LMFDB - Embedded newform 272.4.o.f.225.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,4,Mod(81,272)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			225.7
Root			$5.11455i$ of defining polynomial
Character	$\chi$	$=$	272.225
Dual form			272.4.o.f.81.7

$q$-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 $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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	−0.0155832	−	0.999879i	$-0.504960\pi$
$3$	5.11455	−	5.11455i	0.984295	−	0.984295i	0.999879	+	0.0155832i	$0.00496049\pi$
$4$		0			0
$5$	7.20340	−	7.20340i	0.644292	−	0.644292i	−0.307316	−	0.951608i	$-0.599431\pi$
$5$	7.20340	−	7.20340i	0.644292	−	0.644292i	0.951608	+	0.307316i	$0.0994308\pi$
$6$		0			0
$7$	−19.2581	−	19.2581i	−1.03984	−	1.03984i	−0.999173	−	0.0406680i	$-0.987051\pi$
$7$	−19.2581	−	19.2581i	−1.03984	−	1.03984i	−0.0406680	−	0.999173i	$-0.512949\pi$
$8$		0			0
$9$		−	25.3172i		−	0.937675i
$10$		0			0
$11$	−5.30564	−	5.30564i	−0.145428	−	0.145428i	0.630644	−	0.776072i	$-0.282791\pi$
$11$	−5.30564	−	5.30564i	−0.145428	−	0.145428i	−0.776072	+	0.630644i	$0.782791\pi$
$12$		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	$-0.757464\pi$
$19$		−	114.346i		−	1.38067i	0.723492	−	0.690333i	$-0.242536\pi$
$20$		0			0
$21$	−196.993			−2.04702
$22$		0			0
$23$	63.2207	+	63.2207i	0.573149	+	0.573149i	0.933007	−	0.359858i	$-0.117175\pi$
$23$	63.2207	+	63.2207i	0.573149	+	0.573149i	−0.359858	+	0.933007i	$0.617175\pi$
$24$		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	−0.740529	−	0.672025i	$-0.765425\pi$
$29$	−10.6982	+	10.6982i	−0.0685039	+	0.0685039i	0.672025	+	0.740529i	$0.265425\pi$
$30$		0			0
$31$	143.404	−	143.404i	0.830841	−	0.830841i	−0.156791	−	0.987632i	$-0.550115\pi$
$31$	143.404	−	143.404i	0.830841	−	0.830841i	0.987632	+	0.156791i	$0.0501149\pi$
$32$		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	−0.217264	−	0.976113i	$-0.569713\pi$
$37$	170.788	−	170.788i	0.758849	−	0.758849i	0.976113	+	0.217264i	$0.0697132\pi$
$38$		0			0
$39$	−304.240	+	304.240i	−1.24917	+	1.24917i
$40$		0			0
$41$	243.688	+	243.688i	0.928236	+	0.928236i	0.997592	−	0.0693559i	$-0.0220944\pi$
$41$	243.688	+	243.688i	0.928236	+	0.928236i	−0.0693559	+	0.997592i	$0.522094\pi$
$42$		0			0
$43$		−	201.773i		−	0.715583i	−0.933802	−	0.357791i	$-0.883530\pi$
$43$		−	201.773i		−	0.715583i	0.933802	−	0.357791i	$-0.116470\pi$
$44$		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	$-0.754236\pi$
$53$		−	538.359i		−	1.39527i	0.716453	−	0.697635i	$-0.245764\pi$
$54$		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	$-0.881170\pi$
$59$		−	330.559i		−	0.729409i	0.931123	−	0.364705i	$-0.118830\pi$
$60$		0			0
$61$	−404.260	−	404.260i	−0.848527	−	0.848527i	0.141422	−	0.989949i	$-0.454832\pi$
$61$	−404.260	−	404.260i	−0.848527	−	0.848527i	−0.989949	+	0.141422i	$0.954832\pi$
$62$		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	0.176883	−	0.984232i	$-0.443399\pi$
