LMFDB - Embedded newform 225.4.h.b.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	225.46
Dual form			225.4.h.b.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41896 - 4.36711i) q^{2} +(-10.5860 - 7.69120i) q^{4} +(-1.19043 - 11.1168i) q^{5} -20.8866 q^{7} +(-18.8904 + 13.7247i) q^{8} +O(q^{10})$	\(q+(1.41896 - 4.36711i) q^{2} +(-10.5860 - 7.69120i) q^{4} +(-1.19043 - 11.1168i) q^{5} -20.8866 q^{7} +(-18.8904 + 13.7247i) q^{8} +(-50.2373 - 10.5755i) q^{10} +(2.21213 - 6.80823i) q^{11} +(9.36436 + 28.8205i) q^{13} +(-29.6372 + 91.2138i) q^{14} +(0.784365 + 2.41403i) q^{16} +(-22.6839 + 16.4808i) q^{17} +(-9.78911 + 7.11220i) q^{19} +(-72.8995 + 126.838i) q^{20} +(-26.5933 - 19.3212i) q^{22} +(16.1358 - 49.6607i) q^{23} +(-122.166 + 26.4675i) q^{25} +139.150 q^{26} +(221.106 + 160.643i) q^{28} +(119.295 + 86.6730i) q^{29} +(-172.557 + 125.370i) q^{31} -175.143 q^{32} +(39.7859 + 122.449i) q^{34} +(24.8640 + 232.191i) q^{35} +(-22.0136 - 67.7509i) q^{37} +(17.1694 + 52.8420i) q^{38} +(175.062 + 193.662i) q^{40} +(-159.084 - 489.609i) q^{41} +176.395 q^{43} +(-75.7811 + 55.0582i) q^{44} +(-193.978 - 140.933i) q^{46} +(-181.907 - 132.163i) q^{47} +93.2487 q^{49} +(-57.7618 + 571.067i) q^{50} +(122.533 - 377.118i) q^{52} +(292.206 + 212.300i) q^{53} +(-78.3190 - 16.4870i) q^{55} +(394.555 - 286.661i) q^{56} +(547.785 - 397.989i) q^{58} +(-181.399 - 558.290i) q^{59} +(244.656 - 752.975i) q^{61} +(302.653 + 931.469i) q^{62} +(-254.796 + 784.181i) q^{64} +(309.244 - 138.410i) q^{65} +(347.396 - 252.398i) q^{67} +366.890 q^{68} +(1049.29 + 220.886i) q^{70} +(-321.536 - 233.610i) q^{71} +(-321.174 + 988.472i) q^{73} -327.112 q^{74} +158.329 q^{76} +(-46.2038 + 142.201i) q^{77} +(-989.474 - 718.895i) q^{79} +(25.9025 - 11.5933i) q^{80} -2363.91 q^{82} +(189.917 - 137.983i) q^{83} +(210.217 + 232.553i) q^{85} +(250.298 - 770.337i) q^{86} +(51.6527 + 158.971i) q^{88} +(56.9937 - 175.409i) q^{89} +(-195.589 - 601.962i) q^{91} +(-552.764 + 401.607i) q^{92} +(-835.288 + 606.872i) q^{94} +(90.7180 + 100.357i) q^{95} +(-67.1258 - 48.7698i) q^{97} +(132.316 - 407.227i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8	$ 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8} - 25 q^{10} + 89 q^{11} + 33 q^{13} + 17 q^{14} - 207 q^{16} + 191 q^{17} - 115 q^{19} + 225 q^{20} + 808 q^{22} - 433 q^{23} + 90 q^{25} - 586 q^{26} - 13 q^{28} + 5 q^{29} - 639 q^{31} + 1386 q^{32} - 777 q^{34} + 1030 q^{35} + 699 q^{37} + 2355 q^{38} + 410 q^{40} - 341 q^{41} - 172 q^{43} - 548 q^{44} - 1239 q^{46} - 2319 q^{47} + 1344 q^{49} - 2335 q^{50} + 2344 q^{52} + 927 q^{53} + 1225 q^{55} + 2910 q^{56} + 2410 q^{58} + 1905 q^{59} + 1391 q^{61} + 3832 q^{62} - 3596 q^{64} - 1215 q^{65} - 3611 q^{67} - 3622 q^{68} + 560 q^{70} + 3719 q^{71} + 4593 q^{73} - 4848 q^{74} + 3520 q^{76} - 1368 q^{77} + 775 q^{79} - 9500 q^{80} - 6762 q^{82} + 2447 q^{83} - 8185 q^{85} - 3891 q^{86} - 10960 q^{88} + 5075 q^{89} + 376 q^{91} + 8456 q^{92} + 3573 q^{94} - 3265 q^{95} + 7439 q^{97} - 7082 q^{98}+O(q^{100}) $ 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8 - 25 * q^10 + 89 * q^11 + 33 * q^13 + 17 * q^14 - 207 * q^16 + 191 * q^17 - 115 * q^19 + 225 * q^20 + 808 * q^22 - 433 * q^23 + 90 * q^25 - 586 * q^26 - 13 * q^28 + 5 * q^29 - 639 * q^31 + 1386 * q^32 - 777 * q^34 + 1030 * q^35 + 699 * q^37 + 2355 * q^38 + 410 * q^40 - 341 * q^41 - 172 * q^43 - 548 * q^44 - 1239 * q^46 - 2319 * q^47 + 1344 * q^49 - 2335 * q^50 + 2344 * q^52 + 927 * q^53 + 1225 * q^55 + 2910 * q^56 + 2410 * q^58 + 1905 * q^59 + 1391 * q^61 + 3832 * q^62 - 3596 * q^64 - 1215 * q^65 - 3611 * q^67 - 3622 * q^68 + 560 * q^70 + 3719 * q^71 + 4593 * q^73 - 4848 * q^74 + 3520 * q^76 - 1368 * q^77 + 775 * q^79 - 9500 * q^80 - 6762 * q^82 + 2447 * q^83 - 8185 * q^85 - 3891 * q^86 - 10960 * q^88 + 5075 * q^89 + 376 * q^91 + 8456 * q^92 + 3573 * q^94 - 3265 * q^95 + 7439 * q^97 - 7082 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.41896	−	4.36711i	0.501678	−	1.54401i	−0.304607	−	0.952478i	$-0.598525\pi$
$2$	1.41896	−	4.36711i	0.501678	−	1.54401i	0.806285	−	0.591527i	$-0.201475\pi$
$3$		0			0
$3$		0			0
$4$	−10.5860	−	7.69120i	−1.32325	−	0.961400i
$5$	−1.19043	−	11.1168i	−0.106475	−	0.994315i
$5$	−1.19043	−	11.1168i	−0.106475	−	0.994315i
$6$		0			0
$7$	−20.8866			−1.12777			−0.563884	−	0.825854i	$-0.690694\pi$
$7$	−20.8866			−1.12777			−0.563884	+	0.825854i	$0.690694\pi$
$8$	−18.8904	+	13.7247i	−0.834845	+	0.606550i
$9$		0			0
$10$	−50.2373	−	10.5755i	−1.58864	−	0.334427i
$11$	2.21213	−	6.80823i	0.0606347	−	0.186614i	−0.916151	−	0.400833i	$-0.868721\pi$
$11$	2.21213	−	6.80823i	0.0606347	−	0.186614i	0.976786	+	0.214219i	$0.0687206\pi$
$12$		0			0
$13$	9.36436	+	28.8205i	0.199785	+	0.614875i	0.999887	+	0.0150116i	$0.00477851\pi$
$13$	9.36436	+	28.8205i	0.199785	+	0.614875i	−0.800102	+	0.599864i	$0.795221\pi$
$14$	−29.6372	+	91.2138i	−0.565776	+	1.74128i
$15$		0			0
$16$	0.784365	+	2.41403i	0.0122557	+	0.0377192i
$17$	−22.6839	+	16.4808i	−0.323627	+	0.235128i	−0.737721	−	0.675105i	$-0.764098\pi$
$17$	−22.6839	+	16.4808i	−0.323627	+	0.235128i	0.414095	+	0.910234i	$0.364098\pi$
$18$		0			0
$19$	−9.78911	+	7.11220i	−0.118199	+	0.0858764i	−0.645314	−	0.763917i	$-0.723274\pi$
$19$	−9.78911	+	7.11220i	−0.118199	+	0.0858764i	0.527115	+	0.849794i	$0.323274\pi$
$20$	−72.8995	+	126.838i	−0.815041	+	1.41810i
$21$		0			0
$22$	−26.5933	−	19.3212i	−0.257714	−	0.187241i
$23$	16.1358	−	49.6607i	0.146284	−	0.450217i	−0.850890	−	0.525344i	$-0.823936\pi$
$23$	16.1358	−	49.6607i	0.146284	−	0.450217i	0.997174	+	0.0751279i	$0.0239365\pi$
$24$		0			0
$25$	−122.166	+	26.4675i	−0.977326	+	0.211740i
$26$	139.150			1.04960
$27$		0			0
$28$	221.106	+	160.643i	1.49232	+	1.08424i
$29$	119.295	+	86.6730i	0.763881	+	0.554992i	0.900098	−	0.435687i	$-0.143495\pi$
$29$	119.295	+	86.6730i	0.763881	+	0.554992i	−0.136217	+	0.990679i	$0.543495\pi$
$30$		0			0
$31$	−172.557	+	125.370i	−0.999746	+	0.726358i	−0.962034	−	0.272931i	$-0.912007\pi$
$31$	−172.557	+	125.370i	−0.999746	+	0.726358i	−0.0377122	+	0.999289i	$0.512007\pi$
$32$	−175.143			−0.967538
$33$		0			0
$34$	39.7859	+	122.449i	0.200683	+	0.617640i
$35$	24.8640	+	232.191i	0.120079	+	1.12136i
$36$		0			0
$37$	−22.0136	−	67.7509i	−0.0978111	−	0.301032i	0.890165	−	0.455638i	$-0.150589\pi$
$37$	−22.0136	−	67.7509i	−0.0978111	−	0.301032i	−0.987976	+	0.154607i	$0.950589\pi$
$38$	17.1694	+	52.8420i	0.0732959	+	0.225582i
$39$		0			0
$40$	175.062	+	193.662i	0.691993	+	0.765517i
$41$	−159.084	−	489.609i	−0.605968	−	1.86498i	−0.489994	−	0.871726i	$-0.663001\pi$
$41$	−159.084	−	489.609i	−0.605968	−	1.86498i	−0.115974	−	0.993252i	$-0.536999\pi$
$42$		0			0
$43$	176.395			0.625582			0.312791	−	0.949822i	$-0.398736\pi$
$43$	176.395			0.625582			0.312791	+	0.949822i	$0.398736\pi$
$44$	−75.7811	+	55.0582i	−0.259646	+	0.188644i
$45$		0			0
$46$	−193.978	−	140.933i	−0.621749	−	0.451727i
$47$	−181.907	−	132.163i	−0.564550	−	0.410169i	0.268572	−	0.963260i	$-0.413448\pi$
$47$	−181.907	−	132.163i	−0.564550	−	0.410169i	−0.833121	+	0.553090i	$0.813448\pi$
$48$		0			0
$49$	93.2487			0.271862
$50$	−57.7618	+	571.067i	−0.163375	+	1.61522i
$51$		0			0
$52$	122.533	−	377.118i	0.326775	−	1.00571i
$53$	292.206	+	212.300i	0.757314	+	0.550220i	0.898085	−	0.439822i	$-0.144958\pi$
$53$	292.206	+	212.300i	0.757314	+	0.550220i	−0.140772	+	0.990042i	$0.544958\pi$
$54$		0			0
$55$	−78.3190	−	16.4870i	−0.192010	−	0.0404202i
$56$	394.555	−	286.661i	0.941512	−	0.684049i
$57$		0			0
$58$	547.785	−	397.989i	1.24013	−	0.901009i
$59$	−181.399	−	558.290i	−0.400275	−	1.23192i	−0.924777	−	0.380510i	$-0.875749\pi$
$59$	−181.399	−	558.290i	−0.400275	−	1.23192i	0.524502	−	0.851409i	$-0.324251\pi$
$60$		0			0
