LMFDB - Embedded newform 17.4.b.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, 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:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4669632.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 74x^{2} + 1072 $ x^4 + 74*x^2 + 1072
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.4
Root			$4.44593i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.4.b.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37228 q^{2} +4.44593i q^{3} -2.37228 q^{4} -19.4389i q^{5} +10.5470i q^{6} +14.9929i q^{7} -24.6060 q^{8} +7.23369 q^{9} +O(q^{10})$	\(q+2.37228 q^{2} +4.44593i q^{3} -2.37228 q^{4} -19.4389i q^{5} +10.5470i q^{6} +14.9929i q^{7} -24.6060 q^{8} +7.23369 q^{9} -46.1145i q^{10} +31.1215i q^{11} -10.5470i q^{12} -5.21194 q^{13} +35.5675i q^{14} +86.4239 q^{15} -39.3940 q^{16} +(68.2119 - 16.1286i) q^{17} +17.1603 q^{18} -28.0000 q^{19} +46.1145i q^{20} -66.6576 q^{21} +73.8290i q^{22} -167.194i q^{23} -109.396i q^{24} -252.870 q^{25} -12.3642 q^{26} +152.201i q^{27} -35.5675i q^{28} +136.072i q^{29} +205.022 q^{30} -50.5604i q^{31} +103.394 q^{32} -138.364 q^{33} +(161.818 - 38.2616i) q^{34} +291.446 q^{35} -17.1603 q^{36} -260.558i q^{37} -66.4239 q^{38} -23.1719i q^{39} +478.312i q^{40} +183.225i q^{41} -158.130 q^{42} -348.293 q^{43} -73.8290i q^{44} -140.615i q^{45} -396.630i q^{46} +318.424 q^{47} -175.143i q^{48} +118.212 q^{49} -599.878 q^{50} +(71.7066 + 303.266i) q^{51} +12.3642 q^{52} -408.250 q^{53} +361.063i q^{54} +604.967 q^{55} -368.916i q^{56} -124.486i q^{57} +322.801i q^{58} +108.119 q^{59} -205.022 q^{60} -123.677i q^{61} -119.943i q^{62} +108.454i q^{63} +560.432 q^{64} +101.314i q^{65} -328.239 q^{66} -243.826 q^{67} +(-161.818 + 38.2616i) q^{68} +743.331 q^{69} +691.391 q^{70} +42.7075i q^{71} -177.992 q^{72} +875.172i q^{73} -618.117i q^{74} -1124.24i q^{75} +66.4239 q^{76} -466.603 q^{77} -54.9703i q^{78} +750.553i q^{79} +765.775i q^{80} -481.364 q^{81} +434.662i q^{82} -472.728 q^{83} +158.130 q^{84} +(-313.522 - 1325.96i) q^{85} -826.250 q^{86} -604.967 q^{87} -765.775i q^{88} +376.364 q^{89} -333.578i q^{90} -78.1422i q^{91} +396.630i q^{92} +224.788 q^{93} +755.391 q^{94} +544.288i q^{95} +459.683i q^{96} -303.169i q^{97} +280.432 q^{98} +225.123i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9	$ 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9} + 140 q^{13} + 24 q^{15} - 238 q^{16} + 112 q^{17} + 218 q^{18} - 112 q^{19} + 124 q^{21} - 460 q^{25} - 532 q^{26} + 912 q^{30} + 494 q^{32} - 1036 q^{33} + 406 q^{34} + 936 q^{35} - 218 q^{36} + 56 q^{38} - 1184 q^{42} - 520 q^{43} + 952 q^{47} + 312 q^{49} - 1354 q^{50} + 1160 q^{51} + 532 q^{52} - 576 q^{53} + 168 q^{55} - 1176 q^{59} - 912 q^{60} + 1426 q^{64} + 1904 q^{66} - 240 q^{67} - 406 q^{68} + 1204 q^{69} + 192 q^{70} - 1206 q^{72} - 56 q^{76} + 868 q^{77} - 2408 q^{81} - 2856 q^{83} + 1184 q^{84} + 768 q^{85} - 2248 q^{86} - 168 q^{87} + 1988 q^{89} + 1060 q^{93} + 448 q^{94} + 306 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9 + 140 * q^13 + 24 * q^15 - 238 * q^16 + 112 * q^17 + 218 * q^18 - 112 * q^19 + 124 * q^21 - 460 * q^25 - 532 * q^26 + 912 * q^30 + 494 * q^32 - 1036 * q^33 + 406 * q^34 + 936 * q^35 - 218 * q^36 + 56 * q^38 - 1184 * q^42 - 520 * q^43 + 952 * q^47 + 312 * q^49 - 1354 * q^50 + 1160 * q^51 + 532 * q^52 - 576 * q^53 + 168 * q^55 - 1176 * q^59 - 912 * q^60 + 1426 * q^64 + 1904 * q^66 - 240 * q^67 - 406 * q^68 + 1204 * q^69 + 192 * q^70 - 1206 * q^72 - 56 * q^76 + 868 * q^77 - 2408 * q^81 - 2856 * q^83 + 1184 * q^84 + 768 * q^85 - 2248 * q^86 - 168 * q^87 + 1988 * q^89 + 1060 * q^93 + 448 * q^94 + 306 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.37228			0.838728			0.419364	−	0.907818i	$-0.362253\pi$
$2$	2.37228			0.838728			0.419364	+	0.907818i	$0.362253\pi$
$3$			4.44593i			0.855620i	0.903869	+	0.427810i	$0.140715\pi$
$3$			4.44593i			0.855620i	−0.903869	+	0.427810i	$0.859285\pi$
$4$	−2.37228			−0.296535
$5$		−	19.4389i		−	1.73867i	−0.494228	−	0.869333i	$-0.664549\pi$
$5$		−	19.4389i		−	1.73867i	0.494228	−	0.869333i	$-0.335451\pi$
$6$			10.5470i			0.717633i
$7$			14.9929i			0.809542i	0.914418	+	0.404771i	$0.132649\pi$
$7$			14.9929i			0.809542i	−0.914418	+	0.404771i	$0.867351\pi$
$8$	−24.6060			−1.08744
$9$	7.23369			0.267914
$10$		−	46.1145i		−	1.45827i
$11$			31.1215i			0.853045i	0.904477	+	0.426522i	$0.140261\pi$
$11$			31.1215i			0.853045i	−0.904477	+	0.426522i	$0.859739\pi$
$12$		−	10.5470i		−	0.253721i
$13$	−5.21194			−0.111195			−0.0555974	−	0.998453i	$-0.517706\pi$
$13$	−5.21194			−0.111195			−0.0555974	+	0.998453i	$0.517706\pi$
$14$			35.5675i			0.678986i
$15$	86.4239			1.48764
$16$	−39.3940			−0.615532
$17$	68.2119	−	16.1286i	0.973166	−	0.230103i
$17$	68.2119	−	16.1286i	0.973166	−	0.230103i
$18$	17.1603			0.224707
$19$	−28.0000			−0.338086			−0.169043	−	0.985609i	$-0.554068\pi$
$19$	−28.0000			−0.338086			−0.169043	+	0.985609i	$0.554068\pi$
$20$			46.1145i			0.515575i
$21$	−66.6576			−0.692661
$22$			73.8290i			0.715473i
$23$		−	167.194i		−	1.51575i	−0.652399	−	0.757875i	$-0.726237\pi$
$23$		−	167.194i		−	1.51575i	0.652399	−	0.757875i	$-0.273763\pi$
$24$		−	109.396i		−	0.930436i
$25$	−252.870			−2.02296
$26$	−12.3642			−0.0932622
$27$			152.201i			1.08485i
$28$		−	35.5675i		−	0.240058i
$29$			136.072i			0.871309i	0.900114	+	0.435654i	$0.143483\pi$
$29$			136.072i			0.871309i	−0.900114	+	0.435654i	$0.856517\pi$
$30$	205.022			1.24772
$31$		−	50.5604i		−	0.292933i	−0.989216	−	0.146466i	$-0.953210\pi$
$31$		−	50.5604i		−	0.292933i	0.989216	−	0.146466i	$-0.0467900\pi$
$32$	103.394			0.571177
$33$	−138.364			−0.729882
$34$	161.818	−	38.2616i	0.816222	−	0.192994i
$35$	291.446			1.40752
$36$	−17.1603			−0.0794460
$37$		−	260.558i		−	1.15772i	−0.815428	−	0.578858i	$-0.803499\pi$
$37$		−	260.558i		−	1.15772i	0.815428	−	0.578858i	$-0.196501\pi$
$38$	−66.4239			−0.283563
$39$		−	23.1719i		−	0.0951404i
$40$			478.312i			1.89069i
$41$			183.225i			0.697927i	0.937136	+	0.348964i	$0.113466\pi$
$41$			183.225i			0.697927i	−0.937136	+	0.348964i	$0.886534\pi$
$42$	−158.130			−0.580954
$43$	−348.293			−1.23521			−0.617607	−	0.786486i	$-0.711898\pi$
$43$	−348.293			−1.23521			−0.617607	+	0.786486i	$0.711898\pi$