$71$	694.644	−	694.644i	1.16111	−	1.16111i	0.984232	−	0.176883i	$-0.0566013\pi$
$72$		0			0
$73$	541.386	−	541.386i	0.868006	−	0.868006i	−0.124246	−	0.992251i	$-0.539651\pi$
$73$	541.386	−	541.386i	0.868006	−	0.868006i	0.992251	+	0.124246i	$0.0396511\pi$
$74$		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	0.153758	−	0.988108i	$-0.450862\pi$
$79$	−585.853	−	585.853i	−0.834350	−	0.834350i	−0.988108	+	0.153758i	$0.950862\pi$
$80$		0			0
$81$	771.603			1.05844
$82$		0			0
$83$			670.929i			0.887278i	0.896206	+	0.443639i	$0.146313\pi$
$83$			670.929i			0.887278i	−0.896206	+	0.443639i	$0.853687\pi$
$84$		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	−0.831058	−	0.556185i	$-0.812265\pi$
$97$	−262.597	+	262.597i	−0.274873	+	0.274873i	0.556185	+	0.831058i	$0.312265\pi$
$98$		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	−0.724742	−	0.689020i	$-0.758041\pi$
$107$	−39.5383	+	39.5383i	−0.0357226	+	0.0357226i	0.689020	+	0.724742i	$0.258041\pi$
$108$		0			0
$109$	42.5013	+	42.5013i	0.0373476	+	0.0373476i	0.725534	−	0.688186i	$-0.241593\pi$
$109$	42.5013	+	42.5013i	0.0373476	+	0.0373476i	−0.688186	+	0.725534i	$0.741593\pi$
$110$		0			0
$111$		−	1747.01i		−	1.49386i
$112$		0			0
$113$	1504.22	+	1504.22i	1.25225	+	1.25225i	0.954707	+	0.297547i	$0.0961685\pi$
$113$	1504.22	+	1504.22i	1.25225	+	1.25225i	0.297547	+	0.954707i	$0.403831\pi$
$114$		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	$0.280327\pi$
$127$			2207.42i			1.54233i	−0.636633	+	0.771167i	$0.719673\pi$
$128$		0			0
$129$	−1031.98	−	1031.98i	−0.704345	−	0.704345i
$130$		0			0
$131$	−1613.78	+	1613.78i	−1.07631	+	1.07631i	−0.0794701	+	0.996837i	$0.525323\pi$
$131$	−1613.78	+	1613.78i	−1.07631	+	1.07631i	−0.996837	+	0.0794701i	$0.974677\pi$
$132$		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	−0.128379	−	0.991725i	$-0.540977\pi$
$139$	1414.84	−	1414.84i	0.863346	−	0.863346i	0.991725	+	0.128379i	$0.0409775\pi$
$140$		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	$0.261134\pi$
$151$			2714.26i			1.46280i	−0.681947	+	0.731402i	$0.738866\pi$
$152$		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	0.984196	+	0.177083i	$0.0566660\pi$
$163$	2416.67	+	2416.67i	1.16128	+	1.16128i	0.177083	+	0.984196i	$0.443334\pi$
$164$		0			0
$165$	−390.943	+	390.943i	−0.184454	+	0.184454i
$166$		0			0
$167$	−136.817	+	136.817i	−0.0633967	+	0.0633967i	−0.738094	−	0.674698i	$-0.764274\pi$
$167$	−136.817	+	136.817i	−0.0633967	+	0.0633967i	0.674698	+	0.738094i	$0.264274\pi$
$168$		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	−0.400564	−	0.916269i	$-0.631186\pi$
$173$	1173.47	−	1173.47i	0.515705	−	0.515705i	0.916269	+	0.400564i	$0.131186\pi$
$174$		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	$-0.802478\pi$
$179$		−	2785.07i		−	1.16294i	0.813569	−	0.581469i	$-0.197522\pi$
$180$		0			0
$181$	591.721	+	591.721i	0.242996	+	0.242996i	0.818088	−	0.575092i	$-0.195034\pi$
$181$	591.721	+	591.721i	0.242996	+	0.242996i	−0.575092	+	0.818088i	$0.695034\pi$
