004i	$0.245928\pi$
$702$		0			0
$703$	574019.	+	544326.i	1.16149	+	1.10141i
$704$		0			0
$705$	314547.	+	181604.i	0.632860	+	0.365382i
$706$		0			0
$707$	751.256	+	1301.21i	0.00150297	+	0.00260321i
$708$		0			0
$709$	187900.	+	325452.i	0.373795	+	0.647432i	0.990146	−	0.140040i	$-0.0447230\pi$
$709$	187900.	+	325452.i	0.373795	+	0.647432i	−0.616351	+	0.787472i	$0.711390\pi$
$710$		0			0
$711$			200635.i			0.396888i
$712$		0			0
$713$	49671.7	−	28678.0i	0.0977080	−	0.0564118i
$714$		0			0
$715$			507359.i			0.992438i
$716$		0			0
$717$	245675.	+	141840.i	0.477884	+	0.275906i
$718$		0			0
$719$	−408662.	+	707823.i	−0.790508	+	1.36920i	0.135144	+	0.990826i	$0.456850\pi$
$719$	−408662.	+	707823.i	−0.790508	+	1.36920i	−0.925653	+	0.378374i	$0.876483\pi$
$720$		0			0
$721$			61331.8i			0.117982i
$722$		0			0
$723$	251179.			0.480514
$724$		0			0
$725$	99763.8	+	57598.7i	0.189800	+	0.109581i
$726$		0			0
$727$	−423400.	+	733351.i	−0.801092	+	1.38753i	0.117806	+	0.993037i	$0.462414\pi$
$727$	−423400.	+	733351.i	−0.801092	+	1.38753i	−0.918898	+	0.394495i	$0.870920\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	−514687.	−	891464.i	−0.963182	−	1.66828i
$732$		0			0
$733$	562446.			1.04682			0.523411	−	0.852080i	$-0.324659\pi$
$733$	562446.			1.04682			0.523411	+	0.852080i	$0.324659\pi$
$734$		0			0
$735$	283545.	−	163705.i	0.524864	−	0.303030i
$736$		0			0
$737$	438631.	−	253244.i	0.807540	−	0.466233i
$738$		0			0
$739$	−138927.	+	240628.i	−0.254388	+	0.440613i	−0.964729	−	0.263245i	$-0.915207\pi$
$739$	−138927.	+	240628.i	−0.254388	+	0.440613i	0.710341	+	0.703858i	$0.248541\pi$
$740$		0			0
$741$	375317.	−	395791.i	0.683537	−	0.720824i
$742$		0			0
$743$	220105.	+	127078.i	0.398705	+	0.230193i	0.685925	−	0.727672i	$-0.259398\pi$
$743$	220105.	+	127078.i	0.398705	+	0.230193i	−0.287220	+	0.957865i	$0.592731\pi$
$744$		0			0
$745$	−162759.	−	281906.i	−0.293246	−	0.507917i
$746$		0			0
$747$	−22325.8	−	38669.5i	−0.0400098	−	0.0692990i
$748$		0			0
$749$		−	76278.2i		−	0.135968i
$750$		0			0
$751$	671263.	−	387554.i	1.19018	−	0.687151i	0.231833	−	0.972756i	$-0.425528\pi$
$751$	671263.	−	387554.i	1.19018	−	0.687151i	0.958347	+	0.285605i	$0.0921945\pi$
$752$		0			0
$753$		−	394322.i		−	0.695442i
$754$		0			0
$755$	595715.	+	343936.i	1.04507	+	0.603370i
$756$		0			0
$757$	82777.3	−	143374.i	0.144451	−	0.250196i	−0.784717	−	0.619854i	$-0.787192\pi$
$757$	82777.3	−	143374.i	0.144451	−	0.250196i	0.929168	+	0.369658i	$0.120525\pi$
$758$		0			0
$759$			42986.6i			0.0746189i
$760$		0			0
$761$	88512.4			0.152839			0.0764196	−	0.997076i	$-0.475651\pi$
$761$	88512.4			0.152839			0.0764196	+	0.997076i	$0.475651\pi$
$762$		0			0
$763$	−20031.5	−	11565.2i	−0.0344084	−	0.0198657i