$61$	244.656	−	752.975i	0.513525	−	1.58047i	−0.272424	−	0.962177i	$-0.587825\pi$
$61$	244.656	−	752.975i	0.513525	−	1.58047i	0.785950	−	0.618291i	$-0.212175\pi$
$62$	302.653	+	931.469i	0.619950	+	1.90801i
$63$		0			0
$64$	−254.796	+	784.181i	−0.497648	+	1.53160i
$65$	309.244	−	138.410i	0.590108	−	0.264118i
$66$		0			0
$67$	347.396	−	252.398i	0.633451	−	0.460229i	−0.224143	−	0.974556i	$-0.571958\pi$
$67$	347.396	−	252.398i	0.633451	−	0.460229i	0.857594	+	0.514327i	$0.171958\pi$
$68$	366.890			0.654293
$69$		0			0
$70$	1049.29	+	220.886i	1.79162	+	0.377157i
$71$	−321.536	−	233.610i	−0.537456	−	0.390484i	0.285684	−	0.958324i	$-0.407779\pi$
$71$	−321.536	−	233.610i	−0.537456	−	0.390484i	−0.823139	+	0.567840i	$0.807779\pi$
$72$		0			0
$73$	−321.174	+	988.472i	−0.514940	+	1.58482i	0.268452	+	0.963293i	$0.413488\pi$
$73$	−321.174	+	988.472i	−0.514940	+	1.58482i	−0.783392	+	0.621528i	$0.786512\pi$
$74$	−327.112			−0.513864
$75$		0			0
$76$	158.329			0.238968
$77$	−46.2038	+	142.201i	−0.0683819	+	0.210458i
$78$		0			0
$79$	−989.474	−	718.895i	−1.40917	−	1.02382i	−0.993442	−	0.114334i	$-0.963527\pi$
$79$	−989.474	−	718.895i	−1.40917	−	1.02382i	−0.415729	−	0.909489i	$-0.636473\pi$
$80$	25.9025	−	11.5933i	0.0361998	−	0.0162022i
$81$		0			0
$82$	−2363.91			−3.18354
$83$	189.917	−	137.983i	0.251158	−	0.182477i	−0.455082	−	0.890450i	$-0.650390\pi$
$83$	189.917	−	137.983i	0.251158	−	0.182477i	0.706240	+	0.707973i	$0.250390\pi$
$84$		0			0
$85$	210.217	+	232.553i	0.268250	+	0.296751i
$86$	250.298	−	770.337i	0.313841	−	0.965902i
$87$		0			0
$88$	51.6527	+	158.971i	0.0625705	+	0.192572i
$89$	56.9937	−	175.409i	0.0678800	−	0.208913i	−0.911363	−	0.411604i	$-0.864969\pi$
$89$	56.9937	−	175.409i	0.0678800	−	0.208913i	0.979243	+	0.202691i	$0.0649687\pi$
$90$		0			0
$91$	−195.589	−	601.962i	−0.225311	−	0.693437i
$92$	−552.764	+	401.607i	−0.626410	+	0.455113i
$93$		0			0
$94$	−835.288	+	606.872i	−0.916526	+	0.665895i
$95$	90.7180	+	100.357i	0.0979734	+	0.108383i
$96$		0			0
$97$	−67.1258	−	48.7698i	−0.0702639	−	0.0510497i	0.552099	−	0.833779i	$-0.313827\pi$
$97$	−67.1258	−	48.7698i	−0.0702639	−	0.0510497i	−0.622363	+	0.782729i	$0.713827\pi$
$98$	132.316	−	407.227i	0.136387	−	0.419756i
$99$		0			0
$100$	1496.82	+	659.416i	1.49682	+	0.659416i
$101$	−106.321			−0.104745			−0.0523727	−	0.998628i	$-0.516678\pi$
$101$	−106.321			−0.104745			−0.0523727	+	0.998628i	$0.516678\pi$
$102$		0			0
$103$	−891.178	−	647.479i	−0.852528	−	0.619398i	0.0733140	−	0.997309i	$-0.476642\pi$
$103$	−891.178	−	647.479i	−0.852528	−	0.619398i	−0.925842	+	0.377911i	$0.876642\pi$
$104$	−572.449	−	415.908i	−0.539742	−	0.392146i
$105$		0			0
$106$	1341.77	−	974.850i	1.22947	−	0.893263i
$107$	−941.813			−0.850921			−0.425460	−	0.904977i	$-0.639888\pi$
$107$	−941.813			−0.850921			−0.425460	+	0.904977i	$0.639888\pi$
$108$		0			0
$109$	−187.604	−	577.386i	−0.164855	−	0.507372i	0.834170	−	0.551507i	$-0.185947\pi$
$109$	−187.604	−	577.386i	−0.164855	−	0.507372i	−0.999026	+	0.0441347i	$0.985947\pi$
$110$	−183.132	+	318.633i	−0.158736	+	0.276186i
$111$		0			0
$112$	−16.3827	−	50.4207i	−0.0138216	−	0.0425385i
$113$	−464.434	−	1429.38i	−0.386640	−	1.18996i	−0.935284	−	0.353899i	$-0.884856\pi$
$113$	−464.434	−	1429.38i	−0.386640	−	1.18996i	0.548644	−	0.836056i	$-0.315144\pi$
$114$		0			0
$115$	−571.276	−	120.260i	−0.463233	−	0.0975157i
$116$	−596.242	−	1835.05i	−0.477239	−	1.46879i
$117$		0			0
$118$	−2695.51			−2.10290
$119$	473.789	−	344.228i	0.364976	−	0.265170i
$120$		0			0
$121$	1035.34	+	752.221i	0.777869	+	0.565155i
$122$	−2941.16	−	2136.88i	−2.18263	−	1.58577i
$123$		0			0
$124$	2790.94			2.02124
$125$	439.663	+	1326.58i	0.314597	+	0.949225i
$126$		0			0
$127$	−292.726	+	900.917i	−0.204529	+	0.629476i	0.795203	+	0.606343i	$0.207364\pi$
$127$	−292.726	+	900.917i	−0.204529	+	0.629476i	−0.999732	+	0.0231330i	$0.992636\pi$
$128$	1929.51	+	1401.87i	1.33239	+	0.968037i
$129$		0			0
$130$	−165.648	−	1546.90i	−0.111756	−	1.04363i
$131$	1059.37	−	769.677i	0.706546	−	0.513336i	−0.175511	−	0.984477i	$-0.556158\pi$
$131$	1059.37	−	769.677i	0.706546	−	0.513336i	0.882058	+	0.471142i	$0.156158\pi$
$132$		0			0
$133$	204.461	−	148.549i	0.133301	−	0.0968487i
$134$	−609.309	−	1875.26i	−0.392808	−	1.20894i
$135$		0			0
$136$	202.314	−	622.658i	0.127561	−	0.392592i
$137$	469.062	+	1443.62i	0.292516	+	0.900271i	0.984045	+	0.177922i	$0.0569375\pi$
$137$	469.062	+	1443.62i	0.292516	+	0.900271i	−0.691529	+	0.722349i	$0.743062\pi$
$138$		0			0
$139$	−8.92103	+	27.4561i	−0.00544369	+	0.0167539i	−0.953741	−	0.300628i	$-0.902804\pi$
$139$	−8.92103	+	27.4561i	−0.00544369	+	0.0167539i	0.948298	+	0.317382i	$0.102804\pi$
$140$	1522.62	−	2649.22i	0.919178	−	1.59929i
$141$		0			0
$142$	−1476.45	+	1072.70i	−0.872539	+	0.633937i
$143$	216.932			0.126858
$144$		0			0
$145$	821.512	−	1429.36i	0.470502	−	0.818631i
$146$	3861.03	+	2805.20i	2.18864	+	1.59014i
$147$		0			0
$148$	−288.049	+	886.524i	−0.159983	+	0.492377i
$149$	613.380			0.337249			0.168624	−	0.985680i	$-0.446068\pi$
$149$	613.380			0.337249			0.168624	+	0.985680i	$0.446068\pi$
$150$		0			0
$151$	551.057			0.296983			0.148491	−	0.988914i	$-0.452558\pi$
$151$	551.057			0.296983			0.148491	+	0.988914i	$0.452558\pi$
$152$	87.3074	−	268.704i	0.0465892	−	0.143387i
$153$		0			0
$154$	555.444	+	403.553i	0.290642	+	0.211164i
$155$	1599.13	+	1769.03i	0.828677	+	0.916724i
$156$		0			0
$157$	1900.31			0.965996			0.482998	−	0.875621i	$-0.339548\pi$
$157$	1900.31			0.965996			0.482998	+	0.875621i	$0.339548\pi$
$158$	−4543.51	+	3301.06i	−2.28774	+	1.66214i
$159$		0			0
$160$	208.496	+	1947.03i	0.103019	+	0.962038i
$161$	−337.020	+	1037.24i	−0.164975	+	0.507740i
$162$		0			0
$163$	557.426	+	1715.58i	0.267859	+	0.824384i	0.991021	+	0.133706i	$0.0426879\pi$
$163$	557.426	+	1715.58i	0.267859	+	0.824384i	−0.723162	+	0.690678i	$0.757312\pi$
$164$	−2081.62	+	6406.56i	−0.991141	+	3.05042i
$165$		0			0
$166$	−333.101	−	1025.18i	−0.155745	−	0.479333i
$167$	3298.62	−	2396.59i	1.52847	−	1.11050i	0.571393	−	0.820676i	$-0.306403\pi$
$167$	3298.62	−	2396.59i	1.52847	−	1.11050i	0.957080	−	0.289824i	$-0.0935969\pi$
$168$		0			0
$169$	1034.48	−	751.593i	0.470860	−	0.342100i
$170$	1313.87	−	588.058i	0.592761	−	0.265306i
$171$		0			0
$172$	−1867.33	−	1356.69i	−0.827805	−	0.601435i
$173$	117.934	−	362.964i	0.0518287	−	0.159512i	−0.921792	−	0.387685i	$-0.873275\pi$
$173$	117.934	−	362.964i	0.0518287	−	0.159512i	0.973621	+	0.228172i	$0.0732749\pi$
$174$		0			0
$175$	2551.62	−	552.815i	1.10220	−	0.238794i
$176$	18.1704			0.00778206
$177$		0			0
$178$	−685.156	−	497.795i	−0.288509	−	0.209614i
$179$	383.454	+	278.596i	0.160116	+	0.116331i	0.664958	−	0.746881i	$-0.268449\pi$
$179$	383.454	+	278.596i	0.160116	+	0.116331i	−0.504842	+	0.863212i	$0.668449\pi$
$180$		0			0
$181$	1695.65	−	1231.96i	0.696336	−	0.505917i	−0.182401	−	0.983224i	$-0.558387\pi$
$181$	1695.65	−	1231.96i	0.696336	−	0.505917i	0.878737	+	0.477307i	$0.158387\pi$
$182$	−2906.36			−1.18370
$183$		0			0
$184$	376.767	+	1159.57i	0.150954	+	0.464590i
$185$	−726.966	+	325.373i	−0.288906	+	0.129308i
$186$		0			0
$187$	62.0255	+	190.895i	0.0242554	+	0.0746503i
$188$	909.179	+	2798.16i	0.352706	+	1.08552i
$189$		0			0
$190$	566.994	−	253.773i	0.216495	−	0.0968981i
$191$	−1030.60	−	3171.86i	−0.390428	−	1.20161i	−0.932466	−	0.361259i	$-0.882347\pi$
$191$	−1030.60	−	3171.86i	−0.390428	−	1.20161i	0.542038	−	0.840354i	$-0.317653\pi$
$192$		0			0
$193$	−1050.03			−0.391620			−0.195810	−	0.980642i	$-0.562734\pi$
$193$	−1050.03			−0.391620			−0.195810	+	0.980642i	$0.562734\pi$
$194$	−308.231	+	223.943i	−0.114071	+	0.0828773i
$195$		0			0
$196$	−987.134	−	717.195i	−0.359743	−	0.261368i
$197$	3052.81	+	2217.99i	1.10408	+	0.802160i	0.981721	−	0.190326i	$-0.0609544\pi$