$182$		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	−0.981489	−	0.191518i	$-0.938659\pi$
$193$	−3145.11	−	3145.11i	−1.17301	−	1.17301i	−0.191518	−	0.981489i	$-0.561341\pi$
$194$		0			0
$195$			4383.13i			1.60965i
$196$		0			0
$197$	−536.933	−	536.933i	−0.194187	−	0.194187i	0.603315	−	0.797503i	$-0.293846\pi$
$197$	−536.933	−	536.933i	−0.194187	−	0.194187i	−0.797503	+	0.603315i	$0.793846\pi$
$198$		0			0
$199$	−2389.92	+	2389.92i	−0.851341	+	0.851341i	−0.990298	−	0.138958i	$-0.955625\pi$
$199$	−2389.92	+	2389.92i	−0.851341	+	0.851341i	0.138958	+	0.990298i	$0.455625\pi$
$200$		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	0.644241	−	0.764823i	$-0.277173\pi$
$211$	−369.577	−	369.577i	−0.120582	−	0.120582i	−0.764823	+	0.644241i	$0.777173\pi$
$212$		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	$-0.587058\pi$
$223$		−	6412.65i		−	1.92566i	0.270103	−	0.962832i	$-0.412942\pi$
$224$		0			0
$225$	537.282			0.159195
$226$		0			0
$227$	2472.24	+	2472.24i	0.722856	+	0.722856i	0.969186	−	0.246330i	$-0.0792248\pi$
$227$	2472.24	+	2472.24i	0.722856	+	0.722856i	−0.246330	+	0.969186i	$0.579225\pi$
$228$		0			0
$229$			5308.10i			1.53174i	0.642994	+	0.765872i	$0.277692\pi$
$229$			5308.10i			1.53174i	−0.642994	+	0.765872i	$0.722308\pi$
$230$		0			0
$231$	1045.18	+	1045.18i	0.297695	+	0.297695i
$232$		0			0
$233$	−1278.11	+	1278.11i	−0.359363	+	0.359363i	−0.863578	−	0.504215i	$-0.831782\pi$
$233$	−1278.11	+	1278.11i	−0.359363	+	0.359363i	0.504215	+	0.863578i	$0.331782\pi$
$234$		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	−0.932254	−	0.361803i	$-0.882161\pi$
$241$	−2134.24	+	2134.24i	−0.570451	+	0.570451i	0.361803	+	0.932254i	$0.382161\pi$
$242$		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	$0.136987\pi$
$257$			3437.71i			0.834390i	−0.908817	+	0.417195i	$0.863013\pi$
$258$		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	$0.0896839\pi$
$263$			2371.74i			0.556075i	−0.960570	+	0.278037i	$0.910316\pi$
$264$		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	−0.594336	−	0.804217i	$-0.702585\pi$
$269$	925.976	−	925.976i	0.209880	−	0.209880i	0.804217	+	0.594336i	$0.202585\pi$
$270$		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	−0.904181	−	0.427149i	$-0.859518\pi$
$277$	−2199.21	+	2199.21i	−0.477032	+	0.477032i	0.427149	+	0.904181i	$0.359518\pi$
$278$		0			0
$279$	−3630.58	−	3630.58i	−0.779059	−	0.779059i
$280$		0			0
$281$			2984.98i			0.633697i	0.948476	+	0.316849i	$0.102625\pi$
$281$			2984.98i			0.633697i	−0.948476	+	0.316849i	$0.897375\pi$
$282$		0			0
$283$	4168.69	+	4168.69i	0.875629	+	0.875629i	0.993079	−	0.117450i	$-0.0374718\pi$
$283$	4168.69	+	4168.69i	0.875629	+	0.875629i	−0.117450	+	0.993079i	$0.537472\pi$
$284$		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	−0.292344	−	0.956313i	$-0.594435\pi$
$311$	3641.57	−	3641.57i	0.663969	−	0.663969i	0.956313	+	0.292344i	$0.0944353\pi$
$312$		0			0
$313$	4354.93	+	4354.93i	0.786438	+	0.786438i	0.980908	−	0.194470i	$-0.0622987\pi$