$764$		0			0
$765$	145488.	−	251993.i	0.248602	−	0.430592i
$766$		0			0
$767$	−1.23868e6			−2.10557
$768$		0			0
$769$	266238.	+	461138.i	0.450212	+	0.779790i	0.998399	−	0.0565656i	$-0.0180150\pi$
$769$	266238.	+	461138.i	0.450212	+	0.779790i	−0.548187	+	0.836356i	$0.684682\pi$
$770$		0			0
$771$	646786.			1.08806
$772$		0			0
$773$	372719.	−	215189.i	0.623767	−	0.360132i	−0.154567	−	0.987982i	$-0.549398\pi$
$773$	372719.	−	215189.i	0.623767	−	0.360132i	0.778334	+	0.627850i	$0.216065\pi$
$774$		0			0
$775$	−28853.1	+	16658.3i	−0.0480384	+	0.0277350i
$776$		0			0
$777$	−22495.5	+	38963.3i	−0.0372609	+	0.0645378i
$778$		0			0
$779$	782333.	−	232048.i	1.28919	−	0.382387i
$780$		0			0
$781$	−172371.	−	99518.2i	−0.282593	−	0.163155i
$782$		0			0
$783$	111078.	+	192392.i	0.181177	+	0.313807i
$784$		0			0
$785$	−239192.	−	414293.i	−0.388157	−	0.672308i
$786$		0			0
$787$			399690.i			0.645318i	0.946515	+	0.322659i	$0.104577\pi$
$787$			399690.i			0.645318i	−0.946515	+	0.322659i	$0.895423\pi$
$788$		0			0
$789$	−312659.	+	180514.i	−0.502246	+	0.289972i
$790$		0			0
$791$		−	79843.5i		−	0.127610i
$792$		0			0
$793$	62321.5	+	35981.3i	0.0991041	+	0.0572178i
$794$		0			0
$795$	−305378.	+	528930.i	−0.483174	+	0.836882i
$796$		0			0
$797$			993609.i			1.56422i	0.623138	+	0.782112i	$0.285858\pi$
$797$			993609.i			1.56422i	−0.623138	+	0.782112i	$0.714142\pi$
$798$		0			0
$799$	−1.07961e6			−1.69112
$800$		0			0
$801$	−50020.1	−	28879.1i	−0.0779614	−	0.0450111i
$802$		0			0
$803$	118737.	−	205659.i	0.184143	−	0.318945i
$804$		0			0
$805$	13071.8			0.0201718
$806$		0			0
$807$	162950.	+	282238.i	0.250212	+	0.433379i
$808$		0			0
$809$	162243.			0.247896			0.123948	−	0.992289i	$-0.460444\pi$
$809$	162243.			0.247896			0.123948	+	0.992289i	$0.460444\pi$
$810$		0			0
$811$	208547.	−	120405.i	0.317075	−	0.183064i	−0.333013	−	0.942922i	$-0.608065\pi$
$811$	208547.	−	120405.i	0.317075	−	0.183064i	0.650088	+	0.759859i	$0.274732\pi$
$812$		0			0
$813$	−220433.	+	127267.i	−0.333499	+	0.192546i
$814$		0			0
$815$	23993.4	−	41557.7i	0.0361224	−	0.0625658i
$816$		0			0
$817$	259007.	+	873224.i	0.388032	+	1.30822i
$818$		0			0
$819$	26865.5	+	15510.8i	0.0400523	+	0.0231242i
$820$		0			0
$821$	148698.	+	257553.i	0.220607	+	0.382102i	0.954992	−	0.296630i	$-0.0958629\pi$
$821$	148698.	+	257553.i	0.220607	+	0.382102i	−0.734386	+	0.678733i	$0.762530\pi$
$822$		0			0
$823$	−168468.	−	291795.i	−0.248724	−	0.430803i	0.714448	−	0.699689i	$-0.246678\pi$
$823$	−168468.	−	291795.i	−0.248724	−	0.430803i	−0.963172	+	0.268886i	$0.913345\pi$
$824$		0			0
$825$		−	24969.8i		−	0.0366866i
$826$		0			0
$827$	346639.	−	200132.i	0.506835	−	0.292621i	−0.224697	−	0.974429i	$-0.572139\pi$