$197$	3052.81	+	2217.99i	1.10408	+	0.802160i	0.122358	+	0.992486i	$0.460954\pi$
$198$		0			0
$199$	1810.57			0.644966			0.322483	−	0.946575i	$-0.395483\pi$
$199$	1810.57			0.644966			0.322483	+	0.946575i	$0.395483\pi$
$200$	1944.50	−	2176.67i	0.687485	−	0.769568i
$201$		0			0
$202$	−150.864	+	464.313i	−0.0525484	+	0.161727i
$203$	−2491.66	−	1810.30i	−0.861481	−	0.625902i
$204$		0			0
$205$	−5253.50	+	2351.34i	−1.78986	+	0.801097i
$206$	−4092.15	+	2973.12i	−1.38405	+	1.00557i
$207$		0			0
$208$	−62.2284	+	45.2116i	−0.0207441	+	0.0150714i
$209$	26.7667	+	82.3796i	0.00885882	+	0.0272647i
$210$		0			0
$211$	−188.866	+	581.268i	−0.0616211	+	0.189650i	−0.977128	−	0.212652i	$-0.931790\pi$
$211$	−188.866	+	581.268i	−0.0616211	+	0.189650i	0.915507	+	0.402302i	$0.131790\pi$
$212$	−1460.46	−	4494.84i	−0.473136	−	1.45616i
$213$		0			0
$214$	−1336.39	+	4113.00i	−0.426888	+	1.31383i
$215$	−209.986	−	1960.95i	−0.0666091	−	0.622026i
$216$		0			0
$217$	3604.12	−	2618.55i	1.12748	−	0.819164i
$218$	−2787.71			−0.866089
$219$		0			0
$220$	702.282	+	776.899i	0.215218	+	0.238084i
$221$	−687.406	−	499.430i	−0.209230	−	0.152015i
$222$		0			0
$223$	−846.567	+	2605.46i	−0.254217	+	0.782398i	0.739766	+	0.672864i	$0.234936\pi$
$223$	−846.567	+	2605.46i	−0.254217	+	0.782398i	−0.993983	+	0.109534i	$0.965064\pi$
$224$	3658.14			1.09116
$225$		0			0
$226$	−6901.28			−2.03127
$227$	351.246	−	1081.02i	0.102700	−	0.316079i	−0.886483	−	0.462760i	$-0.846859\pi$
$227$	351.246	−	1081.02i	0.102700	−	0.316079i	0.989184	+	0.146681i	$0.0468591\pi$
$228$		0			0
$229$	4447.65	+	3231.40i	1.28344	+	0.932477i	0.999651	−	0.0264090i	$-0.00840724\pi$
$229$	4447.65	+	3231.40i	1.28344	+	0.932477i	0.283793	+	0.958886i	$0.408407\pi$
$230$	−1335.81	+	2324.18i	−0.382958	+	0.666312i
$231$		0			0
$232$	−3443.09			−0.974353
$233$	−563.468	+	409.383i	−0.158429	+	0.115106i	−0.664175	−	0.747577i	$-0.731217\pi$
$233$	−563.468	+	409.383i	−0.158429	+	0.115106i	0.505746	+	0.862682i	$0.331217\pi$
$234$		0			0
$235$	−1252.68	+	2179.55i	−0.347727	+	0.605013i
$236$	−2373.62	+	7305.26i	−0.654702	+	2.01497i
$237$		0			0
$238$	−830.992	−	2557.53i	−0.226324	−	0.696555i
$239$	−1181.13	+	3635.15i	−0.319669	+	0.983841i	0.654120	+	0.756391i	$0.273039\pi$
$239$	−1181.13	+	3635.15i	−0.319669	+	0.983841i	−0.973790	+	0.227451i	$0.926961\pi$
$240$		0			0
$241$	−715.178	−	2201.09i	−0.191156	−	0.588318i	−1.00000		0.000294720i	$-0.999906\pi$
$241$	−715.178	−	2201.09i	−0.191156	−	0.588318i	0.808844	−	0.588024i	$-0.200094\pi$
$242$	4754.14	−	3454.08i	1.26284	−	0.917508i
$243$		0			0
$244$	−8381.22	+	6089.31i	−2.19899	+	1.59766i
$245$	−111.006	−	1036.63i	−0.0289466	−	0.270317i
$246$		0			0
$247$	−296.646	−	215.526i	−0.0764176	−	0.0555206i
$248$	1539.01	−	4736.57i	0.394060	−	1.21279i
$249$		0			0
$250$	6417.19	−	37.6901i	1.62343	−	0.00953494i
$251$	−4582.81			−1.15245			−0.576224	−	0.817292i	$-0.695474\pi$
$251$	−4582.81			−1.15245			−0.576224	+	0.817292i	$0.695474\pi$
$252$		0			0
$253$	−302.407	−	219.712i	−0.0751470	−	0.0545975i
$254$	3519.03	+	2556.73i	0.869306	+	0.631588i
$255$		0			0
$256$	3523.48	−	2559.96i	0.860225	−	0.624990i
$257$	−2786.16			−0.676250			−0.338125	−	0.941101i	$-0.609793\pi$
$257$	−2786.16			−0.676250			−0.338125	+	0.941101i	$0.609793\pi$
$258$		0			0
$259$	459.788	+	1415.08i	0.110308	+	0.339494i
$260$	−4338.21	−	913.242i	−1.03479	−	0.217834i
$261$		0			0
$262$	−1858.06	−	5718.52i	−0.438135	−	1.34844i
$263$	1204.24	+	3706.26i	0.282344	+	0.868964i	0.987182	+	0.159597i	$0.0510194\pi$
$263$	1204.24	+	3706.26i	0.282344	+	0.868964i	−0.704839	+	0.709368i	$0.748981\pi$
$264$		0			0
$265$	2012.25	−	3501.12i	0.466457	−	0.811593i
$266$	−358.610	−	1103.69i	−0.0826608	−	0.254404i
$267$		0			0
$268$	−5618.79			−1.28068
$269$	3641.06	−	2645.39i	0.825277	−	0.599599i	−0.0929421	−	0.995672i	$-0.529627\pi$
$269$	3641.06	−	2645.39i	0.825277	−	0.599599i	0.918219	+	0.396073i	$0.129627\pi$
$270$		0			0
$271$	−678.744	−	493.136i	−0.152143	−	0.110538i	0.509109	−	0.860702i	$-0.329975\pi$
$271$	−678.744	−	493.136i	−0.152143	−	0.110538i	−0.661253	+	0.750163i	$0.729975\pi$
$272$	−57.5775	−	41.8325i	−0.0128351	−	0.00932526i
$273$		0			0
$274$	6970.04			1.53677
$275$	−90.0494	+	890.282i	−0.0197461	+	0.195222i
$276$		0			0
$277$	92.7237	−	285.374i	0.0201127	−	0.0619006i	−0.940496	−	0.339804i	$-0.889639\pi$
$277$	92.7237	−	285.374i	0.0201127	−	0.0619006i	0.960609	+	0.277903i	$0.0896394\pi$
$278$	107.245	+	77.9182i	0.0231372	+	0.0168102i
$279$		0			0
$280$	−3656.44	−	4044.94i	−0.780408	−	0.863326i
$281$	3594.75	−	2611.74i	0.763149	−	0.554460i	−0.136726	−	0.990609i	$-0.543658\pi$
$281$	3594.75	−	2611.74i	0.763149	−	0.554460i	0.899875	+	0.436149i	$0.143658\pi$
$282$		0			0
$283$	−1807.68	+	1313.35i	−0.379700	+	0.275868i	−0.761222	−	0.648491i	$-0.775400\pi$
$283$	−1807.68	+	1313.35i	−0.379700	+	0.275868i	0.381522	+	0.924360i	$0.375400\pi$
$284$	1607.05	+	4946.00i	0.335779	+	1.03342i
$285$		0			0
$286$	307.817	−	947.365i	0.0636421	−	0.195870i
$287$	3322.71	+	10226.3i	0.683392	+	2.10326i
$288$		0			0
$289$	−1275.26	+	3924.84i	−0.259568	+	0.798869i
$290$	−5076.46	−	5615.83i	−1.02793	−	1.13715i
$291$		0			0
$292$	11002.5	−	7993.79i	2.20504	−	1.60206i
$293$	−2129.37			−0.424571			−0.212286	−	0.977208i	$-0.568091\pi$
$293$	−2129.37			−0.424571			−0.212286	+	0.977208i	$0.568091\pi$
$294$		0			0
$295$	−5990.45	+	2681.18i	−1.18230	+	0.529168i
$296$	1345.70	+	977.711i	0.264248	+	0.191987i
$297$		0			0
$298$	870.361	−	2678.70i	0.169190	−	0.520714i
$299$	1582.35			0.306052
$300$		0			0
$301$	−3684.29			−0.705512
$302$	781.928	−	2406.53i	0.148990	−	0.458543i
$303$		0			0
$304$	−24.8473	−	18.0526i	−0.00468779	−	0.00340588i
$305$	−8661.90	−	1823.43i	−1.62616	−	0.342325i
$306$		0			0
$307$	−6432.86			−1.19591			−0.597953	−	0.801531i	$-0.704019\pi$
$307$	−6432.86			−1.19591			−0.597953	+	0.801531i	$0.704019\pi$
$308$	1582.81	−	1149.98i	0.292821	−	0.212747i
$309$		0			0
$310$	9994.65	−	4473.37i	1.83115	−	0.819582i
$311$	1481.30	−	4558.97i	0.270086	−	0.831239i	−0.720392	−	0.693567i	$-0.756038\pi$
$311$	1481.30	−	4558.97i	0.270086	−	0.831239i	0.990478	−	0.137672i	$-0.0439620\pi$
$312$		0			0
$313$	−109.023	−	335.538i	−0.0196880	−	0.0605933i	0.940730	−	0.339157i	$-0.110142\pi$
$313$	−109.023	−	335.538i	−0.0196880	−	0.0605933i	−0.960418	+	0.278564i	$0.910142\pi$
$314$	2696.46	−	8298.86i	0.484619	−	1.49150i
$315$		0			0
$316$	4945.44	+	15220.5i	0.880388	+	2.70956i
$317$	5476.50	−	3978.91i	0.970318	−	0.704977i	0.0147938	−	0.999891i	$-0.495291\pi$
$317$	5476.50	−	3978.91i	0.970318	−	0.704977i	0.955524	+	0.294913i	$0.0952908\pi$
$318$		0			0
$319$	853.985	−	620.457i	0.149887	−	0.108899i
$320$	9020.88	+	1899.00i	1.57588	+	0.331741i
$321$		0			0
$322$	4051.53	+	2943.61i	0.701189	+	0.509444i
$323$	104.840	−	322.665i	0.0180603	−	0.0555837i
$324$		0			0
$325$	−1906.81	−	3273.03i	−0.325449	−	0.558631i
$326$	8283.09			1.40723
$327$		0			0
$328$	9724.87	+	7065.53i	1.63709	+	1.18942i
$329$	3799.41	+	2760.43i	0.636681	+	0.462576i
$330$		0			0
$331$	6924.44	−	5030.90i	1.14985	−	0.835417i	0.161392	−	0.986890i	$-0.448402\pi$
$331$	6924.44	−	5030.90i	1.14985	−	0.835417i	0.988461	+	0.151473i	$0.0484017\pi$
$332$	−3071.72			−0.507779
$333$		0			0
$334$	−5785.55	−	17806.1i	−0.947818	−	2.91708i
$335$	−3219.41	−	3561.47i	−0.525060	−	0.580847i
$336$		0			0
$337$	−939.394	−	2891.16i	−0.151846	−	0.467334i	0.845982	−	0.533212i	$-0.179015\pi$
$337$	−939.394	−	2891.16i	−0.151846	−	0.467334i	−0.997828	+	0.0658782i	$0.979015\pi$
$338$	−1814.40	−	5584.16i	−0.291984	−	0.898633i
$339$		0			0
$340$	−436.756	−	4078.63i	−0.0696660	−	0.650573i
$341$	471.829	+	1452.14i	0.0749295	+	0.230609i
$342$		0			0
$343$	5216.45			0.821171
$344$	−3332.18	+	2420.97i	−0.522264	+	0.379447i
