LMFDB - Embedded newform 272.4.o.f.81.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,4,Mod(81,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.81"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	272.o (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0485195216$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
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} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 $ x^14 + 119x^12 + 5319x^10 + 112122x^8 + 1120191x^6 + 4382607x^4 + 1699337x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.7
Root			$-5.11455i$ of defining polynomial
Character	$\chi$	$=$	272.81
Dual form			272.4.o.f.225.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.11455 + 5.11455i) q^{3} +(7.20340 + 7.20340i) q^{5} +(-19.2581 + 19.2581i) q^{7} +25.3172i q^{9} +(-5.30564 + 5.30564i) q^{11} -59.4853 q^{13} +73.6843i q^{15} +(-7.18671 - 69.7234i) q^{17} +114.346i q^{19} -196.993 q^{21} +(63.2207 - 63.2207i) q^{23} -21.2220i q^{25} +(8.60667 - 8.60667i) q^{27} +(-10.6982 - 10.6982i) q^{29} +(143.404 + 143.404i) q^{31} -54.2720 q^{33} -277.448 q^{35} +(170.788 + 170.788i) q^{37} +(-304.240 - 304.240i) q^{39} +(243.688 - 243.688i) q^{41} +201.773i q^{43} +(-182.370 + 182.370i) q^{45} -422.485 q^{47} -398.750i q^{49} +(319.847 - 393.360i) q^{51} +538.359i q^{53} -76.4374 q^{55} +(-584.826 + 584.826i) q^{57} +330.559i q^{59} +(-404.260 + 404.260i) q^{61} +(-487.562 - 487.562i) q^{63} +(-428.496 - 428.496i) q^{65} -40.2994 q^{67} +646.691 q^{69} +(694.644 + 694.644i) q^{71} +(541.386 + 541.386i) q^{73} +(108.541 - 108.541i) q^{75} -204.353i q^{77} +(-585.853 + 585.853i) q^{79} +771.603 q^{81} -670.929i q^{83} +(450.477 - 554.014i) q^{85} -109.433i q^{87} -130.858 q^{89} +(1145.57 - 1145.57i) q^{91} +1466.89i q^{93} +(-823.677 + 823.677i) q^{95} +(-262.597 - 262.597i) q^{97} +(-134.324 - 134.324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 6 q^{3} + 6 q^{5} - 10 q^{7} + 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} + 162 q^{23} + 204 q^{27} + 158 q^{29} + 350 q^{31} + 116 q^{33} - 236 q^{35} + 582 q^{37} + 320 q^{39} + 878 q^{41}+ \cdots - 3870 q^{99}+O(q^{100}) $ 14 * q - 6 * q^3 + 6 * q^5 - 10 * q^7 + 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 + 162 * q^23 + 204 * q^27 + 158 * q^29 + 350 * q^31 + 116 * q^33 - 236 * q^35 + 582 * q^37 + 320 * q^39 + 878 * q^41 - 26 * q^45 + 448 * q^47 + 590 * q^51 - 1460 * q^55 + 292 * q^57 - 1130 * q^61 - 114 * q^63 + 20 * q^65 + 64 * q^67 + 2076 * q^69 + 3274 * q^71 - 1426 * q^73 - 946 * q^75 - 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 - 2128 * q^91 + 2444 * q^95 + 1926 * q^97 - 3870 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	5.11455	+	5.11455i	0.984295	+	0.984295i	0.999879	−	0.0155832i	$-0.00496049\pi$
$3$	5.11455	+	5.11455i	0.984295	+	0.984295i	−0.0155832	+	0.999879i	$0.504960\pi$
$4$		0			0
$5$	7.20340	+	7.20340i	0.644292	+	0.644292i	0.951608	−	0.307316i	$-0.0994308\pi$
$5$	7.20340	+	7.20340i	0.644292	+	0.644292i	−0.307316	+	0.951608i	$0.599431\pi$
$6$		0			0
$7$	−19.2581	+	19.2581i	−1.03984	+	1.03984i	−0.0406680	+	0.999173i	$0.512949\pi$
$7$	−19.2581	+	19.2581i	−1.03984	+	1.03984i	−0.999173	+	0.0406680i	$0.987051\pi$
$8$		0			0
$9$			25.3172i			0.937675i
$10$		0			0
$11$	−5.30564	+	5.30564i	−0.145428	+	0.145428i	−0.776072	−	0.630644i	$-0.782791\pi$
$11$	−5.30564	+	5.30564i	−0.145428	+	0.145428i	0.630644	+	0.776072i	$0.282791\pi$
$12$		0			0
$13$	−59.4853			−1.26910			−0.634548	−	0.772883i	$-0.718814\pi$
$13$	−59.4853			−1.26910			−0.634548	+	0.772883i	$0.718814\pi$
$14$		0			0
$15$			73.6843i			1.26835i
$16$		0			0
$17$	−7.18671	−	69.7234i	−0.102531	−	0.994730i
$17$	−7.18671	−	69.7234i	−0.102531	−	0.994730i
$18$		0			0
$19$			114.346i			1.38067i	0.723492	+	0.690333i	$0.242536\pi$
$19$			114.346i			1.38067i	−0.723492	+	0.690333i	$0.757464\pi$
$20$		0			0
$21$	−196.993			−2.04702
$22$		0			0
$23$	63.2207	−	63.2207i	0.573149	−	0.573149i	−0.359858	−	0.933007i	$-0.617175\pi$
$23$	63.2207	−	63.2207i	0.573149	−	0.573149i	0.933007	+	0.359858i	$0.117175\pi$
$24$		0			0
$25$		−	21.2220i		−	0.169776i
$26$		0			0
$27$	8.60667	−	8.60667i	0.0613464	−	0.0613464i
$28$		0			0
$29$	−10.6982	−	10.6982i	−0.0685039	−	0.0685039i	0.672025	−	0.740529i	$-0.265425\pi$
$29$	−10.6982	−	10.6982i	−0.0685039	−	0.0685039i	−0.740529	+	0.672025i	$0.765425\pi$
$30$		0			0
$31$	143.404	+	143.404i	0.830841	+	0.830841i	0.987632	−	0.156791i	$-0.0501149\pi$
$31$	143.404	+	143.404i	0.830841	+	0.830841i	−0.156791	+	0.987632i	$0.550115\pi$
$32$		0			0
$33$	−54.2720			−0.286289
$34$		0			0
$35$	−277.448			−1.33992
$36$		0			0
$37$	170.788	+	170.788i	0.758849	+	0.758849i	0.976113	−	0.217264i	$-0.0697132\pi$
$37$	170.788	+	170.788i	0.758849	+	0.758849i	−0.217264	+	0.976113i	$0.569713\pi$
$38$		0			0
$39$	−304.240	−	304.240i	−1.24917	−	1.24917i
$40$		0			0
$41$	243.688	−	243.688i	0.928236	−	0.928236i	−0.0693559	−	0.997592i	$-0.522094\pi$
$41$	243.688	−	243.688i	0.928236	−	0.928236i	0.997592	+	0.0693559i	$0.0220944\pi$
$42$		0			0
$43$			201.773i			0.715583i	0.933802	+	0.357791i	$0.116470\pi$
$43$			201.773i			0.715583i	−0.933802	+	0.357791i	$0.883530\pi$
$44$		0			0
$45$	−182.370	+	182.370i	−0.604136	+	0.604136i
$46$		0			0
$47$	−422.485			−1.31119			−0.655594	−	0.755114i	$-0.727582\pi$
$47$	−422.485			−1.31119			−0.655594	+	0.755114i	$0.727582\pi$
$48$		0			0
$49$		−	398.750i		−	1.16254i
$50$		0			0
$51$	319.847	−	393.360i	0.878187	−	1.08003i
$52$		0			0
$53$			538.359i			1.39527i	0.716453	+	0.697635i	$0.245764\pi$
$53$			538.359i			1.39527i	−0.716453	+	0.697635i	$0.754236\pi$
$54$		0			0
$55$	−76.4374			−0.187397
$56$		0			0
$57$	−584.826	+	584.826i	−1.35898	+	1.35898i
$58$		0			0
$59$			330.559i			0.729409i	0.931123	+	0.364705i	$0.118830\pi$
$59$			330.559i			0.729409i	−0.931123	+	0.364705i	$0.881170\pi$
$60$		0			0
$61$	−404.260	+	404.260i	−0.848527	+	0.848527i	−0.989949	−	0.141422i	$-0.954832\pi$
$61$	−404.260	+	404.260i	−0.848527	+	0.848527i	0.141422	+	0.989949i	$0.454832\pi$
$62$		0			0
$63$	−487.562	−	487.562i	−0.975032	−	0.975032i
$64$		0			0
$65$	−428.496	−	428.496i	−0.817668	−	0.817668i
$66$		0			0