$313$	4354.93	+	4354.93i	0.786438	+	0.786438i	−0.194470	+	0.980908i	$0.562299\pi$
$314$		0			0
$315$			7024.21i			1.25641i
$316$		0			0
$317$	−3987.39	−	3987.39i	−0.706480	−	0.706480i	0.259313	−	0.965793i	$-0.416504\pi$
$317$	−3987.39	−	3987.39i	−0.706480	−	0.706480i	−0.965793	+	0.259313i	$0.916504\pi$
$318$		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	$-0.897714\pi$
$331$		−	3803.97i		−	0.631678i	0.948813	−	0.315839i	$-0.102286\pi$
$332$		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	−0.908556	−	0.417763i	$-0.862814\pi$
$337$	−3036.29	+	3036.29i	−0.490792	+	0.490792i	0.417763	+	0.908556i	$0.362814\pi$
$338$		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	0.380587	−	0.924745i	$-0.375722\pi$
$347$	−3517.38	−	3517.38i	−0.544158	−	0.544158i	−0.924745	+	0.380587i	$0.875722\pi$
$348$		0			0
$349$		−	9252.17i		−	1.41908i	−0.704667	−	0.709538i	$-0.748904\pi$
$349$		−	9252.17i		−	1.41908i	0.704667	−	0.709538i	$-0.251096\pi$
$350$		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	$0.142111\pi$
$359$			5873.88i			0.863542i	−0.901983	+	0.431771i	$0.857889\pi$
$360$		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	0.963772	−	0.266728i	$-0.0859425\pi$
$367$	4900.71	+	4900.71i	0.697044	+	0.697044i	−0.266728	+	0.963772i	$0.585943\pi$
$368$		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	−0.836566	−	0.547866i	$-0.815440\pi$
$379$	−2130.13	+	2130.13i	−0.288700	+	0.288700i	0.547866	+	0.836566i	$0.315440\pi$
$380$		0			0
$381$	11289.9	+	11289.9i	1.51811	+	1.51811i
$382$		0			0
$383$			1575.67i			0.210216i	0.994461	+	0.105108i	$0.0335188\pi$
$383$			1575.67i			0.210216i	−0.994461	+	0.105108i	$0.966481\pi$
$384$		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	$0.205564\pi$
$389$			9234.92i			1.20367i	−0.798619	+	0.601837i	$0.794436\pi$
$390$		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	0.979261	+	0.202603i	$0.0649402\pi$
$397$	9348.75	+	9348.75i	1.18186	+	1.18186i	0.202603	+	0.979261i	$0.435060\pi$
$398$		0			0
$399$			22525.3i			2.82625i
$400$		0			0
$401$	−8357.23	−	8357.23i	−1.04075	−	1.04075i	−0.999134	−	0.0416145i	$-0.986750\pi$
$401$	−8357.23	−	8357.23i	−1.04075	−	1.04075i	−0.0416145	−	0.999134i	$-0.513250\pi$
$402$		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	0.356456	−	0.934312i	$-0.383985\pi$
$419$	−4956.11	−	4956.11i	−0.577856	−	0.577856i	−0.934312	+	0.356456i	$0.883985\pi$
$420$		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	0.792576	−	0.609774i	$-0.208740\pi$
$431$	1635.67	+	1635.67i	0.182802	+	0.182802i	−0.609774	+	0.792576i	$0.708740\pi$
$432$		0			0
$433$			15470.6i			1.71702i	0.512797	+	0.858510i	$0.328609\pi$
$433$			15470.6i			1.71702i	−0.512797	+	0.858510i	$0.671391\pi$
$434$		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	−0.534648	−	0.845075i	$-0.679556\pi$
$439$	2855.33	−	2855.33i	0.310427	−	0.310427i	0.845075	+	0.534648i	$0.179556\pi$
$440$		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	−0.966325	−	0.257324i	$-0.917159\pi$