$345$		0			0
$346$	−1417.76	−	1030.06i	−0.220287	−	0.160048i
$347$	3629.87	+	2637.26i	0.561561	+	0.407998i	0.832030	−	0.554731i	$-0.187179\pi$
$347$	3629.87	+	2637.26i	0.561561	+	0.407998i	−0.270469	+	0.962729i	$0.587179\pi$
$348$		0			0
$349$	5619.03			0.861833			0.430917	−	0.902392i	$-0.358190\pi$
$349$	5619.03			0.861833			0.430917	+	0.902392i	$0.358190\pi$
$350$	1206.45	−	11927.6i	0.184249	−	1.82160i
$351$		0			0
$352$	−387.439	+	1192.41i	−0.0586664	+	0.180557i
$353$	−9548.02	−	6937.04i	−1.43963	−	1.04595i	−0.988119	−	0.153688i	$-0.950885\pi$
$353$	−9548.02	−	6937.04i	−1.43963	−	1.04595i	−0.451511	−	0.892265i	$-0.649115\pi$
$354$		0			0
$355$	−2214.22	+	3852.55i	−0.331039	+	0.575977i
$356$	−1952.44	+	1418.53i	−0.290672	+	0.211185i
$357$		0			0
$358$	1760.76	−	1279.27i	0.259942	−	0.188859i
$359$	−2836.72	−	8730.53i	−0.417037	−	1.28351i	−0.910416	−	0.413695i	$-0.864238\pi$
$359$	−2836.72	−	8730.53i	−0.417037	−	1.28351i	0.493378	−	0.869815i	$-0.335762\pi$
$360$		0			0
$361$	−2074.30	+	6384.05i	−0.302421	+	0.930756i
$362$	−2974.05	−	9153.19i	−0.431803	−	1.32895i
$363$		0			0
$364$	−2559.30	+	7876.71i	−0.368526	+	1.13421i
$365$	11371.0	+	2393.72i	1.63064	+	0.343268i
$366$		0			0
$367$	763.005	−	554.355i	0.108525	−	0.0788477i	−0.532199	−	0.846619i	$-0.678634\pi$
$367$	763.005	−	554.355i	0.108525	−	0.0788477i	0.640724	+	0.767771i	$0.278634\pi$
$368$	132.539			0.0187746
$369$		0			0
$370$	389.403	+	3636.43i	0.0547138	+	0.510943i
$371$	−6103.19	−	4434.22i	−0.854074	−	0.620521i
$372$		0			0
$373$	442.426	−	1361.65i	0.0614155	−	0.189017i	−0.915641	−	0.401996i	$-0.868317\pi$
$373$	442.426	−	1361.65i	0.0614155	−	0.189017i	0.977057	+	0.212979i	$0.0683165\pi$
$374$	921.669			0.127429
$375$		0			0
$376$	5250.18			0.720100
$377$	−1380.84	+	4249.78i	−0.188639	+	0.580570i
$378$		0			0
$379$	−7369.94	−	5354.58i	−0.998862	−	0.725715i	−0.0370178	−	0.999315i	$-0.511786\pi$
$379$	−7369.94	−	5354.58i	−0.998862	−	0.725715i	−0.961844	+	0.273599i	$0.911786\pi$
$380$	−188.480	−	1760.11i	−0.0254442	−	0.237610i
$381$		0			0
$382$	−15314.2			−2.05116
$383$	−8830.73	+	6415.90i	−1.17814	+	0.855972i	−0.991961	−	0.126543i	$-0.959612\pi$
$383$	−8830.73	+	6415.90i	−1.17814	+	0.855972i	−0.186183	+	0.982515i	$0.559612\pi$
$384$		0			0
$385$	1635.81	+	344.357i	0.216542	+	0.0455846i
$386$	−1489.95	+	4585.58i	−0.196467	+	0.604663i
$387$		0			0
$388$	335.498	+	1032.56i	0.0438978	+	0.135103i
$389$	−376.670	+	1159.27i	−0.0490949	+	0.151099i	−0.972599	−	0.232491i	$-0.925312\pi$
$389$	−376.670	+	1159.27i	−0.0490949	+	0.151099i	0.923504	+	0.383590i	$0.125312\pi$
$390$		0			0
$391$	452.428	+	1392.43i	0.0585173	+	0.180098i
$392$	−1761.50	+	1279.81i	−0.226963	+	0.164898i
$393$		0			0
$394$	14018.0	−	10184.7i	1.79243	−	1.30228i
$395$	−6813.90	+	11855.6i	−0.867961	+	1.51017i
$396$		0			0
$397$	8527.21	+	6195.38i	1.07801	+	0.783217i	0.977334	−	0.211703i	$-0.0679008\pi$
$397$	8527.21	+	6195.38i	1.07801	+	0.783217i	0.100672	+	0.994920i	$0.467901\pi$
$398$	2569.13	−	7906.97i	0.323565	−	0.995830i
$399$		0			0
$400$	−159.716	−	274.151i	−0.0199645	−	0.0342689i
$401$	7392.45			0.920602			0.460301	−	0.887763i	$-0.347742\pi$
$401$	7392.45			0.920602			0.460301	+	0.887763i	$0.347742\pi$
$402$		0			0
$403$	−5229.11	−	3799.17i	−0.646354	−	0.469603i
$404$	1125.51	+	817.733i	0.138605	+	0.100702i
$405$		0			0
$406$	−11441.3	+	8312.62i	−1.39858	+	1.01613i
$407$	−509.960			−0.0621076
$408$		0			0
$409$	−4996.45	−	15377.5i	−0.604056	−	1.85909i	−0.503156	−	0.864196i	$-0.667828\pi$
$409$	−4996.45	−	15377.5i	−0.604056	−	1.85909i	−0.100900	−	0.994897i	$-0.532172\pi$
$410$	2814.07	+	26279.1i	0.338968	+	3.16544i
$411$		0			0
$412$	4454.15	+	13708.5i	0.532622	+	1.63924i
$413$	3788.81	+	11660.8i	0.451417	+	1.38932i
$414$		0			0
$415$	−1760.01	−	1947.01i	−0.208181	−	0.230301i
$416$	−1640.10	−	5047.72i	−0.193300	−	0.594915i
$417$		0			0
$418$	397.741			0.0465410
$419$	−9614.33	+	6985.22i	−1.12098	+	0.814440i	−0.984357	−	0.176183i	$-0.943625\pi$
$419$	−9614.33	+	6985.22i	−1.12098	+	0.814440i	−0.136623	+	0.990623i	$0.543625\pi$
$420$		0			0
$421$	−4162.95	−	3024.56i	−0.481923	−	0.350138i	0.320147	−	0.947368i	$-0.396268\pi$
$421$	−4162.95	−	3024.56i	−0.481923	−	0.350138i	−0.802070	+	0.597230i	$0.796268\pi$
$422$	2270.47	+	1649.59i	0.261907	+	0.190286i
$423$		0			0
$424$	−8433.64			−0.965976
$425$	2334.99	−	2613.78i	0.266503	−	0.298322i
$426$		0			0
$427$	−5110.03	+	15727.1i	−0.579138	+	1.78240i
$428$	9970.07	+	7243.68i	1.12598	+	0.818075i
$429$		0			0
$430$	−8861.64	−	1865.47i	−0.993828	−	0.209212i
$431$	−3177.50	+	2308.59i	−0.355116	+	0.258007i	−0.751012	−	0.660289i	$-0.770434\pi$
$431$	−3177.50	+	2308.59i	−0.355116	+	0.258007i	0.395896	+	0.918295i	$0.370434\pi$
$432$		0			0
$433$	−8905.28	+	6470.07i	−0.988362	+	0.718087i	−0.959562	−	0.281498i	$-0.909169\pi$
$433$	−8905.28	+	6470.07i	−0.988362	+	0.718087i	−0.0287999	+	0.999585i	$0.509169\pi$
$434$	−6321.37	−	19455.2i	−0.699160	−	2.15179i
$435$		0			0
$436$	−2454.81	+	7555.13i	−0.269642	+	0.829874i
$437$	195.243	+	600.895i	0.0213724	+	0.0657774i
$438$		0			0
$439$	−1232.82	+	3794.22i	−0.134030	+	0.412501i	−0.995438	−	0.0954122i	$-0.969583\pi$
$439$	−1232.82	+	3794.22i	−0.134030	+	0.412501i	0.861408	+	0.507914i	$0.169583\pi$
$440$	1705.75	−	763.456i	0.184815	−	0.0827189i
$441$		0			0
$442$	−3156.46	+	2293.30i	−0.339678	+	0.246790i
$443$	−8292.83			−0.889400			−0.444700	−	0.895680i	$-0.646690\pi$
$443$	−8292.83			−0.889400			−0.444700	+	0.895680i	$0.646690\pi$
$444$		0			0
$445$	−2017.83	−	424.775i	−0.214953	−	0.0452500i
$446$	10177.1	+	7394.09i	1.08049	+	0.785023i
$447$		0			0
$448$	5321.81	−	16378.8i	0.561232	−	1.72729i
$449$	−2430.55			−0.255467			−0.127733	−	0.991809i	$-0.540770\pi$
$449$	−2430.55			−0.255467			−0.127733	+	0.991809i	$0.540770\pi$
$450$		0			0
$451$	−3685.28			−0.384774
$452$	−6077.15	+	18703.5i	−0.632401	+	1.94633i
$453$		0			0
$454$	−4222.54	−	3067.85i	−0.436505	−	0.317140i
$455$	−6459.05	+	2890.92i	−0.665505	+	0.297864i
$456$		0			0
$457$	13718.9			1.40425			0.702124	−	0.712055i	$-0.252235\pi$
$457$	13718.9			1.40425			0.702124	+	0.712055i	$0.252235\pi$
$458$	20422.9	−	14838.1i	2.08362	−	1.51384i
$459$		0			0
$460$	5122.60	+	5666.88i	0.519223	+	0.574390i
$461$	4036.52	−	12423.1i	0.407808	−	1.25511i	−0.510719	−	0.859748i	$-0.670621\pi$
$461$	4036.52	−	12423.1i	0.407808	−	1.25511i	0.918527	−	0.395358i	$-0.129379\pi$
$462$		0			0
$463$	−1346.82	−	4145.09i	−0.135188	−	0.416066i	0.860431	−	0.509567i	$-0.170194\pi$
$463$	−1346.82	−	4145.09i	−0.135188	−	0.416066i	−0.995619	+	0.0935008i	$0.970194\pi$
$464$	−115.660	+	355.965i	−0.0115719	+	0.0356147i
$465$		0			0
$466$	988.283	+	3041.62i	0.0982432	+	0.302361i
$467$	−10636.8	+	7728.06i	−1.05398	+	0.765765i	−0.972966	−	0.230948i	$-0.925817\pi$
$467$	−10636.8	+	7728.06i	−1.05398	+	0.765765i	−0.0810186	+	0.996713i	$0.525817\pi$
$468$		0			0
$469$	−7255.92	+	5271.73i	−0.714386	+	0.519032i
$470$	7740.82	+	8563.28i	0.759697	+	0.840414i
$471$		0			0
$472$	11089.1	+	8056.67i	1.08139	+	0.785674i
$473$	390.209	−	1200.94i	0.0379320	−	0.116743i
$474$		0			0
$475$	1007.65	−	1127.96i	0.0973352	−	0.108957i
$476$	−7663.07			−0.737891
$477$		0			0
$478$	14199.1	+	10316.2i	1.35868	+	0.987142i
$479$	−13406.2	−	9740.16i	−1.27880	−	0.929101i	−0.279282	−	0.960209i	$-0.590096\pi$
$479$	−13406.2	−	9740.16i	−1.27880	−	0.929101i	−0.999516	+	0.0311079i	$0.990096\pi$
$480$		0			0
$481$	1746.47	−	1268.89i	0.165556	−	0.120283i
$482$	−10627.2			−1.00427
$483$		0			0
$484$	−5174.69	−	15926.1i	−0.485978	−	1.49569i
$485$	−462.254	+	804.280i	−0.0432781	+	0.0753000i
$486$		0			0
$487$	−5575.10	−	17158.4i	−0.518751	−	1.59655i	−0.776352	−	0.630300i	$-0.782932\pi$