$67$	−40.2994			−0.0734829			−0.0367414	−	0.999325i	$-0.511698\pi$
$67$	−40.2994			−0.0734829			−0.0367414	+	0.999325i	$0.511698\pi$
$68$		0			0
$69$	646.691			1.12830
$70$		0			0
$71$	694.644	+	694.644i	1.16111	+	1.16111i	0.984232	+	0.176883i	$0.0566013\pi$
$71$	694.644	+	694.644i	1.16111	+	1.16111i	0.176883	+	0.984232i	$0.443399\pi$
$72$		0			0
$73$	541.386	+	541.386i	0.868006	+	0.868006i	0.992251	−	0.124246i	$-0.0396511\pi$
$73$	541.386	+	541.386i	0.868006	+	0.868006i	−0.124246	+	0.992251i	$0.539651\pi$
$74$		0			0
$75$	108.541	−	108.541i	0.167110	−	0.167110i
$76$		0			0
$77$		−	204.353i		−	0.302445i
$78$		0			0
$79$	−585.853	+	585.853i	−0.834350	+	0.834350i	−0.988108	−	0.153758i	$-0.950862\pi$
$79$	−585.853	+	585.853i	−0.834350	+	0.834350i	0.153758	+	0.988108i	$0.450862\pi$
$80$		0			0
$81$	771.603			1.05844
$82$		0			0
$83$		−	670.929i		−	0.887278i	−0.896206	−	0.443639i	$-0.853687\pi$
$83$		−	670.929i		−	0.887278i	0.896206	−	0.443639i	$-0.146313\pi$
$84$		0			0
$85$	450.477	−	554.014i	0.574836	−	0.706956i
$86$		0			0
$87$		−	109.433i		−	0.134856i
$88$		0			0
$89$	−130.858			−0.155853			−0.0779266	−	0.996959i	$-0.524830\pi$
$89$	−130.858			−0.155853			−0.0779266	+	0.996959i	$0.524830\pi$
$90$		0			0
$91$	1145.57	−	1145.57i	1.31966	−	1.31966i
$92$		0			0
$93$			1466.89i			1.63559i
$94$		0			0
$95$	−823.677	+	823.677i	−0.889552	+	0.889552i
$96$		0			0
$97$	−262.597	−	262.597i	−0.274873	−	0.274873i	0.556185	−	0.831058i	$-0.312265\pi$
$97$	−262.597	−	262.597i	−0.274873	−	0.274873i	−0.831058	+	0.556185i	$0.812265\pi$
$98$		0			0
$99$	−134.324	−	134.324i	−0.136365	−	0.136365i
$100$		0			0
$101$	169.994			0.167475			0.0837377	−	0.996488i	$-0.473314\pi$
$101$	169.994			0.167475			0.0837377	+	0.996488i	$0.473314\pi$
$102$		0			0
$103$	−146.978			−0.140603			−0.0703017	−	0.997526i	$-0.522396\pi$
$103$	−146.978			−0.140603			−0.0703017	+	0.997526i	$0.522396\pi$
$104$		0			0
$105$	−1419.02	−	1419.02i	−1.31888	−	1.31888i
$106$		0			0
$107$	−39.5383	−	39.5383i	−0.0357226	−	0.0357226i	0.689020	−	0.724742i	$-0.258041\pi$
$107$	−39.5383	−	39.5383i	−0.0357226	−	0.0357226i	−0.724742	+	0.689020i	$0.758041\pi$
$108$		0			0
$109$	42.5013	−	42.5013i	0.0373476	−	0.0373476i	−0.688186	−	0.725534i	$-0.741593\pi$
$109$	42.5013	−	42.5013i	0.0373476	−	0.0373476i	0.725534	+	0.688186i	$0.241593\pi$
$110$		0			0
$111$			1747.01i			1.49386i
$112$		0			0
$113$	1504.22	−	1504.22i	1.25225	−	1.25225i	0.297547	−	0.954707i	$-0.403831\pi$
$113$	1504.22	−	1504.22i	1.25225	−	1.25225i	0.954707	−	0.297547i	$-0.0961685\pi$
$114$		0			0
$115$	910.808			0.738550
$116$		0			0
$117$		−	1506.00i		−	1.19000i
$118$		0			0
$119$	1481.14	+	1204.34i	1.14098	+	0.927744i
$120$		0			0
$121$			1274.70i			0.957701i
$122$		0			0
$123$	2492.71			1.82732
$124$		0			0
$125$	1053.30	−	1053.30i	0.753677	−	0.753677i
$126$		0			0
$127$		−	2207.42i		−	1.54233i	−0.636633	−	0.771167i	$-0.719673\pi$
$127$		−	2207.42i		−	1.54233i	0.636633	−	0.771167i	$-0.280327\pi$
$128$		0			0
$129$	−1031.98	+	1031.98i	−0.704345	+	0.704345i
$130$		0			0
$131$	−1613.78	−	1613.78i	−1.07631	−	1.07631i	−0.996837	−	0.0794701i	$-0.974677\pi$
$131$	−1613.78	−	1613.78i	−1.07631	−	1.07631i	−0.0794701	−	0.996837i	$-0.525323\pi$
$132$		0			0
$133$	−2202.08	−	2202.08i	−1.43567	−	1.43567i
$134$		0			0
$135$	123.995			0.0790500
$136$		0			0
$137$	2477.74			1.54517			0.772583	−	0.634914i	$-0.218964\pi$
$137$	2477.74			1.54517			0.772583	+	0.634914i	$0.218964\pi$
$138$		0			0
$139$	1414.84	+	1414.84i	0.863346	+	0.863346i	0.991725	−	0.128379i	$-0.0409775\pi$
$139$	1414.84	+	1414.84i	0.863346	+	0.863346i	−0.128379	+	0.991725i	$0.540977\pi$
$140$		0			0
$141$	−2160.82	−	2160.82i	−1.29060	−	1.29060i
$142$		0			0
$143$	315.608	−	315.608i	0.184563	−	0.184563i
$144$		0			0
$145$		−	154.128i		−	0.0882731i
$146$		0			0
$147$	2039.43	−	2039.43i	1.14428	−	1.14428i
$148$		0			0
$149$	1665.84			0.915914			0.457957	−	0.888974i	$-0.348581\pi$
$149$	1665.84			0.915914			0.457957	+	0.888974i	$0.348581\pi$
$150$		0			0
$151$		−	2714.26i		−	1.46280i	−0.681947	−	0.731402i	$-0.738866\pi$
$151$		−	2714.26i		−	1.46280i	0.681947	−	0.731402i	$-0.261134\pi$
$152$		0			0
$153$	1765.20	−	181.948i	0.932733	−	0.0961411i
$154$		0			0
$155$			2065.99i			1.07061i
$156$		0			0
$157$	984.223			0.500316			0.250158	−	0.968205i	$-0.419517\pi$
$157$	984.223			0.500316			0.250158	+	0.968205i	$0.419517\pi$
$158$		0			0
$159$	−2753.46	+	2753.46i	−1.37336	+	1.37336i
$160$		0			0
$161$			2435.02i			1.19197i
$162$		0			0
$163$	2416.67	−	2416.67i	1.16128	−	1.16128i	0.177083	−	0.984196i	$-0.443334\pi$
$163$	2416.67	−	2416.67i	1.16128	−	1.16128i	0.984196	−	0.177083i	$-0.0566660\pi$
$164$		0			0
$165$	−390.943	−	390.943i	−0.184454	−	0.184454i
$166$		0			0
$167$	−136.817	−	136.817i	−0.0633967	−	0.0633967i	0.674698	−	0.738094i	$-0.264274\pi$
$167$	−136.817	−	136.817i	−0.0633967	−	0.0633967i	−0.738094	+	0.674698i	$0.764274\pi$
$168$		0			0
$169$	1341.50			0.610605
$170$		0			0
$171$	−2894.91			−1.29462
$172$		0			0
$173$	1173.47	+	1173.47i	0.515705	+	0.515705i	0.916269	−	0.400564i	$-0.131186\pi$
$173$	1173.47	+	1173.47i	0.515705	+	0.515705i	−0.400564	+	0.916269i	$0.631186\pi$
$174$		0			0
$175$	408.696	+	408.696i	0.176540	+	0.176540i
$176$		0			0
$177$	−1690.66	+	1690.66i	−0.717954	+	0.717954i
$178$		0			0
$179$			2785.07i			1.16294i	0.813569	+	0.581469i	$0.197522\pi$
$179$			2785.07i			1.16294i	−0.813569	+	0.581469i	$0.802478\pi$
$180$		0			0
$181$	591.721	−	591.721i	0.242996	−	0.242996i	−0.575092	−	0.818088i	$-0.695034\pi$
$181$	591.721	−	591.721i	0.242996	−	0.242996i	0.818088	+	0.575092i	$0.195034\pi$
$182$		0			0
$183$	−4135.21			−1.67040
$184$		0			0
$185$			2460.51i			0.977841i
$186$		0			0
$187$	408.058	+	331.797i	0.159573	+	0.129751i
$188$		0			0
$189$			331.496i			0.127581i
$190$		0			0
$191$	−3291.32			−1.24687			−0.623433	−	0.781877i	$-0.714262\pi$
$191$	−3291.32			−1.24687			−0.623433	+	0.781877i	$0.714262\pi$
$192$		0			0
$193$	−3145.11	+	3145.11i	−1.17301	+	1.17301i	−0.191518	+	0.981489i	$0.561341\pi$
$193$	−3145.11	+	3145.11i	−1.17301	+	1.17301i	−0.981489	+	0.191518i	$0.938659\pi$
$194$		0			0
$195$		−	4383.13i		−	1.60965i
$196$		0			0