$449$	−11642.0	−	11642.0i	−1.22365	−	1.22365i	−0.257324	−	0.966325i	$-0.582841\pi$
$450$		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	$0.0130916\pi$
$457$			803.388i			0.0822339i	−0.999154	+	0.0411170i	$0.986908\pi$
$458$		0			0
$459$	−661.940	+	538.232i	−0.0673131	+	0.0547332i
$460$		0			0
$461$			6000.31i			0.606208i	0.952957	+	0.303104i	$0.0980230\pi$
$461$			6000.31i			0.606208i	−0.952957	+	0.303104i	$0.901977\pi$
$462$		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	$0.0325661\pi$
$467$			2061.41i			0.204262i	−0.994771	+	0.102131i	$0.967434\pi$
$468$		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	−0.149340	−	0.988786i	$-0.547715\pi$
$479$	8800.27	−	8800.27i	0.839446	−	0.839446i	0.988786	+	0.149340i	$0.0477148\pi$
$480$		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	0.768368	−	0.640008i	$-0.221069\pi$
$487$	1379.51	+	1379.51i	0.128361	+	0.128361i	−0.640008	+	0.768368i	$0.721069\pi$
$488$		0			0
$489$	24720.4			2.28608
$490$		0			0
$491$		−	3745.53i		−	0.344263i	−0.985074	−	0.172132i	$-0.944935\pi$
$491$		−	3745.53i		−	0.344263i	0.985074	−	0.172132i	$-0.0550655\pi$
$492$		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	−0.999614	−	0.0277939i	$-0.991152\pi$
$499$	−11452.3	−	11452.3i	−1.02741	−	1.02741i	−0.0277939	−	0.999614i	$-0.508848\pi$
$500$		0			0
$501$			1399.52i			0.124802i
$502$		0			0
$503$	448.545	+	448.545i	0.0397607	+	0.0397607i	0.726708	−	0.686947i	$-0.241050\pi$
$503$	448.545	+	448.545i	0.0397607	+	0.0397607i	−0.686947	+	0.726708i	$0.741050\pi$
$504$		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	0.382670	−	0.923885i	$-0.375005\pi$
$521$	−6436.15	−	6436.15i	−0.541215	−	0.541215i	−0.923885	+	0.382670i	$0.875005\pi$
$522$		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	−0.991855	−	0.127372i	$-0.959346\pi$
$541$	−10878.1	+	10878.1i	−0.864483	+	0.864483i	0.127372	+	0.991855i	$0.459346\pi$
$542$		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	−0.640540	−	0.767925i	$-0.721290\pi$
$547$	1629.66	−	1629.66i	0.127384	−	0.127384i	0.767925	+	0.640540i	$0.221290\pi$
$548$		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	$-0.880901\pi$
$563$		−	9764.95i		−	0.730983i	0.930815	−	0.365492i	$-0.119099\pi$
$564$		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	$-0.719536\pi$
$569$		−	20941.2i		−	1.54288i	0.636301	−	0.771441i	$-0.280464\pi$
$570$		0			0
$571$	−8141.76	−	8141.76i	−0.596711	−	0.596711i	0.342725	−	0.939436i	$-0.388650\pi$
$571$	−8141.76	−	8141.76i	−0.596711	−	0.596711i	−0.939436	+	0.342725i	$0.888650\pi$
$572$		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	$0.0811007\pi$
$587$			7168.90i			0.504075i	−0.967717	+	0.252038i	$0.918899\pi$
$588$		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	$-0.838293\pi$
$593$		−	14049.0i		−	0.972890i	0.873711	−	0.486445i	$-0.161707\pi$
$594$		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	0.108052	−	0.994145i	$-0.465539\pi$
$601$	−13055.4	−	13055.4i	−0.886094	−	0.886094i	−0.994145	+	0.108052i	$0.965539\pi$