$827$	346639.	−	200132.i	0.506835	−	0.292621i	0.731532	+	0.681807i	$0.238806\pi$
$828$		0			0
$829$			450567.i			0.655617i	0.944744	+	0.327808i	$0.106310\pi$
$829$			450567.i			0.655617i	−0.944744	+	0.327808i	$0.893690\pi$
$830$		0			0
$831$	−376715.	−	217496.i	−0.545520	−	0.314956i
$832$		0			0
$833$	−486602.	+	842819.i	−0.701267	+	1.21463i
$834$		0			0
$835$			795066.i			1.14033i
$836$		0			0
$837$	−64250.3			−0.0917116
$838$		0			0
$839$	−373845.	−	215840.i	−0.531089	−	0.306625i	0.210371	−	0.977622i	$-0.432533\pi$
$839$	−373845.	−	215840.i	−0.531089	−	0.306625i	−0.741460	+	0.670997i	$0.765866\pi$
$840$		0			0
$841$	900052.	−	1.55894e6i	1.27255	−	2.20412i
$842$		0			0
$843$	−197383.			−0.277751
$844$		0			0
$845$	−739510.	−	1.28087e6i	−1.03569	−	1.79387i
$846$		0			0
$847$	−40610.4			−0.0566071
$848$		0			0
$849$	−321594.	+	185672.i	−0.446162	+	0.257592i
$850$		0			0
$851$	237677.	−	137223.i	0.328191	−	0.189481i
$852$		0			0
$853$	190271.	−	329558.i	0.261501	−	0.452933i	−0.705140	−	0.709068i	$-0.749116\pi$
$853$	190271.	−	329558.i	0.261501	−	0.452933i	0.966641	+	0.256135i	$0.0824492\pi$
$854$		0			0
$855$	−177160.	+	186824.i	−0.242345	+	0.255565i
$856$		0			0
$857$	−943560.	−	544765.i	−1.28472	−	0.741732i	−0.307011	−	0.951706i	$-0.599329\pi$
$857$	−943560.	−	544765.i	−1.28472	−	0.741732i	−0.977707	+	0.209973i	$0.932662\pi$
$858$		0			0
$859$	65215.6	+	112957.i	0.0883823	+	0.153083i	0.906827	−	0.421502i	$-0.138497\pi$
$859$	65215.6	+	112957.i	0.0883823	+	0.153083i	−0.818445	+	0.574585i	$0.805164\pi$
$860$		0			0
$861$	23205.1	+	40192.4i	0.0313024	+	0.0542173i
$862$		0			0
$863$		−	253989.i		−	0.341031i	−0.985355	−	0.170515i	$-0.945457\pi$
$863$		−	253989.i		−	0.341031i	0.985355	−	0.170515i	$-0.0545432\pi$
$864$		0			0
$865$	729211.	−	421010.i	0.974588	−	0.562679i
$866$		0			0
$867$			430923.i			0.573273i
$868$		0			0
$869$	−425085.	−	245423.i	−0.562906	−	0.324994i
$870$		0			0
$871$	−1.11481e6	+	1.93091e6i	−1.46948	+	2.54522i
$872$		0			0
$873$			397701.i			0.521829i
$874$		0			0
$875$	57639.8			0.0752846
$876$		0			0
$877$	759687.	+	438606.i	0.987724	+	0.570263i	0.904593	−	0.426276i	$-0.140175\pi$
$877$	759687.	+	438606.i	0.987724	+	0.570263i	0.0831309	+	0.996539i	$0.473508\pi$
$878$		0			0
$879$	−23350.8	+	40444.8i	−0.0302221	+	0.0523461i
$880$		0			0
$881$	−143314.			−0.184645			−0.0923223	−	0.995729i	$-0.529429\pi$
$881$	−143314.			−0.184645			−0.0923223	+	0.995729i	$0.529429\pi$
$882$		0			0
$883$	−140425.	−	243224.i	−0.180104	−	0.311950i	0.761812	−	0.647799i	$-0.224310\pi$
$883$	−140425.	−	243224.i	−0.180104	−	0.311950i	−0.941916	+	0.335849i	$0.890977\pi$
$884$		0			0
$885$	584693.			0.746520
$886$		0			0