$197$	−536.933	+	536.933i	−0.194187	+	0.194187i	−0.797503	−	0.603315i	$-0.793846\pi$
$197$	−536.933	+	536.933i	−0.194187	+	0.194187i	0.603315	+	0.797503i	$0.293846\pi$
$198$		0			0
$199$	−2389.92	−	2389.92i	−0.851341	−	0.851341i	0.138958	−	0.990298i	$-0.455625\pi$
$199$	−2389.92	−	2389.92i	−0.851341	−	0.851341i	−0.990298	+	0.138958i	$0.955625\pi$
$200$		0			0
$201$	−206.113	−	206.113i	−0.0723289	−	0.0723289i
$202$		0			0
$203$	412.056			0.142466
$204$		0			0
$205$	3510.77			1.19611
$206$		0			0
$207$	1600.57	+	1600.57i	0.537427	+	0.537427i
$208$		0			0
$209$	−606.677	−	606.677i	−0.200788	−	0.200788i
$210$		0			0
$211$	−369.577	+	369.577i	−0.120582	+	0.120582i	−0.764823	−	0.644241i	$-0.777173\pi$
$211$	−369.577	+	369.577i	−0.120582	+	0.120582i	0.644241	+	0.764823i	$0.277173\pi$
$212$		0			0
$213$			7105.59i			2.28576i
$214$		0			0
$215$	−1453.45	+	1453.45i	−0.461044	+	0.461044i
$216$		0			0
$217$	−5523.37			−1.72788
$218$		0			0
$219$			5537.89i			1.70875i
$220$		0			0
$221$	427.504	+	4147.52i	0.130122	+	1.26241i
$222$		0			0
$223$			6412.65i			1.92566i	0.270103	+	0.962832i	$0.412942\pi$
$223$			6412.65i			1.92566i	−0.270103	+	0.962832i	$0.587058\pi$
$224$		0			0
$225$	537.282			0.159195
$226$		0			0
$227$	2472.24	−	2472.24i	0.722856	−	0.722856i	−0.246330	−	0.969186i	$-0.579225\pi$
$227$	2472.24	−	2472.24i	0.722856	−	0.722856i	0.969186	+	0.246330i	$0.0792248\pi$
$228$		0			0
$229$		−	5308.10i		−	1.53174i	−0.642994	−	0.765872i	$-0.722308\pi$
$229$		−	5308.10i		−	1.53174i	0.642994	−	0.765872i	$-0.277692\pi$
$230$		0			0
$231$	1045.18	−	1045.18i	0.297695	−	0.297695i
$232$		0			0
$233$	−1278.11	−	1278.11i	−0.359363	−	0.359363i	0.504215	−	0.863578i	$-0.331782\pi$
$233$	−1278.11	−	1278.11i	−0.359363	−	0.359363i	−0.863578	+	0.504215i	$0.831782\pi$
$234$		0			0
$235$	−3043.33	−	3043.33i	−0.844787	−	0.844787i
$236$		0			0
$237$	−5992.75			−1.64249
$238$		0			0
$239$	2239.84			0.606206			0.303103	−	0.952958i	$-0.401977\pi$
$239$	2239.84			0.606206			0.303103	+	0.952958i	$0.401977\pi$
$240$		0			0
$241$	−2134.24	−	2134.24i	−0.570451	−	0.570451i	0.361803	−	0.932254i	$-0.382161\pi$
$241$	−2134.24	−	2134.24i	−0.570451	−	0.570451i	−0.932254	+	0.361803i	$0.882161\pi$
$242$		0			0
$243$	3714.02	+	3714.02i	0.980472	+	0.980472i
$244$		0			0
$245$	2872.36	−	2872.36i	0.749013	−	0.749013i
$246$		0			0
$247$		−	6801.88i		−	1.75220i
$248$		0			0
$249$	3431.50	−	3431.50i	0.873343	−	0.873343i
$250$		0			0
$251$	−1569.93			−0.394793			−0.197396	−	0.980324i	$-0.563249\pi$
$251$	−1569.93			−0.394793			−0.197396	+	0.980324i	$0.563249\pi$
$252$		0			0
$253$			670.853i			0.166704i
$254$		0			0
$255$	5137.52	−	529.548i	1.26166	−	0.130045i
$256$		0			0
$257$		−	3437.71i		−	0.834390i	−0.908817	−	0.417195i	$-0.863013\pi$
$257$		−	3437.71i		−	0.834390i	0.908817	−	0.417195i	$-0.136987\pi$
$258$		0			0
$259$	−6578.12			−1.57816
$260$		0			0
$261$	270.850	−	270.850i	0.0642344	−	0.0642344i
$262$		0			0
$263$		−	2371.74i		−	0.556075i	−0.960570	−	0.278037i	$-0.910316\pi$
$263$		−	2371.74i		−	0.556075i	0.960570	−	0.278037i	$-0.0896839\pi$
$264$		0			0
$265$	−3878.02	+	3878.02i	−0.898961	+	0.898961i
$266$		0			0
$267$	−669.281	−	669.281i	−0.153406	−	0.153406i
$268$		0			0
$269$	925.976	+	925.976i	0.209880	+	0.209880i	0.804217	−	0.594336i	$-0.202585\pi$
$269$	925.976	+	925.976i	0.209880	+	0.209880i	−0.594336	+	0.804217i	$0.702585\pi$
$270$		0			0
$271$	−5679.83			−1.27316			−0.636578	−	0.771213i	$-0.719650\pi$
$271$	−5679.83			−1.27316			−0.636578	+	0.771213i	$0.719650\pi$
$272$		0			0
$273$	11718.2			2.59787
$274$		0			0
$275$	112.596	+	112.596i	0.0246902	+	0.0246902i
$276$		0			0
$277$	−2199.21	−	2199.21i	−0.477032	−	0.477032i	0.427149	−	0.904181i	$-0.359518\pi$
$277$	−2199.21	−	2199.21i	−0.477032	−	0.477032i	−0.904181	+	0.427149i	$0.859518\pi$
$278$		0			0
$279$	−3630.58	+	3630.58i	−0.779059	+	0.779059i
$280$		0			0
$281$		−	2984.98i		−	0.633697i	−0.948476	−	0.316849i	$-0.897375\pi$
$281$		−	2984.98i		−	0.633697i	0.948476	−	0.316849i	$-0.102625\pi$
$282$		0			0
$283$	4168.69	−	4168.69i	0.875629	−	0.875629i	−0.117450	−	0.993079i	$-0.537472\pi$
$283$	4168.69	−	4168.69i	0.875629	−	0.875629i	0.993079	+	0.117450i	$0.0374718\pi$
$284$		0			0
$285$	−8425.47			−1.75116
$286$		0			0
$287$			9385.95i			1.93044i
$288$		0			0
$289$	−4809.70	+	1002.16i	−0.978975	+	0.203982i
$290$		0			0
$291$		−	2686.13i		−	0.541113i
$292$		0			0
$293$	6054.92			1.20728			0.603639	−	0.797258i	$-0.293717\pi$
$293$	6054.92			1.20728			0.603639	+	0.797258i	$0.293717\pi$
$294$		0			0
$295$	−2381.15	+	2381.15i	−0.469953	+	0.469953i
$296$		0			0
$297$			91.3278i			0.0178430i
$298$		0			0
$299$	−3760.70	+	3760.70i	−0.727381	+	0.727381i
$300$		0			0
$301$	−3885.76	−	3885.76i	−0.744092	−	0.744092i
$302$		0			0
$303$	869.442	+	869.442i	0.164845	+	0.164845i
$304$		0			0
$305$	−5824.09			−1.09340
$306$		0			0
$307$	2610.85			0.485372			0.242686	−	0.970105i	$-0.421972\pi$
$307$	2610.85			0.485372			0.242686	+	0.970105i	$0.421972\pi$
$308$		0			0
$309$	−751.725	−	751.725i	−0.138395	−	0.138395i
$310$		0			0
$311$	3641.57	+	3641.57i	0.663969	+	0.663969i	0.956313	−	0.292344i	$-0.0944353\pi$
$311$	3641.57	+	3641.57i	0.663969	+	0.663969i	−0.292344	+	0.956313i	$0.594435\pi$
$312$		0			0
$313$	4354.93	−	4354.93i	0.786438	−	0.786438i	−0.194470	−	0.980908i	$-0.562299\pi$
$313$	4354.93	−	4354.93i	0.786438	−	0.786438i	0.980908	+	0.194470i	$0.0622987\pi$
$314$		0			0
$315$		−	7024.21i		−	1.25641i
$316$		0			0
$317$	−3987.39	+	3987.39i	−0.706480	+	0.706480i	−0.965793	−	0.259313i	$-0.916504\pi$
$317$	−3987.39	+	3987.39i	−0.706480	+	0.706480i	0.259313	+	0.965793i	$0.416504\pi$
$318$		0			0
$319$	113.522			0.0199248
$320$		0			0
$321$		−	404.442i		−	0.0703231i
$322$		0			0
$323$	7972.56	−	821.768i	1.37339	−	0.141562i
$324$		0			0
$325$			1262.40i			0.215462i
$326$		0			0
$327$	434.750			0.0735221
$328$		0			0
$329$	8136.27	−	8136.27i	1.36343	−	1.36343i
$330$		0			0
$331$			3803.97i			0.631678i	0.948813	+	0.315839i	$0.102286\pi$
$331$			3803.97i			0.631678i	−0.948813	+	0.315839i	$0.897714\pi$
$332$		0			0
$333$	−4323.88	+	4323.88i	−0.711554	+	0.711554i
$334$		0			0
$335$	−290.293	−	290.293i	−0.0473444	−	0.0473444i
$336$		0			0