$602$		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	−0.702180	−	0.711999i	$-0.747790\pi$
$607$	146.835	−	146.835i	0.00981854	−	0.00981854i	0.711999	+	0.702180i	$0.247790\pi$
$608$		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	−0.504357	−	0.863495i	$-0.668270\pi$
$617$	5504.14	−	5504.14i	0.359138	−	0.359138i	0.863495	+	0.504357i	$0.168270\pi$
$618$		0			0
$619$	18230.8	+	18230.8i	1.18378	+	1.18378i	0.978758	+	0.205017i	$0.0657249\pi$
$619$	18230.8	+	18230.8i	1.18378	+	1.18378i	0.205017	+	0.978758i	$0.434275\pi$
$620$		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	$0.328231\pi$
$631$			27196.4i			1.71580i	−0.513817	+	0.857900i	$0.671769\pi$
$632$		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	−0.114568	−	0.993415i	$-0.536548\pi$
$641$	14262.7	−	14262.7i	0.878847	−	0.878847i	0.993415	+	0.114568i	$0.0365484\pi$
$642$		0			0
$643$	11897.9	−	11897.9i	0.729714	−	0.729714i	−0.240849	−	0.970563i	$-0.577426\pi$
$643$	11897.9	−	11897.9i	0.729714	−	0.729714i	0.970563	+	0.240849i	$0.0774258\pi$
$644$		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	0.728489	−	0.685057i	$-0.240223\pi$
$653$	724.739	+	724.739i	0.0434322	+	0.0434322i	−0.685057	+	0.728489i	$0.740223\pi$
$654$		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	$0.347649\pi$
$661$			30169.2i			1.77526i	−0.460559	+	0.887629i	$0.652351\pi$
$662$		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	0.401710	−	0.915767i	$-0.368416\pi$
$673$	−8974.98	−	8974.98i	−0.514056	−	0.514056i	−0.915767	+	0.401710i	$0.868416\pi$
$674$		0			0
$675$	−182.651	+	182.651i	−0.0104151	+	0.0104151i
$676$		0			0
$677$	−6185.68	+	6185.68i	−0.351159	+	0.351159i	−0.860541	−	0.509381i	$-0.829874\pi$
$677$	−6185.68	+	6185.68i	−0.351159	+	0.351159i	0.509381	+	0.860541i	$0.329874\pi$
$678$		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	−0.169996	+	0.985445i	$0.554376\pi$
$683$	−20624.3	+	20624.3i	−1.15544	+	1.15544i	−0.985445	+	0.169996i	$0.945624\pi$
$684$		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	0.381716	−	0.924280i	$-0.375333\pi$
$691$	−9855.25	−	9855.25i	−0.542564	−	0.542564i	−0.924280	+	0.381716i	$0.875333\pi$
$692$		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	0.0851786	−	0.996366i	$-0.472854\pi$
$709$	20418.0	−	20418.0i	1.08154	−	1.08154i	0.996366	−	0.0851786i	$-0.0271461\pi$
$710$		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	−0.947335	−	0.320243i	$-0.896235\pi$
$719$	−12089.9	+	12089.9i	−0.627092	+	0.627092i	0.320243	+	0.947335i	$0.396235\pi$
$720$		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	$-0.856031\pi$
$733$		−	17345.9i		−	0.874059i	0.899447	−	0.437029i	$-0.143969\pi$
$734$		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	$-0.825852\pi$
$739$		−	20901.6i		−	1.04043i	0.854035	−	0.520215i	$-0.174148\pi$
$740$		0			0
$741$	34788.5	+	34788.5i	1.72468	+	1.72468i
$742$		0			0
$743$	−9689.52	+	9689.52i	−0.478431	+	0.478431i	−0.904630	−	0.426199i	$-0.859852\pi$