$44$		−	73.8290i		−	0.252958i
$45$		−	140.615i		−	0.465813i
$46$		−	396.630i		−	1.27130i
$47$	318.424			0.988232			0.494116	−	0.869396i	$-0.335492\pi$
$47$	318.424			0.988232			0.494116	+	0.869396i	$0.335492\pi$
$48$		−	175.143i		−	0.526661i
$49$	118.212			0.344641
$50$	−599.878			−1.69671
$51$	71.7066	+	303.266i	0.196881	+	0.832660i
$52$	12.3642			0.0329732
$53$	−408.250			−1.05806			−0.529032	−	0.848602i	$-0.677445\pi$
$53$	−408.250			−1.05806			−0.529032	+	0.848602i	$0.677445\pi$
$54$			361.063i			0.909897i
$55$	604.967			1.48316
$56$		−	368.916i		−	0.880329i
$57$		−	124.486i		−	0.289273i
$58$			322.801i			0.730791i
$59$	108.119			0.238575			0.119288	−	0.992860i	$-0.461939\pi$
$59$	108.119			0.238575			0.119288	+	0.992860i	$0.461939\pi$
$60$	−205.022			−0.441137
$61$		−	123.677i		−	0.259593i	−0.991541	−	0.129796i	$-0.958568\pi$
$61$		−	123.677i		−	0.259593i	0.991541	−	0.129796i	$-0.0414324\pi$
$62$		−	119.943i		−	0.245691i
$63$			108.454i			0.216888i
$64$	560.432			1.09459
$65$			101.314i			0.193330i
$66$	−328.239			−0.612173
$67$	−243.826			−0.444598			−0.222299	−	0.974979i	$-0.571356\pi$
$67$	−243.826			−0.444598			−0.222299	+	0.974979i	$0.571356\pi$
$68$	−161.818	+	38.2616i	−0.288578	+	0.0682338i
$69$	743.331			1.29691
$70$	691.391			1.18053
$71$			42.7075i			0.0713866i	0.999363	+	0.0356933i	$0.0113639\pi$
$71$			42.7075i			0.0713866i	−0.999363	+	0.0356933i	$0.988636\pi$
$72$	−177.992			−0.291341
$73$			875.172i			1.40317i	0.712588	+	0.701583i	$0.247523\pi$
$73$			875.172i			1.40317i	−0.712588	+	0.701583i	$0.752477\pi$
$74$		−	618.117i		−	0.971009i
$75$		−	1124.24i		−	1.73088i
$76$	66.4239			0.100254
$77$	−466.603			−0.690576
$78$		−	54.9703i		−	0.0797970i
$79$			750.553i			1.06891i	0.845197	+	0.534454i	$0.179483\pi$
$79$			750.553i			1.06891i	−0.845197	+	0.534454i	$0.820517\pi$
$80$			765.775i			1.07020i
$81$	−481.364			−0.660308
$82$			434.662i			0.585371i
$83$	−472.728			−0.625165			−0.312582	−	0.949891i	$-0.601194\pi$
$83$	−472.728			−0.625165			−0.312582	+	0.949891i	$0.601194\pi$
$84$	158.130			0.205398
$85$	−313.522	−	1325.96i	−0.400073	−	1.69201i
$86$	−826.250			−1.03601
$87$	−604.967			−0.745509
$88$		−	765.775i		−	0.927635i
$89$	376.364			0.448253			0.224127	−	0.974560i	$-0.428047\pi$
$89$	376.364			0.448253			0.224127	+	0.974560i	$0.428047\pi$
$90$		−	333.578i		−	0.390691i
$91$		−	78.1422i		−	0.0900169i
$92$			396.630i			0.449473i
$93$	224.788			0.250639
$94$	755.391			0.828858
$95$			544.288i			0.587819i
$96$			459.683i			0.488710i
$97$		−	303.169i		−	0.317342i	−0.987332	−	0.158671i	$-0.949279\pi$
$97$		−	303.169i		−	0.317342i	0.987332	−	0.158671i	$-0.0507209\pi$
$98$	280.432			0.289060
$99$			225.123i			0.228543i
$100$	599.878			0.599878
$101$	1484.72			1.46273			0.731363	−	0.681988i	$-0.238884\pi$
$101$	1484.72			1.46273			0.731363	+	0.681988i	$0.238884\pi$
$102$	170.108	+	719.431i	0.165130	+	0.698376i
$103$	−168.000			−0.160714			−0.0803570	−	0.996766i	$-0.525606\pi$
$103$	−168.000			−0.160714			−0.0803570	+	0.996766i	$0.525606\pi$
$104$	128.245			0.120918
$105$			1295.75i			1.20430i
$106$	−968.484			−0.887429