$337$	−3036.29	−	3036.29i	−0.490792	−	0.490792i	0.417763	−	0.908556i	$-0.362814\pi$
$337$	−3036.29	−	3036.29i	−0.490792	−	0.490792i	−0.908556	+	0.417763i	$0.862814\pi$
$338$		0			0
$339$	15386.8			2.46518
$340$		0			0
$341$	−1521.70			−0.241656
$342$		0			0
$343$	1073.65	+	1073.65i	0.169013	+	0.169013i
$344$		0			0
$345$	4658.37	+	4658.37i	0.726952	+	0.726952i
$346$		0			0
$347$	−3517.38	+	3517.38i	−0.544158	+	0.544158i	−0.924745	−	0.380587i	$-0.875722\pi$
$347$	−3517.38	+	3517.38i	−0.544158	+	0.544158i	0.380587	+	0.924745i	$0.375722\pi$
$348$		0			0
$349$			9252.17i			1.41908i	0.704667	+	0.709538i	$0.251096\pi$
$349$			9252.17i			1.41908i	−0.704667	+	0.709538i	$0.748904\pi$
$350$		0			0
$351$	−511.970	+	511.970i	−0.0778545	+	0.0778545i
$352$		0			0
$353$	4673.17			0.704611			0.352305	−	0.935885i	$-0.385398\pi$
$353$	4673.17			0.704611			0.352305	+	0.935885i	$0.385398\pi$
$354$		0			0
$355$			10007.6i			1.49619i
$356$		0			0
$357$	1415.73	+	13735.0i	0.209884	+	2.03623i
$358$		0			0
$359$		−	5873.88i		−	0.863542i	−0.901983	−	0.431771i	$-0.857889\pi$
$359$		−	5873.88i		−	0.863542i	0.901983	−	0.431771i	$-0.142111\pi$
$360$		0			0
$361$	−6215.90			−0.906240
$362$		0			0
$363$	−6519.52	+	6519.52i	−0.942661	+	0.942661i
$364$		0			0
$365$			7799.64i			1.11850i
$366$		0			0
$367$	4900.71	−	4900.71i	0.697044	−	0.697044i	−0.266728	−	0.963772i	$-0.585943\pi$
$367$	4900.71	−	4900.71i	0.697044	−	0.697044i	0.963772	+	0.266728i	$0.0859425\pi$
$368$		0			0
$369$	6169.50	+	6169.50i	0.870384	+	0.870384i
$370$		0			0
$371$	−10367.8	−	10367.8i	−1.45086	−	1.45086i
$372$		0			0
$373$	8242.69			1.14421			0.572105	−	0.820180i	$-0.306127\pi$
$373$	8242.69			1.14421			0.572105	+	0.820180i	$0.306127\pi$
$374$		0			0
$375$	10774.3			1.48368
$376$		0			0
$377$	636.388	+	636.388i	0.0869381	+	0.0869381i
$378$		0			0
$379$	−2130.13	−	2130.13i	−0.288700	−	0.288700i	0.547866	−	0.836566i	$-0.315440\pi$
$379$	−2130.13	−	2130.13i	−0.288700	−	0.288700i	−0.836566	+	0.547866i	$0.815440\pi$
$380$		0			0
$381$	11289.9	−	11289.9i	1.51811	−	1.51811i
$382$		0			0
$383$		−	1575.67i		−	0.210216i	−0.994461	−	0.105108i	$-0.966481\pi$
$383$		−	1575.67i		−	0.210216i	0.994461	−	0.105108i	$-0.0335188\pi$
$384$		0			0
$385$	1472.04	−	1472.04i	0.194863	−	0.194863i
$386$		0			0
$387$	−5108.32			−0.670984
$388$		0			0
$389$		−	9234.92i		−	1.20367i	−0.798619	−	0.601837i	$-0.794436\pi$
$389$		−	9234.92i		−	1.20367i	0.798619	−	0.601837i	$-0.205564\pi$
$390$		0			0
$391$	−4862.31	−	3953.61i	−0.628894	−	0.511362i
$392$		0			0
$393$		−	16507.5i		−	2.11881i
$394$		0			0
$395$	−8440.28			−1.07513
$396$		0			0
$397$	9348.75	−	9348.75i	1.18186	−	1.18186i	0.202603	−	0.979261i	$-0.435060\pi$
$397$	9348.75	−	9348.75i	1.18186	−	1.18186i	0.979261	−	0.202603i	$-0.0649402\pi$
$398$		0			0
$399$		−	22525.3i		−	2.82625i
$400$		0			0
$401$	−8357.23	+	8357.23i	−1.04075	+	1.04075i	−0.0416145	+	0.999134i	$0.513250\pi$
$401$	−8357.23	+	8357.23i	−1.04075	+	1.04075i	−0.999134	+	0.0416145i	$0.986750\pi$
$402$		0			0
$403$	−8530.41	−	8530.41i	−1.05442	−	1.05442i
$404$		0			0
$405$	5558.17	+	5558.17i	0.681945	+	0.681945i
$406$		0			0
$407$	−1812.28			−0.220716
$408$		0			0
$409$	11726.5			1.41770			0.708848	−	0.705361i	$-0.249215\pi$
$409$	11726.5			1.41770			0.708848	+	0.705361i	$0.249215\pi$
$410$		0			0
$411$	12672.5	+	12672.5i	1.52090	+	1.52090i
$412$		0			0
$413$	−6365.95	−	6365.95i	−0.758470	−	0.758470i
$414$		0			0
$415$	4832.97	−	4832.97i	0.571666	−	0.571666i
$416$		0			0
$417$			14472.5i			1.69957i
$418$		0			0
$419$	−4956.11	+	4956.11i	−0.577856	+	0.577856i	−0.934312	−	0.356456i	$-0.883985\pi$
$419$	−4956.11	+	4956.11i	−0.577856	+	0.577856i	0.356456	+	0.934312i	$0.383985\pi$
$420$		0			0
$421$	−14909.1			−1.72595			−0.862973	−	0.505250i	$-0.831400\pi$
$421$	−14909.1			−1.72595			−0.862973	+	0.505250i	$0.831400\pi$
$422$		0			0
$423$		−	10696.2i		−	1.22947i
$424$		0			0
$425$	−1479.67	+	152.516i	−0.168881	+	0.0174074i
$426$		0			0
$427$		−	15570.6i		−	1.76467i
$428$		0			0
$429$	3228.38			0.363328
$430$		0			0
$431$	1635.67	−	1635.67i	0.182802	−	0.182802i	−0.609774	−	0.792576i	$-0.708740\pi$
$431$	1635.67	−	1635.67i	0.182802	−	0.182802i	0.792576	+	0.609774i	$0.208740\pi$
$432$		0			0
$433$		−	15470.6i		−	1.71702i	−0.512797	−	0.858510i	$-0.671391\pi$
$433$		−	15470.6i		−	1.71702i	0.512797	−	0.858510i	$-0.328609\pi$
$434$		0			0
$435$	788.293	−	788.293i	0.0868868	−	0.0868868i
$436$		0			0
$437$	7229.00	+	7229.00i	0.791327	+	0.791327i
$438$		0			0
$439$	2855.33	+	2855.33i	0.310427	+	0.310427i	0.845075	−	0.534648i	$-0.179556\pi$
$439$	2855.33	+	2855.33i	0.310427	+	0.310427i	−0.534648	+	0.845075i	$0.679556\pi$
$440$		0			0
$441$	10095.2			1.09008
$442$		0			0
$443$	5047.61			0.541353			0.270676	−	0.962670i	$-0.412753\pi$
$443$	5047.61			0.541353			0.270676	+	0.962670i	$0.412753\pi$
$444$		0			0
$445$	−942.624	−	942.624i	−0.100415	−	0.100415i
$446$		0			0
$447$	8520.04	+	8520.04i	0.901530	+	0.901530i
$448$		0			0
$449$	−11642.0	+	11642.0i	−1.22365	+	1.22365i	−0.257324	+	0.966325i	$0.582841\pi$
$449$	−11642.0	+	11642.0i	−1.22365	+	1.22365i	−0.966325	+	0.257324i	$0.917159\pi$
$450$		0			0
$451$			2585.84i			0.269984i
$452$		0			0
$453$	13882.2	−	13882.2i	1.43983	−	1.43983i
$454$		0			0
$455$	16504.1			1.70049
$456$		0			0
$457$		−	803.388i		−	0.0822339i	−0.999154	−	0.0411170i	$-0.986908\pi$
$457$		−	803.388i		−	0.0822339i	0.999154	−	0.0411170i	$-0.0130916\pi$
$458$		0			0
$459$	−661.940	−	538.232i	−0.0673131	−	0.0547332i
$460$		0			0
$461$		−	6000.31i		−	0.606208i	−0.952957	−	0.303104i	$-0.901977\pi$
$461$		−	6000.31i		−	0.606208i	0.952957	−	0.303104i	$-0.0980230\pi$
$462$		0			0
$463$	−5485.58			−0.550619			−0.275310	−	0.961356i	$-0.588780\pi$
$463$	−5485.58			−0.550619			−0.275310	+	0.961356i	$0.588780\pi$
$464$		0			0
$465$	−10566.6	+	10566.6i	−1.05379	+	1.05379i
$466$		0			0
$467$		−	2061.41i		−	0.204262i	−0.994771	−	0.102131i	$-0.967434\pi$
$467$		−	2061.41i		−	0.204262i	0.994771	−	0.102131i	$-0.0325661\pi$
$468$		0			0
$469$	776.090	−	776.090i	0.0764105	−	0.0764105i
$470$		0			0
$471$	5033.86	+	5033.86i	0.492458	+	0.492458i
$472$		0			0
$473$	−1070.53	−	1070.53i	−0.104066	−	0.104066i
$474$		0			0