$487$	−5575.10	−	17158.4i	−0.518751	−	1.59655i	0.257601	−	0.966251i	$-0.417068\pi$
$488$	5712.68	+	17581.8i	0.529920	+	1.63092i
$489$		0			0
$490$	−4684.57	−	986.154i	−0.431892	−	0.0909181i
$491$	73.1446	+	225.116i	0.00672295	+	0.0206911i	0.954362	−	0.298653i	$-0.0965374\pi$
$491$	73.1446	+	225.116i	0.00672295	+	0.0206911i	−0.947639	+	0.319344i	$0.896537\pi$
$492$		0			0
$493$	−4134.52			−0.377706
$494$	−1362.15	+	989.662i	−0.124061	+	0.0901357i
$495$		0			0
$496$	−437.994	−	318.221i	−0.0396502	−	0.0288075i
$497$	6715.79	+	4879.31i	0.606125	+	0.440376i
$498$		0			0
$499$	−8234.07			−0.738692			−0.369346	−	0.929292i	$-0.620418\pi$
$499$	−8234.07			−0.738692			−0.369346	+	0.929292i	$0.620418\pi$
$500$	5548.73	−	17424.8i	0.496293	−	1.55852i
$501$		0			0
$502$	−6502.82	+	20013.6i	−0.578157	+	1.77939i
$503$	11126.9	+	8084.18i	0.986331	+	0.716611i	0.959115	−	0.283018i	$-0.0913356\pi$
$503$	11126.9	+	8084.18i	0.986331	+	0.716611i	0.0272165	+	0.999630i	$0.491336\pi$
$504$		0			0
$505$	126.567	+	1181.94i	0.0111528	+	0.104150i
$506$	−1388.61	+	1008.88i	−0.121998	+	0.0886370i
$507$		0			0
$508$	10027.9	−	7285.72i	0.875822	−	0.636322i
$509$	2429.43	+	7477.02i	0.211557	+	0.651107i	0.999380	+	0.0352046i	$0.0112083\pi$
$509$	2429.43	+	7477.02i	0.211557	+	0.651107i	−0.787823	+	0.615902i	$0.788792\pi$
$510$		0			0
$511$	6708.23	−	20645.8i	0.580733	−	1.78731i
$512$	−283.894	−	873.736i	−0.0245048	−	0.0754181i
$513$		0			0
$514$	−3953.45	+	12167.5i	−0.339259	+	1.04413i
$515$	−6137.00	+	10677.8i	−0.525104	+	0.913632i
$516$		0			0
$517$	−1302.20	+	946.102i	−0.110775	+	0.0804826i
$518$	6832.24			0.579520
$519$		0			0
$520$	−3942.10	+	6858.90i	−0.332447	+	0.578428i
$521$	−4634.20	−	3366.95i	−0.389689	−	0.283126i	0.375639	−	0.926766i	$-0.377423\pi$
$521$	−4634.20	−	3366.95i	−0.389689	−	0.283126i	−0.765328	+	0.643640i	$0.777423\pi$
$522$		0			0
$523$	1426.67	−	4390.83i	0.119281	−	0.367108i	−0.873535	−	0.486761i	$-0.838178\pi$
$523$	1426.67	−	4390.83i	0.119281	−	0.367108i	0.992816	+	0.119653i	$0.0381782\pi$
$524$	−17134.3			−1.42846
$525$		0			0
$526$	17894.4			1.48333
$527$	1848.06	−	5687.75i	0.152757	−	0.470137i
$528$		0			0
$529$	7637.48	+	5548.96i	0.627721	+	0.456066i
$530$	−12434.5	−	13755.6i	−1.01909	−	1.12737i
$531$		0			0
$532$	−3306.95			−0.269501
$533$	12621.1	−	9169.75i	1.02567	−	0.745189i
$534$		0			0
$535$	1121.16	+	10469.9i	0.0906020	+	0.846083i
$536$	−3098.37	+	9535.80i	−0.249681	+	0.768440i
$537$		0			0
$538$	−6386.17	−	19654.6i	−0.511761	−	1.57504i
$539$	206.278	−	634.858i	0.0164843	−	0.0507334i
$540$		0			0
$541$	−3356.50	−	10330.3i	−0.266742	−	0.820947i	−0.991287	−	0.131720i	$-0.957950\pi$
$541$	−3356.50	−	10330.3i	−0.266742	−	0.820947i	0.724545	−	0.689227i	$-0.242050\pi$
$542$	−3116.69	+	2264.41i	−0.246999	+	0.179455i
$543$		0			0
$544$	3972.93	−	2886.50i	0.313121	−	0.227496i
$545$	−6195.35	+	2772.89i	−0.486935	+	0.217941i
$546$		0			0
$547$	15861.6	+	11524.1i	1.23984	+	0.900795i	0.997588	−	0.0694188i	$-0.0221145\pi$
$547$	15861.6	+	11524.1i	1.23984	+	0.900795i	0.242250	+	0.970214i	$0.422114\pi$
$548$	6137.70	−	18889.9i	0.478448	−	1.47251i
$549$		0			0
$550$	3760.18	+	1656.53i	0.291517	+	0.128427i
$551$	−1784.23			−0.137950
$552$		0			0
$553$	20666.7	+	15015.2i	1.58922	+	1.15464i
$554$	−1114.69	−	809.868i	−0.0854847	−	0.0621083i
$555$		0			0
$556$	305.609	−	222.038i	0.0233106	−	0.0169362i
$557$	15810.5			1.20271			0.601356	−	0.798981i	$-0.294627\pi$
$557$	15810.5			1.20271			0.601356	+	0.798981i	$0.294627\pi$
$558$		0			0
$559$	1651.83	+	5083.81i	0.124982	+	0.384655i
$560$	−541.014	+	242.145i	−0.0408250	+	0.0182723i
$561$		0			0
$562$	−6304.94	−	19404.6i	−0.473234	−	1.45647i
$563$	−1370.22	−	4217.10i	−0.102572	−	0.315683i	0.886581	−	0.462573i	$-0.153074\pi$
$563$	−1370.22	−	4217.10i	−0.102572	−	0.315683i	−0.989153	+	0.146890i	$0.953074\pi$
$564$		0			0
$565$	−15337.3	+	6864.59i	−1.14202	+	0.511143i
$566$	3170.54	+	9757.91i	0.235455	+	0.724656i
$567$		0			0
$568$	9280.16			0.685541
$569$	13932.2	−	10122.3i	1.02648	−	0.745784i	0.0588813	−	0.998265i	$-0.481247\pi$
$569$	13932.2	−	10122.3i	1.02648	−	0.745784i	0.967602	+	0.252481i	$0.0812466\pi$
$570$		0			0
$571$	8869.36	+	6443.97i	0.650037	+	0.472280i	0.863284	−	0.504719i	$-0.168404\pi$
$571$	8869.36	+	6443.97i	0.650037	+	0.472280i	−0.213247	+	0.976998i	$0.568404\pi$
$572$	−2296.45	−	1668.47i	−0.167866	−	0.121962i
$573$		0			0
$574$	49373.9			3.59029
$575$	−656.841	+	6493.92i	−0.0476385	+	0.470983i
$576$		0			0
$577$	2343.22	−	7211.69i	0.169063	−	0.520323i	−0.830250	−	0.557392i	$-0.811802\pi$
$577$	2343.22	−	7211.69i	0.169063	−	0.520323i	0.999313	+	0.0370689i	$0.0118021\pi$
$578$	15330.7	+	11138.4i	1.10324	+	0.801549i
$579$		0			0
$580$	−19690.0	+	8812.79i	−1.40963	+	0.630916i
$581$	−3966.71	+	2881.98i	−0.283248	+	0.205792i
$582$		0			0
$583$	2091.79	−	1519.77i	0.148599	−	0.107963i
$584$	−7499.35	−	23080.6i	−0.531379	−	1.63542i
$585$		0			0
$586$	−3021.49	+	9299.20i	−0.212998	+	0.655540i
$587$	−5100.60	−	15698.0i	−0.358644	−	1.10379i	−0.953866	−	0.300232i	$-0.902936\pi$
$587$	−5100.60	−	15698.0i	−0.358644	−	1.10379i	0.595222	−	0.803561i	$-0.297064\pi$
$588$		0			0
$589$	797.521	−	2454.52i	0.0557917	−	0.171709i
$590$	3208.82	+	29965.4i	0.223907	+	2.09094i
$591$		0			0
$592$	146.286	−	106.283i	0.0101559	−	0.00737871i
$593$	13417.3			0.929144			0.464572	−	0.885535i	$-0.346208\pi$
$593$	13417.3			0.929144			0.464572	+	0.885535i	$0.346208\pi$
$594$		0			0
$595$	−4390.72	−	4857.23i	−0.302524	−	0.334667i
$596$	−6493.26	−	4717.63i	−0.446266	−	0.324231i
$597$		0			0
$598$	2245.29	−	6910.29i	0.153540	−	0.472546i
$599$	20049.4			1.36761			0.683804	−	0.729666i	$-0.260325\pi$
$599$	20049.4			1.36761			0.683804	+	0.729666i	$0.260325\pi$
$600$		0			0
$601$	−15238.7			−1.03428			−0.517138	−	0.855902i	$-0.673003\pi$
$601$	−15238.7			−1.03428			−0.517138	+	0.855902i	$0.673003\pi$
$602$	−5227.86	+	16089.7i	−0.353940	+	1.08931i
$603$		0			0
$604$	−5833.51	−	4238.29i	−0.392984	−	0.285519i
$605$	7129.77	−	12405.2i	0.479118	−	0.833622i
$606$		0			0
$607$	15851.9			1.05998			0.529990	−	0.848004i	$-0.322196\pi$
$607$	15851.9			1.05998			0.529990	+	0.848004i	$0.322196\pi$
$608$	1714.49	−	1245.65i	0.114362	−	0.0830887i
$609$		0			0
$610$	−20254.0	+	35240.1i	−1.34436	+	2.33906i
$611$	2105.57	−	6480.27i	0.139414	−	0.429073i
$612$		0			0
$613$	7633.08	+	23492.2i	0.502932	+	1.54786i	0.804220	+	0.594331i	$0.202583\pi$
$613$	7633.08	+	23492.2i	0.502932	+	1.54786i	−0.301289	+	0.953533i	$0.597417\pi$
$614$	−9127.97	+	28093.0i	−0.599959	+	1.84648i
$615$		0			0
$616$	−1078.85	−	3320.35i	−0.0705650	−	0.217177i
$617$	−4880.65	+	3546.00i	−0.318456	+	0.231372i	−0.735517	−	0.677507i	$-0.763060\pi$
$617$	−4880.65	+	3546.00i	−0.318456	+	0.231372i	0.417060	+	0.908879i	$0.363060\pi$
$618$		0			0
$619$	−20176.2	+	14658.9i	−1.31010	+	0.951842i	−0.310099	+	0.950704i	$0.600362\pi$
$619$	−20176.2	+	14658.9i	−1.31010	+	0.951842i	−0.999999	+	0.00113799i	$0.999638\pi$
$620$	−3322.42	−	31026.3i	−0.215212	−	2.00975i
$621$		0			0
$622$	−17807.6	−	12938.0i	−1.14794	−	0.834028i
$623$	−1190.40	+	3663.68i	−0.0765529	+	0.235606i
$624$		0			0
$625$	14223.9	−	6466.84i	0.910332	−	0.413878i
$626$	−1620.03			−0.103433
$627$		0			0
$628$	−20116.8	−	14615.7i	−1.27826	−	0.928709i
$629$	1615.94	+	1174.05i	0.102435	+	0.0744237i
$630$		0			0
$631$	−6256.11	+	4545.33i	−0.394694	+	0.286762i	−0.767376	−	0.641197i	$-0.778438\pi$
$631$	−6256.11	+	4545.33i	−0.394694	+	0.286762i	0.372682	+	0.927959i	$0.378438\pi$
$632$	28558.1			1.79744
$633$		0			0
$634$	−9605.39	−	29562.4i	−0.601702	−	1.85185i
$635$	10363.8	+	2181.69i	0.647675	+	0.136343i
$636$		0			0
$637$	873.214	+	2687.48i	0.0543140	+	0.167161i
$638$	−1497.83	−	4609.85i	−0.0929462	−	0.286059i
$639$		0			0
$640$	13287.3	−	23118.7i	0.820668	−	1.42789i