$887$	−214235.	+	123689.i	−0.272297	+	0.157211i	−0.629931	−	0.776651i	$-0.716917\pi$
$887$	−214235.	+	123689.i	−0.272297	+	0.157211i	0.357634	+	0.933862i	$0.383584\pi$
$888$		0			0
$889$	52866.6	−	30522.5i	0.0668925	−	0.0386204i
$890$		0			0
$891$	24076.8	−	41702.3i	0.0303280	−	0.0525297i
$892$		0			0
$893$	928967.	+	222667.i	1.16492	+	0.279224i
$894$		0			0
$895$	−573098.	−	330878.i	−0.715456	−	0.413069i
$896$		0			0
$897$	−94616.1	−	163880.i	−0.117593	−	0.203676i
$898$		0			0
$899$	362585.	+	628016.i	0.448632	+	0.777054i
$900$		0			0
$901$		−	1.81544e6i		−	2.23631i
$902$		0			0
$903$	−44861.9	+	25901.0i	−0.0550177	+	0.0317645i
$904$		0			0
$905$		−	929801.i		−	1.13525i
$906$		0			0
$907$	−967269.	−	558453.i	−1.17580	−	0.678847i	−0.220759	−	0.975328i	$-0.570853\pi$
$907$	−967269.	−	558453.i	−1.17580	−	0.678847i	−0.955039	+	0.296481i	$0.904187\pi$
$908$		0			0
$909$	−5133.52	+	8891.51i	−0.00621280	+	0.0107609i
$910$		0			0
$911$		−	1.08226e6i		−	1.30405i	−0.758198	−	0.652025i	$-0.773920\pi$
$911$		−	1.08226e6i		−	1.30405i	0.758198	−	0.652025i	$-0.226080\pi$
$912$		0			0
$913$	109238.			0.131049
$914$		0			0
$915$	−29417.5	−	16984.2i	−0.0351369	−	0.0202863i
$916$		0			0
$917$	5656.69	−	9797.68i	0.00672704	−	0.0116516i
$918$		0			0
$919$	−920659.			−1.09010			−0.545052	−	0.838402i	$-0.683490\pi$
$919$	−920659.			−1.09010			−0.545052	+	0.838402i	$0.683490\pi$
$920$		0			0
$921$	−22825.0	−	39534.1i	−0.0269087	−	0.0466072i
$922$		0			0
$923$	876182.			1.02847
$924$		0			0
$925$	−138060.	+	79709.2i	−0.161356	+	0.0931591i
$926$		0			0
$927$	−362947.	+	209548.i	−0.422361	+	0.243850i
$928$		0			0
$929$	−282674.	+	489605.i	−0.327532	+	0.567302i	−0.982022	−	0.188769i	$-0.939550\pi$
$929$	−282674.	+	489605.i	−0.327532	+	0.567302i	0.654489	+	0.756071i	$0.272884\pi$
$930$		0			0
$931$	592532.	−	624854.i	0.683616	−	0.720907i
$932$		0			0
$933$	−269745.	−	155737.i	−0.309878	−	0.178908i
$934$		0			0
$935$	355931.	+	616491.i	0.407139	+	0.705186i
$936$		0			0
$937$	140444.	+	243257.i	0.159965	+	0.277068i	0.934856	−	0.355027i	$-0.115528\pi$
$937$	140444.	+	243257.i	0.159965	+	0.277068i	−0.774891	+	0.632095i	$0.782195\pi$
$938$		0			0
$939$		−	209996.i		−	0.238166i
$940$		0			0
$941$	−1.21593e6	+	702015.i	−1.37318	+	0.792807i	−0.991327	−	0.131416i	$-0.958048\pi$
$941$	−1.21593e6	+	702015.i	−1.37318	+	0.792807i	−0.381854	+	0.924223i	$0.624714\pi$
$942$		0			0
$943$		−	283102.i		−	0.318361i
$944$		0			0
$945$	−12681.3	−	7321.54i	−0.0142004	−	0.00819858i
$946$		0			0
$947$	−458463.	+	794081.i	−0.511215	+	0.885451i	0.488700	+	0.872452i	$0.337471\pi$
$947$	−458463.	+	794081.i	−0.511215	+	0.885451i	−0.999916	+	0.0129993i	$0.995862\pi$
$948$		0			0
$949$			1.04539e6i			1.16077i
$950$		0			0
$951$	262056.			0.289757