$475$	2426.64			0.234404
$476$		0			0
$477$	−13629.8			−1.30831
$478$		0			0
$479$	8800.27	+	8800.27i	0.839446	+	0.839446i	0.988786	−	0.149340i	$-0.0477148\pi$
$479$	8800.27	+	8800.27i	0.839446	+	0.839446i	−0.149340	+	0.988786i	$0.547715\pi$
$480$		0			0
$481$	−10159.4	−	10159.4i	−0.963053	−	0.963053i
$482$		0			0
$483$	−12454.0	+	12454.0i	−1.17325	+	1.17325i
$484$		0			0
$485$		−	3783.19i		−	0.354197i
$486$		0			0
$487$	1379.51	−	1379.51i	0.128361	−	0.128361i	−0.640008	−	0.768368i	$-0.721069\pi$
$487$	1379.51	−	1379.51i	0.128361	−	0.128361i	0.768368	+	0.640008i	$0.221069\pi$
$488$		0			0
$489$	24720.4			2.28608
$490$		0			0
$491$			3745.53i			0.344263i	0.985074	+	0.172132i	$0.0550655\pi$
$491$			3745.53i			0.344263i	−0.985074	+	0.172132i	$0.944935\pi$
$492$		0			0
$493$	−669.033	+	822.803i	−0.0611191	+	0.0751667i
$494$		0			0
$495$		−	1935.18i		−	0.175717i
$496$		0			0
$497$	−26755.1			−2.41475
$498$		0			0
$499$	−11452.3	+	11452.3i	−1.02741	+	1.02741i	−0.0277939	+	0.999614i	$0.508848\pi$
$499$	−11452.3	+	11452.3i	−1.02741	+	1.02741i	−0.999614	+	0.0277939i	$0.991152\pi$
$500$		0			0
$501$		−	1399.52i		−	0.124802i
$502$		0			0
$503$	448.545	−	448.545i	0.0397607	−	0.0397607i	−0.686947	−	0.726708i	$-0.741050\pi$
$503$	448.545	−	448.545i	0.0397607	−	0.0397607i	0.726708	+	0.686947i	$0.241050\pi$
$504$		0			0
$505$	1224.53	+	1224.53i	0.107903	+	0.107903i
$506$		0			0
$507$	6861.16	+	6861.16i	0.601016	+	0.601016i
$508$		0			0
$509$	16119.6			1.40371			0.701854	−	0.712321i	$-0.252356\pi$
$509$	16119.6			1.40371			0.701854	+	0.712321i	$0.252356\pi$
$510$		0			0
$511$	−20852.1			−1.80518
$512$		0			0
$513$	984.134	+	984.134i	0.0846990	+	0.0846990i
$514$		0			0
$515$	−1058.74	−	1058.74i	−0.0905896	−	0.0905896i
$516$		0			0
$517$	2241.56	−	2241.56i	0.190684	−	0.190684i
$518$		0			0
$519$			12003.5i			1.01521i
$520$		0			0
$521$	−6436.15	+	6436.15i	−0.541215	+	0.541215i	−0.923885	−	0.382670i	$-0.875005\pi$
$521$	−6436.15	+	6436.15i	−0.541215	+	0.541215i	0.382670	+	0.923885i	$0.375005\pi$
$522$		0			0
$523$	683.977			0.0571859			0.0285929	−	0.999591i	$-0.490897\pi$
$523$	683.977			0.0571859			0.0285929	+	0.999591i	$0.490897\pi$
$524$		0			0
$525$			4180.59i			0.347535i
$526$		0			0
$527$	8967.99	−	11029.2i	0.741275	−	0.911650i
$528$		0			0
$529$			4173.29i			0.343001i
$530$		0			0
$531$	−8368.84			−0.683949
$532$		0			0
$533$	−14495.9	+	14495.9i	−1.17802	+	1.17802i
$534$		0			0
$535$		−	569.621i		−	0.0460315i
$536$		0			0
$537$	−14244.4	+	14244.4i	−1.14467	+	1.14467i
$538$		0			0
$539$	2115.63	+	2115.63i	0.169066	+	0.169066i
$540$		0			0
$541$	−10878.1	−	10878.1i	−0.864483	−	0.864483i	0.127372	−	0.991855i	$-0.459346\pi$
$541$	−10878.1	−	10878.1i	−0.864483	−	0.864483i	−0.991855	+	0.127372i	$0.959346\pi$
$542$		0			0
$543$	6052.77			0.478360
$544$		0			0
$545$	612.308			0.0481255
$546$		0			0
$547$	1629.66	+	1629.66i	0.127384	+	0.127384i	0.767925	−	0.640540i	$-0.221290\pi$
$547$	1629.66	+	1629.66i	0.127384	+	0.127384i	−0.640540	+	0.767925i	$0.721290\pi$
$548$		0			0
$549$	−10234.7	−	10234.7i	−0.795642	−	0.795642i
$550$		0			0
$551$	1223.30	−	1223.30i	0.0945811	−	0.0945811i
$552$		0			0
$553$		−	22564.9i		−	1.73518i
$554$		0			0
$555$	−12584.4	+	12584.4i	−0.962484	+	0.962484i
$556$		0			0
$557$	−11472.4			−0.872711			−0.436356	−	0.899774i	$-0.643731\pi$
$557$	−11472.4			−0.872711			−0.436356	+	0.899774i	$0.643731\pi$
$558$		0			0
$559$		−	12002.5i		−	0.908143i
$560$		0			0
$561$	390.037	+	3784.02i	0.0293536	+	0.284780i
$562$		0			0
$563$			9764.95i			0.730983i	0.930815	+	0.365492i	$0.119099\pi$
$563$			9764.95i			0.730983i	−0.930815	+	0.365492i	$0.880901\pi$
$564$		0			0
$565$	21670.9			1.61363
$566$		0			0
$567$	−14859.6	+	14859.6i	−1.10061	+	1.10061i
$568$		0			0
$569$			20941.2i			1.54288i	0.636301	+	0.771441i	$0.280464\pi$
$569$			20941.2i			1.54288i	−0.636301	+	0.771441i	$0.719536\pi$
$570$		0			0
$571$	−8141.76	+	8141.76i	−0.596711	+	0.596711i	−0.939436	−	0.342725i	$-0.888650\pi$
$571$	−8141.76	+	8141.76i	−0.596711	+	0.596711i	0.342725	+	0.939436i	$0.388650\pi$
$572$		0			0
$573$	−16833.6	−	16833.6i	−1.22728	−	1.22728i
$574$		0			0
$575$	−1341.67	−	1341.67i	−0.0973069	−	0.0973069i
$576$		0			0
$577$	12336.4			0.890069			0.445035	−	0.895513i	$-0.353191\pi$
$577$	12336.4			0.890069			0.445035	+	0.895513i	$0.353191\pi$
$578$		0			0
$579$	−32171.7			−2.30917
$580$		0			0
$581$	12920.8	+	12920.8i	0.922628	+	0.922628i
$582$		0			0
$583$	−2856.34	−	2856.34i	−0.202912	−	0.202912i
$584$		0			0
$585$	10848.3	−	10848.3i	0.766707	−	0.766707i
$586$		0			0
$587$		−	7168.90i		−	0.504075i	−0.967717	−	0.252038i	$-0.918899\pi$
$587$		−	7168.90i		−	0.504075i	0.967717	−	0.252038i	$-0.0811007\pi$
$588$		0			0
$589$	−16397.6	+	16397.6i	−1.14711	+	1.14711i
$590$		0			0
$591$	−5492.34			−0.382275
$592$		0			0
$593$			14049.0i			0.972890i	0.873711	+	0.486445i	$0.161707\pi$
$593$			14049.0i			0.972890i	−0.873711	+	0.486445i	$0.838293\pi$
$594$		0			0
$595$	1993.94	+	19344.6i	0.137384	+	1.33286i
$596$		0			0
$597$		−	24446.7i		−	1.67594i
$598$		0			0
$599$	11818.7			0.806173			0.403086	−	0.915162i	$-0.367937\pi$
$599$	11818.7			0.806173			0.403086	+	0.915162i	$0.367937\pi$
$600$		0			0
$601$	−13055.4	+	13055.4i	−0.886094	+	0.886094i	−0.994145	−	0.108052i	$-0.965539\pi$
$601$	−13055.4	+	13055.4i	−0.886094	+	0.886094i	0.108052	+	0.994145i	$0.465539\pi$
$602$		0			0
$603$		−	1020.27i		−	0.0689031i
$604$		0			0
$605$	−9182.18	+	9182.18i	−0.617039	+	0.617039i
$606$		0			0
$607$	146.835	+	146.835i	0.00981854	+	0.00981854i	0.711999	−	0.702180i	$-0.247790\pi$
$607$	146.835	+	146.835i	0.00981854	+	0.00981854i	−0.702180	+	0.711999i	$0.747790\pi$
$608$		0			0
$609$	2107.48	+	2107.48i	0.140229	+	0.140229i
$610$		0			0
$611$	25131.7			1.66402
$612$		0			0
$613$	8407.55			0.553961			0.276980	−	0.960876i	$-0.410666\pi$
$613$	8407.55			0.553961			0.276980	+	0.960876i	$0.410666\pi$
$614$		0			0
$615$	17956.0	+	17956.0i	1.17733	+	1.17733i
$616$		0			0
$617$	5504.14	+	5504.14i	0.359138	+	0.359138i	0.863495	−	0.504357i	$-0.168270\pi$
$617$	5504.14	+	5504.14i	0.359138	+	0.359138i	−0.504357	+	0.863495i	$0.668270\pi$
$618$		0			0
$619$	18230.8	−	18230.8i	1.18378	−	1.18378i	0.205017	−	0.978758i	$-0.434275\pi$