$641$	2359.86	+	7262.89i	0.145411	+	0.447530i	0.997064	−	0.0765769i	$-0.0243991\pi$
$641$	2359.86	+	7262.89i	0.145411	+	0.447530i	−0.851652	+	0.524107i	$0.824399\pi$
$642$		0			0
$643$	7388.44			0.453144			0.226572	−	0.973994i	$-0.427248\pi$
$643$	7388.44			0.453144			0.226572	+	0.973994i	$0.427248\pi$
$644$	11545.4	−	8388.19i	0.706445	−	0.513262i
$645$		0			0
$646$	−1260.35	−	915.696i	−0.0767612	−	0.0557702i
$647$	−7026.88	−	5105.32i	−0.426978	−	0.310218i	0.353461	−	0.935449i	$-0.385005\pi$
$647$	−7026.88	−	5105.32i	−0.426978	−	0.310218i	−0.780440	+	0.625231i	$0.785005\pi$
$648$		0			0
$649$	−4202.25			−0.254164
$650$	−16999.4	+	3682.95i	−1.02580	+	0.222242i
$651$		0			0
$652$	7293.95	−	22448.5i	0.438118	−	1.34839i
$653$	−1693.57	−	1230.45i	−0.101492	−	0.0737383i	0.535882	−	0.844293i	$-0.319979\pi$
$653$	−1693.57	−	1230.45i	−0.101492	−	0.0737383i	−0.637374	+	0.770555i	$0.719979\pi$
$654$		0			0
$655$	−9817.44	−	10860.5i	−0.585647	−	0.647872i
$656$	1057.15	−	768.064i	0.0629188	−	0.0457132i
$657$		0			0
$658$	17446.3	−	12675.5i	1.03363	−	0.750975i
$659$	−5205.85	−	16022.0i	−0.307726	−	0.947082i	−0.978646	−	0.205553i	$-0.934101\pi$
$659$	−5205.85	−	16022.0i	−0.307726	−	0.947082i	0.670921	−	0.741529i	$-0.265899\pi$
$660$		0			0
$661$	2694.78	−	8293.69i	0.158570	−	0.488029i	−0.839935	−	0.542687i	$-0.817407\pi$
$661$	2694.78	−	8293.69i	0.158570	−	0.488029i	0.998505	+	0.0546581i	$0.0174069\pi$
$662$	−12145.0	−	37378.4i	−0.713033	−	2.19449i
$663$		0			0
$664$	−1693.84	+	5213.09i	−0.0989964	+	0.304680i
$665$	−1894.79	−	2096.11i	−0.110491	−	0.122231i
$666$		0			0
$667$	6229.16	−	4525.75i	0.361610	−	0.262725i
$668$	−53352.0			−3.09019
$669$		0			0
$670$	−20121.5	+	9005.92i	−1.16024	+	0.519297i
$671$	−4585.21	−	3331.35i	−0.263801	−	0.191662i
$672$		0			0
$673$	−1291.14	+	3973.73i	−0.0739522	+	0.227602i	−0.981200	−	0.192996i	$-0.938180\pi$
$673$	−1291.14	+	3973.73i	−0.0739522	+	0.227602i	0.907247	+	0.420598i	$0.138180\pi$
$674$	−13959.0			−0.797743
$675$		0			0
$676$	−16731.7			−0.951962
$677$	3140.53	−	9665.55i	0.178287	−	0.548711i	−0.821481	−	0.570235i	$-0.806852\pi$
$677$	3140.53	−	9665.55i	0.178287	−	0.548711i	0.999768	+	0.0215246i	$0.00685203\pi$
$678$		0			0
$679$	1402.03	+	1018.63i	0.0792414	+	0.0575722i
$680$	−7162.79	−	1507.85i	−0.403942	−	0.0850343i
$681$		0			0
$682$	7011.16			0.393653
$683$	−21827.4	+	15858.5i	−1.22284	+	0.888447i	−0.996333	−	0.0855619i	$-0.972731\pi$
$683$	−21827.4	+	15858.5i	−1.22284	+	0.888447i	−0.226510	+	0.974009i	$0.572731\pi$
$684$		0			0
$685$	15490.1	−	6932.99i	0.864008	−	0.386710i
$686$	7401.92	−	22780.8i	0.411963	−	1.26789i
$687$		0			0
$688$	138.358	+	425.823i	0.00766695	+	0.0235964i
$689$	−3382.28	+	10409.6i	−0.187017	+	0.575579i
$690$		0			0
$691$	−7369.06	−	22679.6i	−0.405690	−	1.24859i	−0.920317	−	0.391173i	$-0.872070\pi$
$691$	−7369.06	−	22679.6i	−0.405690	−	1.24859i	0.514627	−	0.857414i	$-0.327930\pi$
$692$	−4040.09	+	2935.30i	−0.221938	+	0.161247i
$693$		0			0
$694$	16667.8	−	12109.9i	0.911674	−	0.662370i
$695$	315.844	+	66.4886i	0.0172383	+	0.00362886i
$696$		0			0
$697$	11677.8	+	8484.41i	0.634617	+	0.461076i
$698$	7973.17	−	24538.9i	0.432363	−	1.33068i
$699$		0			0
$700$	−31263.4	−	13772.9i	−1.68806	−	0.743668i
$701$	14171.1			0.763532			0.381766	−	0.924259i	$-0.375316\pi$
$701$	14171.1			0.763532			0.381766	+	0.924259i	$0.375316\pi$
$702$		0			0
$703$	697.351	+	506.655i	0.0374127	+	0.0271819i
$704$	4775.24	+	3469.42i	0.255644	+	0.185737i
$705$		0			0
$706$	−43843.0	+	31853.8i	−2.33719	+	1.69807i
$707$	2220.67			0.118129
$708$		0			0
$709$	518.246	+	1595.00i	0.0274516	+	0.0844872i	0.963844	−	0.266468i	$-0.0858568\pi$
$709$	518.246	+	1595.00i	0.0274516	+	0.0844872i	−0.936392	+	0.350956i	$0.885857\pi$
$710$	13682.6	+	15136.4i	0.723237	+	0.800081i
$711$		0			0
$712$	1330.79	+	4095.76i	0.0700471	+	0.215583i
$713$	3441.63	+	10592.2i	0.180771	+	0.556357i
$714$		0			0
$715$	−258.242	−	2411.59i	−0.0135073	−	0.126137i
$716$	−1916.52	−	5898.45i	−0.100033	−	0.307871i
$717$		0			0
$718$	−42152.3			−2.19096
$719$	−1265.43	+	919.390i	−0.0656365	+	0.0476877i	−0.620120	−	0.784507i	$-0.712916\pi$
$719$	−1265.43	+	919.390i	−0.0656365	+	0.0476877i	0.554483	+	0.832195i	$0.312916\pi$
$720$		0			0
$721$	18613.6	+	13523.6i	0.961454	+	0.698537i
$722$	24936.5	+	18117.4i	1.28537	+	0.933879i
$723$		0			0
$724$	−27425.5			−1.40782
$725$	−16867.8	−	7431.02i	−0.864075	−	0.380664i
$726$		0			0
$727$	−8380.64	+	25793.0i	−0.427539	+	1.31583i	0.473003	+	0.881061i	$0.343170\pi$
$727$	−8380.64	+	25793.0i	−0.427539	+	1.31583i	−0.900542	+	0.434769i	$0.856830\pi$
$728$	11956.5	+	8686.90i	0.608704	+	0.442250i
$729$		0			0
$730$	26588.5	−	46261.6i	1.34806	−	2.34551i
$731$	−4001.33	+	2907.14i	−0.202455	+	0.147092i
$732$		0			0
$733$	−16839.9	+	12234.9i	−0.848564	+	0.616518i	−0.924750	−	0.380576i	$-0.875726\pi$
$733$	−16839.9	+	12234.9i	−0.848564	+	0.616518i	0.0761856	+	0.997094i	$0.475726\pi$
$734$	−1338.26	−	4118.73i	−0.0672969	−	0.207119i
$735$		0			0
$736$	−2826.07	+	8697.74i	−0.141536	+	0.435602i
$737$	−949.900	−	2923.49i	−0.0474763	−	0.146117i
$738$		0			0
$739$	825.951	−	2542.01i	0.0411138	−	0.126535i	−0.928393	−	0.371600i	$-0.878809\pi$
$739$	825.951	−	2542.01i	0.0411138	−	0.126535i	0.969507	+	0.245065i	$0.0788093\pi$
$740$	10198.2	+	2146.84i	0.506612	+	0.106648i
$741$		0			0
$742$	−28024.9	+	20361.3i	−1.38656	+	1.00739i
$743$	2816.14			0.139050			0.0695250	−	0.997580i	$-0.477852\pi$
$743$	2816.14			0.139050			0.0695250	+	0.997580i	$0.477852\pi$
$744$		0			0
$745$	−730.186	−	6818.82i	−0.0359087	−	0.335332i
$746$	−5318.68	−	3864.25i	−0.261033	−	0.189652i
$747$		0			0
$748$	811.607	−	2497.87i	0.0396728	−	0.122100i
$749$	19671.2			0.959642
$750$		0			0
$751$	23808.4			1.15683			0.578416	−	0.815742i	$-0.303671\pi$
$751$	23808.4			1.15683			0.578416	+	0.815742i	$0.303671\pi$
$752$	176.364	−	542.792i	0.00855229	−	0.0263212i
$753$		0			0
$754$	16599.9	+	12060.5i	0.801768	+	0.582518i
$755$	−655.995	−	6125.98i	−0.0316213	−	0.295295i
$756$		0			0
$757$	12391.0			0.594923			0.297462	−	0.954734i	$-0.403860\pi$
$757$	12391.0			0.594923			0.297462	+	0.954734i	$0.403860\pi$
$758$	−33841.6	+	24587.4i	−1.62161	+	1.17817i
$759$		0			0
$760$	−3091.06	−	650.703i	−0.147532	−	0.0310572i
$761$	−4229.13	+	13015.9i	−0.201453	+	0.620009i	0.798387	+	0.602144i	$0.205687\pi$
$761$	−4229.13	+	13015.9i	−0.201453	+	0.620009i	−0.999840	+	0.0178645i	$0.994313\pi$
$762$		0			0
$763$	3918.41	+	12059.6i	0.185919	+	0.572198i
$764$	−13485.5	+	41504.0i	−0.638596	+	1.96540i
$765$		0			0
$766$	15488.5	+	47668.6i	0.730576	+	2.24848i
$767$	14391.5	−	10456.1i	0.677507	−	0.492238i
$768$		0			0
$769$	−8825.89	+	6412.38i	−0.413875	+	0.300698i	−0.775169	−	0.631754i	$-0.782335\pi$
$769$	−8825.89	+	6412.38i	−0.413875	+	0.300698i	0.361294	+	0.932452i	$0.382335\pi$
$770$	3825.00	−	6655.15i	0.179017	−	0.311474i
$771$		0			0
$772$	11115.6	+	8075.98i	0.518213	+	0.376504i
$773$	6054.07	−	18632.5i	0.281694	−	0.866966i	−0.705676	−	0.708535i	$-0.749356\pi$
$773$	6054.07	−	18632.5i	0.281694	−	0.866966i	0.987370	−	0.158431i	$-0.0506436\pi$
$774$		0			0
$775$	17762.3	−	19883.1i	0.823279	−	0.921575i
$776$	1937.38			0.0896236
$777$		0			0
$778$	4528.18	+	3289.91i	0.208667	+	0.151606i
$779$	5039.49	+	3661.40i	0.231782	+	0.168400i
$780$		0			0
$781$	−2301.75	+	1672.32i	−0.105458	+	0.0766200i
$782$	6722.86			0.307428
$783$		0			0
$784$	73.1410	+	225.105i	0.00333186	+	0.0102544i
$785$	−2262.19	−	21125.4i	−0.102855	−	0.960505i
$786$		0			0
$787$	−68.2587	−	210.079i	−0.00309169	−	0.00951524i	0.949499	−	0.313771i	$-0.101592\pi$
$787$	−68.2587	−	210.079i	−0.00309169	−	0.00951524i	−0.952590	+	0.304256i	$0.901592\pi$
$788$	−15258.1	−	46959.5i	−0.689780	−	2.12292i