$952$		0			0
$953$	−1.31224e6	−	757621.i	−1.44486	−	0.834192i	−0.446694	−	0.894687i	$-0.647399\pi$
$953$	−1.31224e6	−	757621.i	−1.44486	−	0.834192i	−0.998169	+	0.0604947i	$0.980732\pi$
$954$		0			0
$955$	916648.	−	1.58768e6i	1.00507	−	1.74083i
$956$		0			0
$957$	−543493.			−0.593431
$958$		0			0
$959$	4554.61	+	7888.82i	0.00495238	+	0.00857778i
$960$		0			0
$961$	713792.			0.772902
$962$		0			0
$963$	451397.	−	260614.i	0.486750	−	0.281025i
$964$		0			0
$965$	15109.5	−	8723.48i	0.0162254	−	0.00936775i
$966$		0			0
$967$	660547.	−	1.14410e6i	0.706400	−	1.22352i	−0.259784	−	0.965667i	$-0.583651\pi$
$967$	660547.	−	1.14410e6i	0.706400	−	1.22352i	0.966184	−	0.257854i	$-0.0830155\pi$
$968$		0			0
$969$	178385.	−	744223.i	0.189982	−	0.792603i
$970$		0			0
$971$	902679.	+	521162.i	0.957403	+	0.552757i	0.895373	−	0.445317i	$-0.146909\pi$
$971$	902679.	+	521162.i	0.957403	+	0.552757i	0.0620301	+	0.998074i	$0.480243\pi$
$972$		0			0
$973$	63898.9	+	110676.i	0.0674944	+	0.116904i
$974$		0			0
$975$	54960.1	+	95193.8i	0.0578147	+	0.100138i
$976$		0			0
$977$		−	1.19511e6i		−	1.25204i	−0.779808	−	0.626019i	$-0.784683\pi$
$977$		−	1.19511e6i		−	1.25204i	0.779808	−	0.626019i	$-0.215317\pi$
$978$		0			0
$979$	122372.	−	70651.6i	0.127678	−	0.0737152i
$980$		0			0
$981$		−	158056.i		−	0.164237i
$982$		0			0
$983$	−904865.	−	522424.i	−0.936433	−	0.540650i	−0.0475925	−	0.998867i	$-0.515155\pi$
$983$	−904865.	−	522424.i	−0.936433	−	0.540650i	−0.888840	+	0.458217i	$0.848488\pi$
$984$		0			0
$985$	115323.	−	199745.i	0.118862	−	0.205875i
$986$		0			0
$987$			54330.3i			0.0557709i
$988$		0			0
$989$	315993.			0.323061
$990$		0			0
$991$	−1.06594e6	−	615421.i	−1.08539	−	0.626650i	−0.153045	−	0.988219i	$-0.548908\pi$
$991$	−1.06594e6	−	615421.i	−1.08539	−	0.626650i	−0.932345	+	0.361569i	$0.882241\pi$
$992$		0			0
$993$	−71488.0	+	123821.i	−0.0724994	+	0.125573i
$994$		0			0
$995$	974299.			0.984116
$996$		0			0
$997$	−729969.	−	1.26434e6i	−0.734369	−	1.27196i	−0.955000	−	0.296607i	$-0.904145\pi$
$997$	−729969.	−	1.26434e6i	−0.734369	−	1.27196i	0.220631	−	0.975357i	$-0.429188\pi$
$998$		0			0
$999$	−307434.			−0.308050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.5.l.a.217.7	yes	14
3.2	odd	2		684.5.y.e.217.1		14
19.12	odd	6	inner	228.5.l.a.145.7	✓	14
57.50	even	6		684.5.y.e.145.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.a.145.7	✓	14	19.12	odd	6	inner
228.5.l.a.217.7	yes	14	1.1	even	1	trivial
684.5.y.e.145.1		14	57.50	even	6