$619$	18230.8	−	18230.8i	1.18378	−	1.18378i	0.978758	−	0.205017i	$-0.0657249\pi$
$620$		0			0
$621$		−	1088.24i		−	0.0703213i
$622$		0			0
$623$	2520.08	−	2520.08i	0.162063	−	0.162063i
$624$		0			0
$625$	12521.9			0.801400
$626$		0			0
$627$		−	6205.75i		−	0.395270i
$628$		0			0
$629$	10680.5	−	13135.3i	0.677044	−	0.832656i
$630$		0			0
$631$		−	27196.4i		−	1.71580i	−0.513817	−	0.857900i	$-0.671769\pi$
$631$		−	27196.4i		−	1.71580i	0.513817	−	0.857900i	$-0.328231\pi$
$632$		0			0
$633$	−3780.44			−0.237376
$634$		0			0
$635$	15900.9	−	15900.9i	0.993714	−	0.993714i
$636$		0			0
$637$			23719.8i			1.47537i
$638$		0			0
$639$	−17586.5	+	17586.5i	−1.08875	+	1.08875i
$640$		0			0
$641$	14262.7	+	14262.7i	0.878847	+	0.878847i	0.993415	−	0.114568i	$-0.0365484\pi$
$641$	14262.7	+	14262.7i	0.878847	+	0.878847i	−0.114568	+	0.993415i	$0.536548\pi$
$642$		0			0
$643$	11897.9	+	11897.9i	0.729714	+	0.729714i	0.970563	−	0.240849i	$-0.0774258\pi$
$643$	11897.9	+	11897.9i	0.729714	+	0.729714i	−0.240849	+	0.970563i	$0.577426\pi$
$644$		0			0
$645$	−14867.5			−0.907607
$646$		0			0
$647$	−176.304			−0.0107128			−0.00535642	−	0.999986i	$-0.501705\pi$
$647$	−176.304			−0.0107128			−0.00535642	+	0.999986i	$0.501705\pi$
$648$		0			0
$649$	−1753.83	−	1753.83i	−0.106077	−	0.106077i
$650$		0			0
$651$	−28249.6	−	28249.6i	−1.70075	−	1.70075i
$652$		0			0
$653$	724.739	−	724.739i	0.0434322	−	0.0434322i	−0.685057	−	0.728489i	$-0.740223\pi$
$653$	724.739	−	724.739i	0.0434322	−	0.0434322i	0.728489	+	0.685057i	$0.240223\pi$
$654$		0			0
$655$		−	23249.4i		−	1.38691i
$656$		0			0
$657$	−13706.4	+	13706.4i	−0.813907	+	0.813907i
$658$		0			0
$659$	−19408.0			−1.14724			−0.573619	−	0.819123i	$-0.694461\pi$
$659$	−19408.0			−1.14724			−0.573619	+	0.819123i	$0.694461\pi$
$660$		0			0
$661$		−	30169.2i		−	1.77526i	−0.460559	−	0.887629i	$-0.652351\pi$
$661$		−	30169.2i		−	1.77526i	0.460559	−	0.887629i	$-0.347649\pi$
$662$		0			0
$663$	−19026.2	+	23399.2i	−1.11450	+	1.37066i
$664$		0			0
$665$		−	31724.9i		−	1.84999i
$666$		0			0
$667$	−1352.70			−0.0785259
$668$		0			0
$669$	−32797.8	+	32797.8i	−1.89542	+	1.89542i
$670$		0			0
$671$		−	4289.72i		−	0.246800i
$672$		0			0
$673$	−8974.98	+	8974.98i	−0.514056	+	0.514056i	−0.915767	−	0.401710i	$-0.868416\pi$
$673$	−8974.98	+	8974.98i	−0.514056	+	0.514056i	0.401710	+	0.915767i	$0.368416\pi$
$674$		0			0
$675$	−182.651	−	182.651i	−0.0104151	−	0.0104151i
$676$		0			0
$677$	−6185.68	−	6185.68i	−0.351159	−	0.351159i	0.509381	−	0.860541i	$-0.329874\pi$
$677$	−6185.68	−	6185.68i	−0.351159	−	0.351159i	−0.860541	+	0.509381i	$0.829874\pi$
$678$		0			0
$679$	10114.3			0.571649
$680$		0			0
$681$	25288.8			1.42301
$682$		0			0
$683$	−20624.3	−	20624.3i	−1.15544	−	1.15544i	−0.985445	−	0.169996i	$-0.945624\pi$
$683$	−20624.3	−	20624.3i	−1.15544	−	1.15544i	−0.169996	−	0.985445i	$-0.554376\pi$
$684$		0			0
$685$	17848.2	+	17848.2i	0.995538	+	0.995538i
$686$		0			0
$687$	27148.5	−	27148.5i	1.50769	−	1.50769i
$688$		0			0
$689$		−	32024.5i		−	1.77073i
$690$		0			0
$691$	−9855.25	+	9855.25i	−0.542564	+	0.542564i	−0.924280	−	0.381716i	$-0.875333\pi$
$691$	−9855.25	+	9855.25i	−0.542564	+	0.542564i	0.381716	+	0.924280i	$0.375333\pi$
$692$		0			0
$693$	5173.66			0.283595
$694$		0			0
$695$			20383.3i			1.11249i
$696$		0			0
$697$	−18742.1	−	15239.4i	−1.01852	−	0.828171i
$698$		0			0
$699$		−	13073.9i		−	0.707439i
$700$		0			0
$701$	15777.8			0.850101			0.425051	−	0.905170i	$-0.360256\pi$
$701$	15777.8			0.850101			0.425051	+	0.905170i	$0.360256\pi$
$702$		0			0
$703$	−19528.9	+	19528.9i	−1.04772	+	1.04772i
$704$		0			0
$705$		−	31130.5i		−	1.66304i
$706$		0			0
$707$	−3273.76	+	3273.76i	−0.174148	+	0.174148i
$708$		0			0
$709$	20418.0	+	20418.0i	1.08154	+	1.08154i	0.996366	+	0.0851786i	$0.0271461\pi$
$709$	20418.0	+	20418.0i	1.08154	+	1.08154i	0.0851786	+	0.996366i	$0.472854\pi$
$710$		0			0
$711$	−14832.2	−	14832.2i	−0.782349	−	0.782349i
$712$		0			0
$713$	18132.2			0.952391
$714$		0			0
$715$	4546.90			0.237824
$716$		0			0
$717$	11455.8	+	11455.8i	0.596686	+	0.596686i
$718$		0			0
$719$	−12089.9	−	12089.9i	−0.627092	−	0.627092i	0.320243	−	0.947335i	$-0.396235\pi$
$719$	−12089.9	−	12089.9i	−0.627092	−	0.627092i	−0.947335	+	0.320243i	$0.896235\pi$
$720$		0			0
$721$	2830.52	−	2830.52i	0.146205	−	0.146205i
$722$		0			0
$723$		−	21831.4i		−	1.12298i
$724$		0			0
$725$	−227.038	+	227.038i	−0.0116303	+	0.0116303i
$726$		0			0
$727$	600.010			0.0306095			0.0153048	−	0.999883i	$-0.495128\pi$
$727$	600.010			0.0306095			0.0153048	+	0.999883i	$0.495128\pi$
$728$		0			0
$729$			17157.8i			0.871707i
$730$		0			0
$731$	14068.3	−	1450.08i	0.711811	−	0.0733697i
$732$		0			0
$733$			17345.9i			0.874059i	0.899447	+	0.437029i	$0.143969\pi$
$733$			17345.9i			0.874059i	−0.899447	+	0.437029i	$0.856031\pi$
$734$		0			0
$735$	29381.6			1.47450
$736$		0			0
$737$	213.814	−	213.814i	0.0106865	−	0.0106865i
$738$		0			0
$739$			20901.6i			1.04043i	0.854035	+	0.520215i	$0.174148\pi$
$739$			20901.6i			1.04043i	−0.854035	+	0.520215i	$0.825852\pi$
$740$		0			0
$741$	34788.5	−	34788.5i	1.72468	−	1.72468i
$742$		0			0
$743$	−9689.52	−	9689.52i	−0.478431	−	0.478431i	0.426199	−	0.904630i	$-0.359852\pi$
$743$	−9689.52	−	9689.52i	−0.478431	−	0.478431i	−0.904630	+	0.426199i	$0.859852\pi$
$744$		0			0
$745$	11999.7	+	11999.7i	0.590116	+	0.590116i
$746$		0			0
$747$	16986.1			0.831978
$748$		0			0
$749$	1522.87			0.0742916
$750$		0			0
$751$	5932.79	+	5932.79i	0.288270	+	0.288270i	0.836396	−	0.548126i	$-0.184659\pi$
$751$	5932.79	+	5932.79i	0.288270	+	0.288270i	−0.548126	+	0.836396i	$0.684659\pi$
$752$		0			0
$753$	−8029.48	−	8029.48i	−0.388593	−	0.388593i
$754$		0			0
$755$	19551.9	−	19551.9i	0.942472	−	0.942472i
$756$		0			0
$757$			9816.43i			0.471313i	0.971836	+	0.235657i	$0.0757241\pi$
$757$			9816.43i			0.471313i	−0.971836	+	0.235657i	$0.924276\pi$
$758$		0			0
$759$	−3431.11	+	3431.11i	−0.164086	+	0.164086i
$760$		0			0
$761$	−2354.92			−0.112176			−0.0560879	−	0.998426i	$-0.517863\pi$
$761$	−2354.92			−0.112176			−0.0560879	+	0.998426i	$0.517863\pi$
$762$		0			0
$763$			1636.99i			0.0776710i
$764$		0			0