$789$		0			0
$790$	42105.8	+	46579.6i	1.89628	+	2.09776i
$791$	9700.44	+	29854.9i	0.436040	+	1.34199i
$792$		0			0
$793$	23992.2			1.07439
$794$	39155.6	−	28448.2i	1.75010	−	1.27152i
$795$		0			0
$796$	−19166.8	−	13925.5i	−0.853453	−	0.620070i
$797$	−4303.89	−	3126.96i	−0.191282	−	0.138974i	0.488023	−	0.872831i	$-0.337718\pi$
$797$	−4303.89	−	3126.96i	−0.191282	−	0.138974i	−0.679304	+	0.733857i	$0.737718\pi$
$798$		0			0
$799$	6304.51			0.279146
$800$	21396.5	−	4635.60i	0.945600	−	0.204867i
$801$		0			0
$802$	10489.6	−	32283.6i	0.461845	−	1.42141i
$803$	6019.27	+	4373.25i	0.264527	+	0.192190i
$804$		0			0
$805$	11932.0	+	2511.82i	0.522419	+	0.109975i
$806$	−24011.3	+	17445.2i	−1.04933	+	0.762384i
$807$		0			0
$808$	2008.44	−	1459.21i	0.0874462	−	0.0635334i
$809$	4360.64	+	13420.7i	0.189508	+	0.583246i	0.999997	−	0.00250814i	$-0.000798367\pi$
$809$	4360.64	+	13420.7i	0.189508	+	0.583246i	−0.810489	+	0.585754i	$0.800798\pi$
$810$		0			0
$811$	3644.37	−	11216.2i	0.157794	−	0.485641i	−0.840639	−	0.541596i	$-0.817820\pi$
$811$	3644.37	−	11216.2i	0.157794	−	0.485641i	0.998433	+	0.0559550i	$0.0178203\pi$
$812$	12453.5	+	38327.8i	0.538215	+	1.65646i
$813$		0			0
$814$	−723.613	+	2227.05i	−0.0311580	+	0.0958945i
$815$	18408.2	−	8239.06i	0.791178	−	0.354113i
$816$		0			0
$817$	−1726.75	+	1254.56i	−0.0739430	+	0.0537227i
$818$	−74245.0			−3.17349
$819$		0			0
$820$	73698.4	+	15514.3i	3.13861	+	0.660712i
$821$	10290.4	+	7476.40i	0.437438	+	0.317817i	0.784616	−	0.619982i	$-0.212860\pi$
$821$	10290.4	+	7476.40i	0.437438	+	0.317817i	−0.347178	+	0.937799i	$0.612860\pi$
$822$		0			0
$823$	8227.97	−	25323.1i	0.348492	−	1.07255i	−0.611196	−	0.791480i	$-0.709311\pi$
$823$	8227.97	−	25323.1i	0.348492	−	1.07255i	0.959688	−	0.281069i	$-0.0906888\pi$
$824$	25721.1			1.08742
$825$		0			0
$826$	56300.0			2.37158
$827$	10181.1	−	31334.1i	0.428090	−	1.31752i	−0.471915	−	0.881644i	$-0.656437\pi$
$827$	10181.1	−	31334.1i	0.428090	−	1.31752i	0.900005	−	0.435880i	$-0.143563\pi$
$828$		0			0
$829$	−21383.8	−	15536.2i	−0.895886	−	0.650899i	0.0415198	−	0.999138i	$-0.486780\pi$
$829$	−21383.8	−	15536.2i	−0.895886	−	0.650899i	−0.937406	+	0.348238i	$0.886780\pi$
$830$	−11000.2	+	4923.41i	−0.460025	+	0.205897i
$831$		0			0
$832$	−24986.5			−1.04117
$833$	−2115.24	+	1536.81i	−0.0879818	+	0.0639225i
$834$		0			0
$835$	−30569.1	−	33817.1i	−1.26693	−	1.40154i
$836$	350.244	−	1077.94i	0.0144898	−	0.0445950i
$837$		0			0
$838$	16862.9	+	51898.5i	0.695129	+	2.13939i
$839$	−11883.3	+	36573.2i	−0.488985	+	1.50494i	0.337140	+	0.941455i	$0.390541\pi$
$839$	−11883.3	+	36573.2i	−0.488985	+	1.50494i	−0.826125	+	0.563487i	$0.809459\pi$
$840$		0			0
$841$	−817.499	−	2516.00i	−0.0335192	−	0.103161i
$842$	−19115.6	+	13888.3i	−0.782385	+	0.568436i
$843$		0			0
$844$	6469.99	−	4700.72i	0.263870	−	0.191713i
$845$	−9586.77	−	10605.4i	−0.390290	−	0.431758i
$846$		0			0
$847$	−21624.8	−	15711.3i	−0.877256	−	0.637364i
$848$	−283.302	+	871.914i	−0.0114724	+	0.0353086i
$849$		0			0
$850$	−8101.39	−	13906.0i	−0.326912	−	0.561143i
$851$	−3719.76			−0.149838
$852$		0			0
$853$	−35536.3	−	25818.7i	−1.42643	−	1.03636i	−0.990668	−	0.136295i	$-0.956481\pi$
$853$	−35536.3	−	25818.7i	−1.42643	−	1.03636i	−0.435757	−	0.900064i	$-0.643519\pi$
$854$	61430.8	+	44632.1i	2.46150	+	1.78838i
$855$		0			0
$856$	17791.2	−	12926.1i	0.710387	−	0.516126i
$857$	−15225.8			−0.606889			−0.303445	−	0.952849i	$-0.598137\pi$
$857$	−15225.8			−0.606889			−0.303445	+	0.952849i	$0.598137\pi$
$858$		0			0
$859$	10212.5	+	31430.8i	0.405641	+	1.24844i	0.920359	+	0.391076i	$0.127897\pi$
$859$	10212.5	+	31430.8i	0.405641	+	1.24844i	−0.514717	+	0.857360i	$0.672103\pi$
$860$	−12859.1	+	22373.7i	−0.509876	+	0.887137i
$861$		0			0
$862$	5573.11	+	17152.3i	0.220210	+	0.677736i
$863$	−3459.32	−	10646.7i	−0.136450	−	0.419950i	0.859363	−	0.511367i	$-0.170861\pi$
$863$	−3459.32	−	10646.7i	−0.136450	−	0.419950i	−0.995813	+	0.0914163i	$0.970861\pi$
$864$		0			0
$865$	−4175.39	−	878.966i	−0.164124	−	0.0345500i
$866$	15619.2	+	48071.1i	0.612891	+	1.88628i
$867$		0			0
$868$	−58293.1			−2.27949
$869$	−7083.24	+	5146.28i	−0.276505	+	0.200892i
$870$		0			0
$871$	10527.4	+	7648.60i	0.409537	+	0.297546i
$872$	11468.3	+	8332.24i	0.445375	+	0.323584i
$873$		0			0
$874$	2901.21			0.112283
$875$	−9183.06	−	27707.8i	−0.354793	−	1.07051i
$876$		0			0
$877$	1253.38	−	3857.51i	0.0482596	−	0.148528i	−0.924023	−	0.382337i	$-0.875119\pi$
$877$	1253.38	−	3857.51i	0.0482596	−	0.148528i	0.972282	+	0.233810i	$0.0751193\pi$
$878$	14820.4	+	10767.7i	0.569664	+	0.413885i
$879$		0			0
$880$	−21.6305	−	201.996i	−0.000828597	−	0.00773782i
$881$	27685.0	−	20114.4i	1.05872	−	0.769205i	0.0848689	−	0.996392i	$-0.472953\pi$
$881$	27685.0	−	20114.4i	1.05872	−	0.769205i	0.973851	+	0.227187i	$0.0729529\pi$
$882$		0			0
$883$	−3696.79	+	2685.88i	−0.140891	+	0.102363i	−0.655998	−	0.754762i	$-0.727752\pi$
$883$	−3696.79	+	2685.88i	−0.140891	+	0.102363i	0.515107	+	0.857126i	$0.327752\pi$
$884$	3435.69	+	10574.0i	0.130718	+	0.402308i
$885$		0			0
$886$	−11767.2	+	36215.7i	−0.446192	+	1.37324i
$887$	3406.01	+	10482.6i	0.128932	+	0.396812i	0.994597	−	0.103812i	$-0.0331040\pi$
$887$	3406.01	+	10482.6i	0.128932	+	0.396812i	−0.865665	+	0.500624i	$0.833104\pi$
$888$		0			0
$889$	6114.03	−	18817.1i	0.230662	−	0.709903i
$890$	−4718.25	+	8209.32i	−0.177703	+	0.309188i
$891$		0			0
$892$	29000.9	−	21070.4i	1.08859	−	0.790908i
$893$	2720.68			0.101953
$894$		0			0
$895$	2640.62	−	4594.43i	0.0986213	−	0.171592i
$896$	−40300.7	−	29280.2i	−1.50263	−	1.09172i
$897$		0			0
$898$	−3448.85	+	10614.5i	−0.128162	+	0.394442i
$899$	−31451.4			−1.16681
$900$		0			0
$901$	−10127.3			−0.374459
$902$	−5229.27	+	16094.0i	−0.193033	+	0.594094i
$903$		0			0
$904$	28391.1	+	20627.4i	1.04455	+	0.758912i
$905$	−15714.0	−	17383.6i	−0.577184	−	0.638510i
$906$		0			0
$907$	−16496.6			−0.603926			−0.301963	−	0.953320i	$-0.597642\pi$
$907$	−16496.6			−0.603926			−0.301963	+	0.953320i	$0.597642\pi$
$908$	−12032.7	+	8742.24i	−0.439777	+	0.319517i
$909$		0			0
$910$	3459.82	+	32309.4i	0.126035	+	1.17697i
$911$	290.870	−	895.206i	0.0105784	−	0.0325571i	−0.945628	−	0.325250i	$-0.894551\pi$
$911$	290.870	−	895.206i	0.0105784	−	0.0325571i	0.956206	+	0.292693i	$0.0945515\pi$
$912$		0			0
$913$	−519.297	−	1598.23i	−0.0188239	−	0.0579340i
$914$	19466.5	−	59911.7i	0.704480	−	2.16817i
$915$		0			0
$916$	−22229.5	−	68415.5i	−0.801839	−	2.46781i
$917$	−22126.6	+	16075.9i	−0.796821	+	0.578924i
$918$		0			0
$919$	−15461.3	+	11233.3i	−0.554975	+	0.403213i	−0.829616	−	0.558334i	$-0.811441\pi$
$919$	−15461.3	+	11233.3i	−0.554975	+	0.403213i	0.274642	+	0.961547i	$0.411441\pi$
$920$	12442.2	−	5568.82i	0.445876	−	0.199564i
$921$		0			0
$922$	−48525.5	−	35255.9i	−1.73330	−	1.25932i
$923$	3721.78	−	11454.5i	0.132724	−	0.408481i
$924$		0			0
$925$	4482.50	+	7694.19i	0.159334	+	0.273496i
$926$	−20013.1			−0.710228
$927$		0			0
$928$	−20893.7	−	15180.2i	−0.739084	−	0.536976i
$929$	−12394.5	−	9005.17i	−0.437731	−	0.318030i	0.347002	−	0.937864i	$-0.387200\pi$
$929$	−12394.5	−	9005.17i	−0.437731	−	0.318030i	−0.784733	+	0.619834i	$0.787200\pi$
$930$		0			0
$931$	−912.821	+	663.203i	−0.0321337	+	0.0233465i
$932$	9113.54			0.320305
$933$		0			0
$934$	18656.1	+	57417.7i	0.653584	+	2.01152i
$935$	2048.30	−	916.771i	0.0716434	−	0.0320659i
$936$		0			0
$937$	−4579.47	−	14094.1i	−0.159663	−	0.491393i	0.838940	−	0.544224i	$-0.183176\pi$
$937$	−4579.47	−	14094.1i	−0.159663	−	0.491393i	−0.998604	+	0.0528303i	$0.983176\pi$
$938$	12726.4	+	39167.7i	0.442996	+	1.36340i
$939$		0			0
$940$	30024.3	−	13438.2i	1.04179	−	0.466281i
$941$	2858.33	+	8797.04i	0.0990212	+	0.304756i	0.988281	−	0.152647i	$-0.0487797\pi$