$743$	−9689.52	+	9689.52i	−0.478431	+	0.478431i	0.426199	+	0.904630i	$0.359852\pi$
$744$		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	−0.548126	−	0.836396i	$-0.684659\pi$
$751$	5932.79	−	5932.79i	0.288270	−	0.288270i	0.836396	+	0.548126i	$0.184659\pi$
$752$		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	$-0.924276\pi$
$757$		−	9816.43i		−	0.471313i	0.971836	−	0.235657i	$-0.0757241\pi$
$758$		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	$-0.857169\pi$
$773$		−	18646.5i		−	0.867617i	0.901005	−	0.433809i	$-0.142831\pi$
$774$		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	0.132209	−	0.991222i	$-0.457793\pi$
$787$	24803.2	−	24803.2i	1.12343	−	1.12343i	0.991222	−	0.132209i	$-0.0422071\pi$
$788$		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	$-0.952496\pi$
$797$		−	6690.88i		−	0.297369i	0.988885	−	0.148684i	$-0.0475039\pi$
$798$		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	0.911881	−	0.410454i	$-0.134630\pi$
$809$	11538.0	+	11538.0i	0.501428	+	0.501428i	−0.410454	+	0.911881i	$0.634630\pi$
$810$		0			0
$811$	9955.38	−	9955.38i	0.431049	−	0.431049i	−0.457936	−	0.888985i	$-0.651411\pi$
$811$	9955.38	−	9955.38i	0.431049	−	0.431049i	0.888985	+	0.457936i	$0.151411\pi$
$812$		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	−0.140272	+	0.990113i	$0.544798\pi$
$821$	−26591.4	+	26591.4i	−1.13038	+	1.13038i	−0.990113	+	0.140272i	$0.955202\pi$
$822$		0			0
$823$	9739.31	+	9739.31i	0.412504	+	0.412504i	0.882610	−	0.470106i	$-0.155784\pi$
$823$	9739.31	+	9739.31i	0.412504	+	0.412504i	−0.470106	+	0.882610i	$0.655784\pi$
$824$		0			0
$825$		−	1151.76i		−	0.0486050i
$826$		0			0
$827$	15347.3	+	15347.3i	0.645319	+	0.645319i	0.951858	−	0.306539i	$-0.0991709\pi$
$827$	15347.3	+	15347.3i	0.645319	+	0.645319i	−0.306539	+	0.951858i	$0.599171\pi$
$828$		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	0.232789	−	0.972527i	$-0.425215\pi$
$839$	−17977.2	−	17977.2i	−0.739738	−	0.739738i	−0.972527	+	0.232789i	$0.925215\pi$
$840$		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	−0.578300	−	0.815824i	$-0.696284\pi$
$853$	5917.40	−	5917.40i	0.237524	−	0.237524i	0.815824	+	0.578300i	$0.196284\pi$
$854$		0			0
$855$	−20853.2	+	20853.2i	−0.834111	+	0.834111i
$856$		0			0
$857$	−2391.48	−	2391.48i	−0.0953225	−	0.0953225i	0.657837	−	0.753160i	$-0.271471\pi$
$857$	−2391.48	−	2391.48i	−0.0953225	−	0.0953225i	−0.753160	+	0.657837i	$0.771471\pi$
$858$		0			0
$859$		−	12621.6i		−	0.501331i	−0.968074	−	0.250666i	$-0.919351\pi$
$859$		−	12621.6i		−	0.501331i	0.968074	−	0.250666i	$-0.0806495\pi$
$860$		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	0.978990	+	0.203907i	$0.0653641\pi$
$877$	30721.8	+	30721.8i	1.18290	+	1.18290i	0.203907	+	0.978990i	$0.434636\pi$
$878$		0			0
$879$	30968.2	−	30968.2i	1.18832	−	1.18832i
$880$		0			0
$881$	2080.26	−	2080.26i	0.0795524	−	0.0795524i	−0.666211	−	0.745763i	$-0.732085\pi$
$881$	2080.26	−	2080.26i	0.0795524	−	0.0795524i	0.745763	+	0.666211i	$0.232085\pi$