$765$	14026.1	+	11404.8i	0.662895	+	0.539009i
$766$		0			0
$767$		−	19663.4i		−	0.925691i
$768$		0			0
$769$	−12476.8			−0.585078			−0.292539	−	0.956254i	$-0.594500\pi$
$769$	−12476.8			−0.585078			−0.292539	+	0.956254i	$0.594500\pi$
$770$		0			0
$771$	17582.3	−	17582.3i	0.821286	−	0.821286i
$772$		0			0
$773$			18646.5i			0.867617i	0.901005	+	0.433809i	$0.142831\pi$
$773$			18646.5i			0.867617i	−0.901005	+	0.433809i	$0.857169\pi$
$774$		0			0
$775$	3043.31	−	3043.31i	0.141057	−	0.141057i
$776$		0			0
$777$	−33644.1	−	33644.1i	−1.55338	−	1.55338i
$778$		0			0
$779$	27864.6	+	27864.6i	1.28158	+	1.28158i
$780$		0			0
$781$	−7371.07			−0.337718
$782$		0			0
$783$	−184.152			−0.00840495
$784$		0			0
$785$	7089.76	+	7089.76i	0.322349	+	0.322349i
$786$		0			0
$787$	24803.2	+	24803.2i	1.12343	+	1.12343i	0.991222	+	0.132209i	$0.0422071\pi$
$787$	24803.2	+	24803.2i	1.12343	+	1.12343i	0.132209	+	0.991222i	$0.457793\pi$
$788$		0			0
$789$	12130.4	−	12130.4i	0.547342	−	0.547342i
$790$		0			0
$791$			57936.7i			2.60429i
$792$		0			0
$793$	24047.5	−	24047.5i	1.07686	−	1.07686i
$794$		0			0
$795$	−39668.6			−1.76969
$796$		0			0
$797$			6690.88i			0.297369i	0.988885	+	0.148684i	$0.0475039\pi$
$797$			6690.88i			0.297369i	−0.988885	+	0.148684i	$0.952496\pi$
$798$		0			0
$799$	3036.28	+	29457.1i	0.134438	+	1.30428i
$800$		0			0
$801$		−	3312.97i		−	0.146140i
$802$		0			0
$803$	−5744.80			−0.252465
$804$		0			0
$805$	−17540.5	+	17540.5i	−0.767975	+	0.767975i
$806$		0			0
$807$			9471.90i			0.413168i
$808$		0			0
$809$	11538.0	−	11538.0i	0.501428	−	0.501428i	−0.410454	−	0.911881i	$-0.634630\pi$
$809$	11538.0	−	11538.0i	0.501428	−	0.501428i	0.911881	+	0.410454i	$0.134630\pi$
$810$		0			0
$811$	9955.38	+	9955.38i	0.431049	+	0.431049i	0.888985	−	0.457936i	$-0.151411\pi$
$811$	9955.38	+	9955.38i	0.431049	+	0.431049i	−0.457936	+	0.888985i	$0.651411\pi$
$812$		0			0
$813$	−29049.8	−	29049.8i	−1.25316	−	1.25316i
$814$		0			0
$815$	34816.5			1.49640
$816$		0			0
$817$	−23071.8			−0.987981
$818$		0			0
$819$	29002.8	+	29002.8i	1.23741	+	1.23741i
$820$		0			0
$821$	−26591.4	−	26591.4i	−1.13038	−	1.13038i	−0.990113	−	0.140272i	$-0.955202\pi$
$821$	−26591.4	−	26591.4i	−1.13038	−	1.13038i	−0.140272	−	0.990113i	$-0.544798\pi$
$822$		0			0
$823$	9739.31	−	9739.31i	0.412504	−	0.412504i	−0.470106	−	0.882610i	$-0.655784\pi$
$823$	9739.31	−	9739.31i	0.412504	−	0.412504i	0.882610	+	0.470106i	$0.155784\pi$
$824$		0			0
$825$			1151.76i			0.0486050i
$826$		0			0
$827$	15347.3	−	15347.3i	0.645319	−	0.645319i	−0.306539	−	0.951858i	$-0.599171\pi$
$827$	15347.3	−	15347.3i	0.645319	−	0.645319i	0.951858	+	0.306539i	$0.0991709\pi$
$828$		0			0
$829$	−4760.05			−0.199425			−0.0997125	−	0.995016i	$-0.531792\pi$
$829$	−4760.05			−0.199425			−0.0997125	+	0.995016i	$0.531792\pi$
$830$		0			0
$831$		−	22495.9i		−	0.939080i
$832$		0			0
$833$	−27802.2	+	2865.70i	−1.15641	+	0.119197i
$834$		0			0
$835$		−	1971.10i		−	0.0816920i
$836$		0			0
$837$	2468.46			0.101938
$838$		0			0
$839$	−17977.2	+	17977.2i	−0.739738	+	0.739738i	−0.972527	−	0.232789i	$-0.925215\pi$
$839$	−17977.2	+	17977.2i	−0.739738	+	0.739738i	0.232789	+	0.972527i	$0.425215\pi$
$840$		0			0
$841$		−	24160.1i		−	0.990614i
$842$		0			0
$843$	15266.8	−	15266.8i	0.623745	−	0.623745i
$844$		0			0
$845$	9663.36	+	9663.36i	0.393408	+	0.393408i
$846$		0			0
$847$	−24548.3	−	24548.3i	−0.995857	−	0.995857i
$848$		0			0
$849$	42642.0			1.72376
$850$		0			0
$851$	21594.7			0.869867
$852$		0			0
$853$	5917.40	+	5917.40i	0.237524	+	0.237524i	0.815824	−	0.578300i	$-0.196284\pi$
$853$	5917.40	+	5917.40i	0.237524	+	0.237524i	−0.578300	+	0.815824i	$0.696284\pi$
$854$		0			0
$855$	−20853.2	−	20853.2i	−0.834111	−	0.834111i
$856$		0			0
$857$	−2391.48	+	2391.48i	−0.0953225	+	0.0953225i	−0.753160	−	0.657837i	$-0.771471\pi$
$857$	−2391.48	+	2391.48i	−0.0953225	+	0.0953225i	0.657837	+	0.753160i	$0.271471\pi$
$858$		0			0
$859$			12621.6i			0.501331i	0.968074	+	0.250666i	$0.0806495\pi$
$859$			12621.6i			0.501331i	−0.968074	+	0.250666i	$0.919351\pi$
$860$		0			0
$861$	−48004.9	+	48004.9i	−1.90012	+	1.90012i
$862$		0			0
$863$	−21528.6			−0.849180			−0.424590	−	0.905386i	$-0.639582\pi$
$863$	−21528.6			−0.849180			−0.424590	+	0.905386i	$0.639582\pi$
$864$		0			0
$865$			16905.9i			0.664529i
$866$		0			0
$867$	−29725.1	−	19473.8i	−1.16438	−	0.762822i
$868$		0			0
$869$		−	6216.66i		−	0.242676i
$870$		0			0
$871$	2397.22			0.0932569
$872$		0			0
$873$	6648.23	−	6648.23i	0.257742	−	0.257742i
$874$		0			0
$875$			40569.0i			1.56741i
$876$		0			0
$877$	30721.8	−	30721.8i	1.18290	−	1.18290i	0.203907	−	0.978990i	$-0.434636\pi$
$877$	30721.8	−	30721.8i	1.18290	−	1.18290i	0.978990	−	0.203907i	$-0.0653641\pi$
$878$		0			0
$879$	30968.2	+	30968.2i	1.18832	+	1.18832i
$880$		0			0
$881$	2080.26	+	2080.26i	0.0795524	+	0.0795524i	0.745763	−	0.666211i	$-0.232085\pi$
$881$	2080.26	+	2080.26i	0.0795524	+	0.0795524i	−0.666211	+	0.745763i	$0.732085\pi$
$882$		0			0
$883$	−6159.39			−0.234745			−0.117373	−	0.993088i	$-0.537447\pi$
$883$	−6159.39			−0.234745			−0.117373	+	0.993088i	$0.537447\pi$
$884$		0			0
$885$	−24357.0			−0.925144
$886$		0			0
$887$	−8560.72	−	8560.72i	−0.324060	−	0.324060i	0.526263	−	0.850322i	$-0.323593\pi$
$887$	−8560.72	−	8560.72i	−0.324060	−	0.324060i	−0.850322	+	0.526263i	$0.823593\pi$
$888$		0			0
$889$	42510.7	+	42510.7i	1.60378	+	1.60378i
$890$		0			0
$891$	−4093.85	+	4093.85i	−0.153927	+	0.153927i
$892$		0			0
$893$		−	48309.3i		−	1.81031i
$894$		0			0
$895$	−20062.0	+	20062.0i	−0.749271	+	0.749271i
$896$		0			0
$897$	−38468.6			−1.43192
$898$		0			0
$899$		−	3068.34i		−	0.113832i
$900$		0			0
$901$	37536.2	−	3869.03i	1.38792	−	0.143059i
$902$		0			0
$903$		−	39747.8i		−	1.46481i
$904$		0			0
$905$	8524.81			0.313121
$906$		0			0
$907$	−14510.4	+	14510.4i	−0.531214	+	0.531214i	−0.920934	−	0.389719i	$-0.872572\pi$
$907$	−14510.4	+	14510.4i	−0.531214	+	0.531214i	0.389719	+	0.920934i	$0.372572\pi$
$908$		0			0
$909$			4303.77i			0.157038i
$910$		0			0
$911$	11912.7	−	11912.7i	0.433244	−	0.433244i	−0.456487	−	0.889730i	$-0.650892\pi$
$911$	11912.7	−	11912.7i	0.433244	−	0.433244i	0.889730	+	0.456487i	$0.150892\pi$
$912$		0			0