$941$	2858.33	+	8797.04i	0.0990212	+	0.304756i	−0.889260	+	0.457403i	$0.848780\pi$
$942$		0			0
$943$	−26881.3			−0.928287
$944$	1205.44	−	875.806i	0.0415613	−	0.0301960i
$945$		0			0
$946$	−4690.94	−	3408.17i	−0.161222	−	0.117134i
$947$	20053.3	+	14569.6i	0.688114	+	0.499944i	0.876040	−	0.482239i	$-0.160176\pi$
$947$	20053.3	+	14569.6i	0.688114	+	0.499944i	−0.187925	+	0.982183i	$0.560176\pi$
$948$		0			0
$949$	−31495.9			−1.07734
$950$	−3496.11	−	6001.05i	−0.119399	−	0.204947i
$951$		0			0
$952$	−4225.64	+	13005.2i	−0.143859	+	0.442753i
$953$	31314.9	+	22751.6i	1.06442	+	0.773343i	0.974900	−	0.222642i	$-0.0714682\pi$
$953$	31314.9	+	22751.6i	1.06442	+	0.773343i	0.0895152	+	0.995985i	$0.471468\pi$
$954$		0			0
$955$	−34034.1	+	15232.8i	−1.15321	+	0.516150i
$956$	40462.1	−	29397.5i	1.36887	−	0.994542i
$957$		0			0
$958$	−61559.2	+	44725.3i	−2.07608	+	1.50836i
$959$	−9797.09	−	30152.4i	−0.329890	−	1.01530i
$960$		0			0
$961$	4852.33	−	14933.9i	0.162879	−	0.501290i
$962$	−3063.19	−	9427.53i	−0.102662	−	0.315962i
$963$		0			0
$964$	−9358.14	+	28801.4i	−0.312661	+	0.962272i
$965$	1249.98	+	11672.9i	0.0416978	+	0.389394i
$966$		0			0
$967$	19661.0	−	14284.6i	0.653832	−	0.475036i	−0.210743	−	0.977542i	$-0.567588\pi$
$967$	19661.0	−	14284.6i	0.653832	−	0.475036i	0.864574	+	0.502505i	$0.167588\pi$
$968$	−29882.0			−0.992195
$969$		0			0
$970$	2856.46	+	3159.95i	0.0945519	+	0.104598i
$971$	23936.0	+	17390.5i	0.791084	+	0.574757i	0.908285	−	0.418352i	$-0.137392\pi$
$971$	23936.0	+	17390.5i	0.791084	+	0.574757i	−0.117201	+	0.993108i	$0.537392\pi$
$972$		0			0
$973$	186.330	−	573.464i	0.00613922	−	0.0188946i
$974$	−82843.3			−2.72533
$975$		0			0
$976$	2009.60			0.0659075
$977$	7047.69	−	21690.6i	0.230784	−	0.710279i	−0.766869	−	0.641803i	$-0.778186\pi$
$977$	7047.69	−	21690.6i	0.230784	−	0.710279i	0.997653	−	0.0684755i	$-0.0218135\pi$
$978$		0			0
$979$	−1068.14	−	776.052i	−0.0348703	−	0.0253348i
$980$	−6797.78	+	11827.5i	−0.221579	+	0.385527i
$981$		0			0
$982$	1086.89			0.0353200
$983$	3741.86	−	2718.62i	0.121411	−	0.0882101i	−0.525423	−	0.850841i	$-0.676093\pi$
$983$	3741.86	−	2718.62i	0.121411	−	0.0882101i	0.646834	+	0.762631i	$0.276093\pi$
$984$		0			0
$985$	21022.8	−	36577.8i	0.680043	−	1.18321i
$986$	−5866.71	+	18055.9i	−0.189487	+	0.583181i
$987$		0			0
$988$	1482.65	+	4563.13i	0.0477423	+	0.146936i
$989$	2846.27	−	8759.93i	0.0915128	−	0.281648i
$990$		0			0
$991$	14828.1	+	45636.3i	0.475309	+	1.46285i	0.845541	+	0.533910i	$0.179278\pi$
$991$	14828.1	+	45636.3i	0.475309	+	1.46285i	−0.370233	+	0.928939i	$0.620722\pi$
$992$	30222.1	−	21957.7i	0.967292	−	0.702779i
$993$		0			0
$994$	30837.9	−	22405.0i	0.984022	−	0.714934i
$995$	−2155.36	−	20127.8i	−0.0686729	−	0.641299i
$996$		0			0
$997$	−5387.06	−	3913.93i	−0.171123	−	0.124328i	0.498927	−	0.866644i	$-0.333728\pi$
$997$	−5387.06	−	3913.93i	−0.171123	−	0.124328i	−0.670050	+	0.742316i	$0.733728\pi$
$998$	−11683.8	+	35959.0i	−0.370585	+	1.14054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.b.46.6		28
3.2	odd	2		25.4.d.a.21.2	yes	28
15.2	even	4		125.4.e.b.24.3		56
15.8	even	4		125.4.e.b.24.12		56
15.14	odd	2		125.4.d.a.101.6		28
25.6	even	5	inner	225.4.h.b.181.6		28
75.8	even	20		125.4.e.b.99.3		56
75.17	even	20		125.4.e.b.99.12		56
75.41	odd	10		625.4.a.c.1.3		14
75.44	odd	10		125.4.d.a.26.6		28
75.56	odd	10		25.4.d.a.6.2	✓	28
75.59	odd	10		625.4.a.d.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.6.2	✓	28	75.56	odd	10
25.4.d.a.21.2	yes	28	3.2	odd	2
125.4.d.a.26.6		28	75.44	odd	10
125.4.d.a.101.6		28	15.14	odd	2
125.4.e.b.24.3		56	15.2	even	4
125.4.e.b.24.12		56	15.8	even	4
125.4.e.b.99.3		56	75.8	even	20
125.4.e.b.99.12		56	75.17	even	20
225.4.h.b.46.6		28	1.1	even	1	trivial
225.4.h.b.181.6		28	25.6	even	5	inner
625.4.a.c.1.3		14	75.41	odd	10
625.4.a.d.1.12		14	75.59	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41896 - 4.36711i) q^{2} +(-10.5860 - 7.69120i) q^{4} +(-1.19043 - 11.1168i) q^{5} -20.8866 q^{7} +(-18.8904 + 13.7247i) q^{8} +O(q^{10})\)	\(q+(1.41896 - 4.36711i) q^{2} +(-10.5860 - 7.69120i) q^{4} +(-1.19043 - 11.1168i) q^{5} -20.8866 q^{7} +(-18.8904 + 13.7247i) q^{8} +(-50.2373 - 10.5755i) q^{10} +(2.21213 - 6.80823i) q^{11} +(9.36436 + 28.8205i) q^{13} +(-29.6372 + 91.2138i) q^{14} +(0.784365 + 2.41403i) q^{16} +(-22.6839 + 16.4808i) q^{17} +(-9.78911 + 7.11220i) q^{19} +(-72.8995 + 126.838i) q^{20} +(-26.5933 - 19.3212i) q^{22} +(16.1358 - 49.6607i) q^{23} +(-122.166 + 26.4675i) q^{25} +139.150 q^{26} +(221.106 + 160.643i) q^{28} +(119.295 + 86.6730i) q^{29} +(-172.557 + 125.370i) q^{31} -175.143 q^{32} +(39.7859 + 122.449i) q^{34} +(24.8640 + 232.191i) q^{35} +(-22.0136 - 67.7509i) q^{37} +(17.1694 + 52.8420i) q^{38} +(175.062 + 193.662i) q^{40} +(-159.084 - 489.609i) q^{41} +176.395 q^{43} +(-75.7811 + 55.0582i) q^{44} +(-193.978 - 140.933i) q^{46} +(-181.907 - 132.163i) q^{47} +93.2487 q^{49} +(-57.7618 + 571.067i) q^{50} +(122.533 - 377.118i) q^{52} +(292.206 + 212.300i) q^{53} +(-78.3190 - 16.4870i) q^{55} +(394.555 - 286.661i) q^{56} +(547.785 - 397.989i) q^{58} +(-181.399 - 558.290i) q^{59} +(244.656 - 752.975i) q^{61} +(302.653 + 931.469i) q^{62} +(-254.796 + 784.181i) q^{64} +(309.244 - 138.410i) q^{65} +(347.396 - 252.398i) q^{67} +366.890 q^{68} +(1049.29 + 220.886i) q^{70} +(-321.536 - 233.610i) q^{71} +(-321.174 + 988.472i) q^{73} -327.112 q^{74} +158.329 q^{76} +(-46.2038 + 142.201i) q^{77} +(-989.474 - 718.895i) q^{79} +(25.9025 - 11.5933i) q^{80} -2363.91 q^{82} +(189.917 - 137.983i) q^{83} +(210.217 + 232.553i) q^{85} +(250.298 - 770.337i) q^{86} +(51.6527 + 158.971i) q^{88} +(56.9937 - 175.409i) q^{89} +(-195.589 - 601.962i) q^{91} +(-552.764 + 401.607i) q^{92} +(-835.288 + 606.872i) q^{94} +(90.7180 + 100.357i) q^{95} +(-67.1258 - 48.7698i) q^{97} +(132.316 - 407.227i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8}+O(q^{10}) \) 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8	\( 28 q + q^{2} - 31 q^{4} + 20 q^{5} - 16 q^{7} - 100 q^{8} - 25 q^{10} + 89 q^{11} + 33 q^{13} + 17 q^{14} - 207 q^{16} + 191 q^{17} - 115 q^{19} + 225 q^{20} + 808 q^{22} - 433 q^{23} + 90 q^{25} - 586 q^{26} - 13 q^{28} + 5 q^{29} - 639 q^{31} + 1386 q^{32} - 777 q^{34} + 1030 q^{35} + 699 q^{37} + 2355 q^{38} + 410 q^{40} - 341 q^{41} - 172 q^{43} - 548 q^{44} - 1239 q^{46} - 2319 q^{47} + 1344 q^{49} - 2335 q^{50} + 2344 q^{52} + 927 q^{53} + 1225 q^{55} + 2910 q^{56} + 2410 q^{58} + 1905 q^{59} + 1391 q^{61} + 3832 q^{62} - 3596 q^{64} - 1215 q^{65} - 3611 q^{67} - 3622 q^{68} + 560 q^{70} + 3719 q^{71} + 4593 q^{73} - 4848 q^{74} + 3520 q^{76} - 1368 q^{77} + 775 q^{79} - 9500 q^{80} - 6762 q^{82} + 2447 q^{83} - 8185 q^{85} - 3891 q^{86} - 10960 q^{88} + 5075 q^{89} + 376 q^{91} + 8456 q^{92} + 3573 q^{94} - 3265 q^{95} + 7439 q^{97} - 7082 q^{98}+O(q^{100}) \) 28 * q + q^2 - 31 * q^4 + 20 * q^5 - 16 * q^7 - 100 * q^8 - 25 * q^10 + 89 * q^11 + 33 * q^13 + 17 * q^14 - 207 * q^16 + 191 * q^17 - 115 * q^19 + 225 * q^20 + 808 * q^22 - 433 * q^23 + 90 * q^25 - 586 * q^26 - 13 * q^28 + 5 * q^29 - 639 * q^31 + 1386 * q^32 - 777 * q^34 + 1030 * q^35 + 699 * q^37 + 2355 * q^38 + 410 * q^40 - 341 * q^41 - 172 * q^43 - 548 * q^44 - 1239 * q^46 - 2319 * q^47 + 1344 * q^49 - 2335 * q^50 + 2344 * q^52 + 927 * q^53 + 1225 * q^55 + 2910 * q^56 + 2410 * q^58 + 1905 * q^59 + 1391 * q^61 + 3832 * q^62 - 3596 * q^64 - 1215 * q^65 - 3611 * q^67 - 3622 * q^68 + 560 * q^70 + 3719 * q^71 + 4593 * q^73 - 4848 * q^74 + 3520 * q^76 - 1368 * q^77 + 775 * q^79 - 9500 * q^80 - 6762 * q^82 + 2447 * q^83 - 8185 * q^85 - 3891 * q^86 - 10960 * q^88 + 5075 * q^89 + 376 * q^91 + 8456 * q^92 + 3573 * q^94 - 3265 * q^95 + 7439 * q^97 - 7082 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more