684.5.y.e.217.1		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	228.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 2.59808i) q^{3} +(13.2075 - 22.8760i) q^{5} +3.95127 q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 2.59808i) q^{3} +(13.2075 - 22.8760i) q^{5} +3.95127 q^{7} +(13.5000 + 23.3827i) q^{9} -66.0544 q^{11} +(251.823 - 145.390i) q^{13} +(-118.867 + 68.6281i) q^{15} +(203.993 - 353.326i) q^{17} +(-248.401 + 261.951i) q^{19} +(-17.7807 - 10.2657i) q^{21} +(62.6209 + 108.463i) q^{23} +(-36.3749 - 63.0032i) q^{25} -140.296i q^{27} +(-1371.33 + 791.736i) q^{29} -457.962i q^{31} +(297.245 + 171.614i) q^{33} +(52.1863 - 90.3894i) q^{35} -2191.32i q^{37} -1510.94 q^{39} +(-1957.61 - 1130.22i) q^{41} +(1261.53 - 2185.04i) q^{43} +713.204 q^{45} +(-1323.10 - 2291.68i) q^{47} -2385.39 q^{49} +(-1835.93 + 1059.98i) q^{51} +(3853.60 - 2224.88i) q^{53} +(-872.412 + 1511.06i) q^{55} +(1798.37 - 533.415i) q^{57} +(-3689.16 - 2129.93i) q^{59} +(123.741 + 214.326i) q^{61} +(53.3422 + 92.3913i) q^{63} -7680.93i q^{65} +(-6640.45 + 3833.86i) q^{67} -650.775i q^{69} +(2609.52 + 1506.61i) q^{71} +(-1797.57 + 3113.47i) q^{73} +378.019i q^{75} -260.999 q^{77} +(6435.38 + 3715.47i) q^{79} +(-364.500 + 631.333i) q^{81} -1653.76 q^{83} +(-5388.46 - 9333.08i) q^{85} +8227.96 q^{87} +(-1852.60 + 1069.60i) q^{89} +(995.019 - 574.474i) q^{91} +(-1189.82 + 2060.83i) q^{93} +(2711.65 + 9142.12i) q^{95} +(12756.3 + 7364.84i) q^{97} +(-891.734 - 1544.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 63 q^{3} - 30 q^{5} + 106 q^{7} + 189 q^{9}+O(q^{10}) \) 14 * q - 63 * q^3 - 30 * q^5 + 106 * q^7 + 189 * q^9	\( 14 q - 63 q^{3} - 30 q^{5} + 106 q^{7} + 189 q^{9} - 264 q^{11} + 57 q^{13} + 270 q^{15} + 282 q^{17} + 2 q^{19} - 477 q^{21} + 96 q^{23} - 465 q^{25} - 630 q^{29} + 1188 q^{33} + 1434 q^{35} - 342 q^{39} - 228 q^{41} - 2093 q^{43} - 1620 q^{45} - 4710 q^{47} + 4440 q^{49} - 2538 q^{51} + 2364 q^{53} + 6368 q^{55} + 1143 q^{57} + 11838 q^{59} - 1661 q^{61} + 1431 q^{63} - 20319 q^{67} + 624 q^{71} + 5851 q^{73} - 1080 q^{77} - 13299 q^{79} - 5103 q^{81} + 12252 q^{83} - 5740 q^{85} + 3780 q^{87} - 20010 q^{89} + 15951 q^{91} + 855 q^{93} + 7770 q^{95} + 44904 q^{97} - 3564 q^{99}+O(q^{100}) \) 14 * q - 63 * q^3 - 30 * q^5 + 106 * q^7 + 189 * q^9 - 264 * q^11 + 57 * q^13 + 270 * q^15 + 282 * q^17 + 2 * q^19 - 477 * q^21 + 96 * q^23 - 465 * q^25 - 630 * q^29 + 1188 * q^33 + 1434 * q^35 - 342 * q^39 - 228 * q^41 - 2093 * q^43 - 1620 * q^45 - 4710 * q^47 + 4440 * q^49 - 2538 * q^51 + 2364 * q^53 + 6368 * q^55 + 1143 * q^57 + 11838 * q^59 - 1661 * q^61 + 1431 * q^63 - 20319 * q^67 + 624 * q^71 + 5851 * q^73 - 1080 * q^77 - 13299 * q^79 - 5103 * q^81 + 12252 * q^83 - 5740 * q^85 + 3780 * q^87 - 20010 * q^89 + 15951 * q^91 + 855 * q^93 + 7770 * q^95 + 44904 * q^97 - 3564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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