$882$		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	−0.850322	−	0.526263i	$-0.823593\pi$
$887$	−8560.72	+	8560.72i	−0.324060	+	0.324060i	0.526263	+	0.850322i	$0.323593\pi$
$888$		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	0.389719	−	0.920934i	$-0.372572\pi$
$907$	−14510.4	−	14510.4i	−0.531214	−	0.531214i	−0.920934	+	0.389719i	$0.872572\pi$
$908$		0			0
$909$		−	4303.77i		−	0.157038i
$910$		0			0
$911$	11912.7	+	11912.7i	0.433244	+	0.433244i	0.889730	−	0.456487i	$-0.150892\pi$
$911$	11912.7	+	11912.7i	0.433244	+	0.433244i	−0.456487	+	0.889730i	$0.650892\pi$
$912$		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	0.969512	−	0.245044i	$-0.0788026\pi$
$929$	20513.6	+	20513.6i	0.724467	+	0.724467i	−0.245044	+	0.969512i	$0.578803\pi$
$930$		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	$0.192657\pi$
$937$			32638.3i			1.13794i	−0.822360	+	0.568968i	$0.807343\pi$
$938$		0			0
$939$	44547.0			1.54818
$940$		0			0
$941$	4905.12	+	4905.12i	0.169928	+	0.169928i	0.786948	−	0.617020i	$-0.211660\pi$
$941$	4905.12	+	4905.12i	0.169928	+	0.169928i	−0.617020	+	0.786948i	$0.711660\pi$
$942$		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	−0.326549	−	0.945180i	$-0.605886\pi$
$947$	18028.4	−	18028.4i	0.618631	−	0.618631i	0.945180	+	0.326549i	$0.105886\pi$
$948$		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	$0.0215970\pi$
$967$			4077.37i			0.135594i	−0.997699	+	0.0677970i	$0.978403\pi$
$968$		0			0
$969$	44979.0	−	36573.1i	1.49116	−	1.21248i
$970$		0			0
$971$			30916.5i			1.02179i	0.859644	+	0.510894i	$0.170686\pi$
$971$			30916.5i			1.02179i	−0.859644	+	0.510894i	$0.829314\pi$
$972$		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	$0.178769\pi$
$977$			32526.6i			1.06512i	−0.846394	+	0.532558i	$0.821231\pi$
$978$		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	−0.993315	−	0.115439i	$-0.963172\pi$
$983$	−27056.0	+	27056.0i	−0.877875	+	0.877875i	0.115439	+	0.993315i	$0.463172\pi$
$984$		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	0.320829	−	0.947137i	$-0.396038\pi$
$991$	39556.5	−	39556.5i	1.26797	−	1.26797i	0.947137	−	0.320829i	$-0.103962\pi$
$992$		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	0.981178	−	0.193104i	$-0.0618556\pi$
$997$	24809.0	+	24809.0i	0.788074	+	0.788074i	−0.193104	+	0.981178i	$0.561856\pi$
$998$		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.225.7		14
4.3	odd	2		136.4.k.b.89.1	yes	14
17.13	even	4	inner	272.4.o.f.81.7		14
68.43	odd	8		2312.4.a.l.1.2		14
68.47	odd	4		136.4.k.b.81.1	✓	14
68.59	odd	8		2312.4.a.l.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.1	✓	14	68.47	odd	4
136.4.k.b.89.1	yes	14	4.3	odd	2
272.4.o.f.81.7		14	17.13	even	4	inner
272.4.o.f.225.7		14	1.1	even	1	trivial
2312.4.a.l.1.2		14	68.43	odd	8
2312.4.a.l.1.13		14	68.59	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 $\F_{q}$

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

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