$913$	3559.71	+	3559.71i	0.129035	+	0.129035i
$914$		0			0
$915$	−29787.6	−	29787.6i	−1.07623	−	1.07623i
$916$		0			0
$917$	62156.6			2.23838
$918$		0			0
$919$	18874.6			0.677492			0.338746	−	0.940878i	$-0.389997\pi$
$919$	18874.6			0.677492			0.338746	+	0.940878i	$0.389997\pi$
$920$		0			0
$921$	13353.3	+	13353.3i	0.477749	+	0.477749i
$922$		0			0
$923$	−41321.1	−	41321.1i	−1.47357	−	1.47357i
$924$		0			0
$925$	3624.47	−	3624.47i	0.128834	−	0.128834i
$926$		0			0
$927$		−	3721.07i		−	0.131840i
$928$		0			0
$929$	20513.6	−	20513.6i	0.724467	−	0.724467i	−0.245044	−	0.969512i	$-0.578803\pi$
$929$	20513.6	−	20513.6i	0.724467	−	0.724467i	0.969512	+	0.245044i	$0.0788026\pi$
$930$		0			0
$931$	45595.3			1.60508
$932$		0			0
$933$			37249.9i			1.30708i
$934$		0			0
$935$	549.334	+	5329.47i	0.0192140	+	0.186409i
$936$		0			0
$937$		−	32638.3i		−	1.13794i	−0.822360	−	0.568968i	$-0.807343\pi$
$937$		−	32638.3i		−	1.13794i	0.822360	−	0.568968i	$-0.192657\pi$
$938$		0			0
$939$	44547.0			1.54818
$940$		0			0
$941$	4905.12	−	4905.12i	0.169928	−	0.169928i	−0.617020	−	0.786948i	$-0.711660\pi$
$941$	4905.12	−	4905.12i	0.169928	−	0.169928i	0.786948	+	0.617020i	$0.211660\pi$
$942$		0			0
$943$		−	30812.3i		−	1.06403i
$944$		0			0
$945$	−2387.90	+	2387.90i	−0.0821994	+	0.0821994i
$946$		0			0
$947$	18028.4	+	18028.4i	0.618631	+	0.618631i	0.945180	−	0.326549i	$-0.105886\pi$
$947$	18028.4	+	18028.4i	0.618631	+	0.618631i	−0.326549	+	0.945180i	$0.605886\pi$
$948$		0			0
$949$	−32204.5	−	32204.5i	−1.10158	−	1.10158i
$950$		0			0
$951$	−40787.4			−1.39077
$952$		0			0
$953$	−45137.1			−1.53424			−0.767121	−	0.641502i	$-0.778312\pi$
$953$	−45137.1			−1.53424			−0.767121	+	0.641502i	$0.778312\pi$
$954$		0			0
$955$	−23708.7	−	23708.7i	−0.803345	−	0.803345i
$956$		0			0
$957$	580.615	+	580.615i	0.0196119	+	0.0196119i
$958$		0			0
$959$	−47716.6	+	47716.6i	−1.60673	+	1.60673i
$960$		0			0
$961$			11338.3i			0.380593i
$962$		0			0
$963$	1001.00	−	1001.00i	0.0334962	−	0.0334962i
$964$		0			0
$965$	−45311.1			−1.51152
$966$		0			0
$967$		−	4077.37i		−	0.135594i	−0.997699	−	0.0677970i	$-0.978403\pi$
$967$		−	4077.37i		−	0.135594i	0.997699	−	0.0677970i	$-0.0215970\pi$
$968$		0			0
$969$	44979.0	+	36573.1i	1.49116	+	1.21248i
$970$		0			0
$971$		−	30916.5i		−	1.02179i	−0.859644	−	0.510894i	$-0.829314\pi$
$971$		−	30916.5i		−	1.02179i	0.859644	−	0.510894i	$-0.170686\pi$
$972$		0			0
$973$	−54494.3			−1.79548
$974$		0			0
$975$	−6456.59	+	6456.59i	−0.212078	+	0.212078i
$976$		0			0
$977$		−	32526.6i		−	1.06512i	−0.846394	−	0.532558i	$-0.821231\pi$
$977$		−	32526.6i		−	1.06512i	0.846394	−	0.532558i	$-0.178769\pi$
$978$		0			0
$979$	694.287	−	694.287i	0.0226655	−	0.0226655i
$980$		0			0
$981$	1076.01	+	1076.01i	0.0350199	+	0.0350199i
$982$		0			0
$983$	−27056.0	−	27056.0i	−0.877875	−	0.877875i	0.115439	−	0.993315i	$-0.463172\pi$
$983$	−27056.0	−	27056.0i	−0.877875	−	0.877875i	−0.993315	+	0.115439i	$0.963172\pi$
$984$		0			0
$985$	−7735.49			−0.250227
$986$		0			0
$987$	83226.7			2.68403
$988$		0			0
$989$	12756.2	+	12756.2i	0.410135	+	0.410135i
$990$		0			0
$991$	39556.5	+	39556.5i	1.26797	+	1.26797i	0.947137	+	0.320829i	$0.103962\pi$
$991$	39556.5	+	39556.5i	1.26797	+	1.26797i	0.320829	+	0.947137i	$0.396038\pi$
$992$		0			0
$993$	−19455.6	+	19455.6i	−0.621758	+	0.621758i
$994$		0			0
$995$		−	34431.1i		−	1.09702i
$996$		0			0
$997$	24809.0	−	24809.0i	0.788074	−	0.788074i	−0.193104	−	0.981178i	$-0.561856\pi$
$997$	24809.0	−	24809.0i	0.788074	−	0.788074i	0.981178	+	0.193104i	$0.0618556\pi$
$998$		0			0
$999$	2939.84			0.0931054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.4.o.f.81.7		14
4.3	odd	2		136.4.k.b.81.1	✓	14
17.4	even	4	inner	272.4.o.f.225.7		14
68.15	odd	8		2312.4.a.l.1.13		14
68.19	odd	8		2312.4.a.l.1.2		14
68.55	odd	4		136.4.k.b.89.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.1	✓	14	4.3	odd	2
136.4.k.b.89.1	yes	14	68.55	odd	4
272.4.o.f.81.7		14	1.1	even	1	trivial
272.4.o.f.225.7		14	17.4	even	4	inner
2312.4.a.l.1.2		14	68.19	odd	8
2312.4.a.l.1.13		14	68.15	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	272.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.11455 + 5.11455i) q^{3} +(7.20340 + 7.20340i) q^{5} +(-19.2581 + 19.2581i) q^{7} +25.3172i q^{9} +(-5.30564 + 5.30564i) q^{11} -59.4853 q^{13} +73.6843i q^{15} +(-7.18671 - 69.7234i) q^{17} +114.346i q^{19} -196.993 q^{21} +(63.2207 - 63.2207i) q^{23} -21.2220i q^{25} +(8.60667 - 8.60667i) q^{27} +(-10.6982 - 10.6982i) q^{29} +(143.404 + 143.404i) q^{31} -54.2720 q^{33} -277.448 q^{35} +(170.788 + 170.788i) q^{37} +(-304.240 - 304.240i) q^{39} +(243.688 - 243.688i) q^{41} +201.773i q^{43} +(-182.370 + 182.370i) q^{45} -422.485 q^{47} -398.750i q^{49} +(319.847 - 393.360i) q^{51} +538.359i q^{53} -76.4374 q^{55} +(-584.826 + 584.826i) q^{57} +330.559i q^{59} +(-404.260 + 404.260i) q^{61} +(-487.562 - 487.562i) q^{63} +(-428.496 - 428.496i) q^{65} -40.2994 q^{67} +646.691 q^{69} +(694.644 + 694.644i) q^{71} +(541.386 + 541.386i) q^{73} +(108.541 - 108.541i) q^{75} -204.353i q^{77} +(-585.853 + 585.853i) q^{79} +771.603 q^{81} -670.929i q^{83} +(450.477 - 554.014i) q^{85} -109.433i q^{87} -130.858 q^{89} +(1145.57 - 1145.57i) q^{91} +1466.89i q^{93} +(-823.677 + 823.677i) q^{95} +(-262.597 - 262.597i) q^{97} +(-134.324 - 134.324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 6 q^{3} + 6 q^{5} - 10 q^{7} + 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} + 162 q^{23} + 204 q^{27} + 158 q^{29} + 350 q^{31} + 116 q^{33} - 236 q^{35} + 582 q^{37} + 320 q^{39} + 878 q^{41}+ \cdots - 3870 q^{99}+O(q^{100}) \) 14 * q - 6 * q^3 + 6 * q^5 - 10 * q^7 + 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 + 162 * q^23 + 204 * q^27 + 158 * q^29 + 350 * q^31 + 116 * q^33 - 236 * q^35 + 582 * q^37 + 320 * q^39 + 878 * q^41 - 26 * q^45 + 448 * q^47 + 590 * q^51 - 1460 * q^55 + 292 * q^57 - 1130 * q^61 - 114 * q^63 + 20 * q^65 + 64 * q^67 + 2076 * q^69 + 3274 * q^71 - 1426 * q^73 - 946 * q^75 - 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 - 2128 * q^91 + 2444 * q^95 + 1926 * q^97 - 3870 * q^99

Introduction

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