$107$		−	1096.53i		−	0.990703i	−0.868693	−	0.495351i	$-0.835039\pi$
$107$		−	1096.53i		−	0.990703i	0.868693	−	0.495351i	$-0.164961\pi$
$108$		−	361.063i		−	0.321697i
$109$			828.018i			0.727613i	0.931475	+	0.363806i	$0.118523\pi$
$109$			828.018i			0.727613i	−0.931475	+	0.363806i	$0.881477\pi$
$110$	1435.15			1.24397
$111$	1158.42			0.990565
$112$		−	590.632i		−	0.498299i
$113$		−	1711.01i		−	1.42441i	−0.701973	−	0.712204i	$-0.747697\pi$
$113$		−	1711.01i		−	1.42441i	0.701973	−	0.712204i	$-0.252303\pi$
$114$		−	295.316i		−	0.242622i
$115$	−3250.05			−2.63538
$116$		−	322.801i		−	0.258374i
$117$	−37.7015			−0.0297907
$118$	256.490			0.200100
$119$	241.815	+	1022.70i	0.186278	+	0.787819i
$120$	−2126.54			−1.61772
$121$	362.451			0.272315
$122$		−	293.396i		−	0.217728i
$123$	−814.608			−0.597160
$124$			119.943i			0.0868649i
$125$			2485.64i			1.77858i
$126$			257.284i			0.181910i
$127$	−1131.46			−0.790555			−0.395277	−	0.918562i	$-0.629352\pi$
$127$	−1131.46			−0.790555			−0.395277	+	0.918562i	$0.629352\pi$
$128$	502.350			0.346890
$129$		−	1548.49i		−	1.05687i
$130$			240.346i			0.162152i
$131$		−	1525.41i		−	1.01737i	−0.860952	−	0.508687i	$-0.830131\pi$
$131$		−	1525.41i		−	1.01737i	0.860952	−	0.508687i	$-0.169869\pi$
$132$	328.239			0.216436
$133$		−	419.802i		−	0.273695i
$134$	−578.424			−0.372897
$135$	2958.61			1.88620
$136$	−1678.42	+	396.860i	−1.05826	+	0.250224i
$137$	430.495			0.268465			0.134232	−	0.990950i	$-0.457143\pi$
$137$	430.495			0.268465			0.134232	+	0.990950i	$0.457143\pi$
$138$	1763.39			1.08775
$139$		−	1073.93i		−	0.655323i	−0.944795	−	0.327662i	$-0.893739\pi$
$139$		−	1073.93i		−	0.655323i	0.944795	−	0.327662i	$-0.106261\pi$
$140$	−691.391			−0.417380
$141$			1415.69i			0.845551i
$142$			101.314i			0.0598739i
$143$		−	162.203i		−	0.0948541i
$144$	−284.964			−0.164910
$145$	2645.09			1.51491
$146$			2076.15i			1.17687i
$147$			525.562i			0.294882i
$148$			618.117i			0.343304i
$149$	−1821.57			−1.00153			−0.500767	−	0.865582i	$-0.666948\pi$
$149$	−1821.57			−1.00153			−0.500767	+	0.865582i	$0.666948\pi$
$150$		−	2667.02i		−	1.45174i
$151$	150.608			0.0811676			0.0405838	−	0.999176i	$-0.487078\pi$
$151$	150.608			0.0811676			0.0405838	+	0.999176i	$0.487078\pi$
$152$	688.967			0.367649
$153$	493.424	−	116.669i	0.260725	−	0.0616480i
$154$	−1106.91			−0.579205
$155$	−982.837			−0.509312
$156$			54.9703i			0.0282125i
$157$	1457.75			0.741026			0.370513	−	0.928827i	$-0.379182\pi$
$157$	1457.75			0.741026			0.370513	+	0.928827i	$0.379182\pi$
$158$			1780.52i			0.896524i
$159$		−	1815.05i		−	0.905301i
$160$		−	2009.86i		−	0.993085i
$161$	2506.72			1.22706
$162$	−1141.93			−0.553818
$163$			2573.11i			1.23645i	0.786001	+	0.618225i	$0.212148\pi$
$163$			2573.11i			1.23645i	−0.786001	+	0.618225i	$0.787852\pi$
$164$		−	434.662i		−	0.206960i
$165$			2689.64i			1.26902i
$166$	−1121.44			−0.524343
$167$			1563.48i			0.724466i	0.932088	+	0.362233i	$0.117986\pi$
$167$			1563.48i			0.724466i	−0.932088	+	0.362233i	$0.882014\pi$
$168$	1640.17			0.753227
$169$	−2169.84			−0.987636
$170$	−743.761	−	3145.56i	−0.335552	−	1.41914i
$171$	−202.543			−0.0905782
$172$	826.250			0.366285
$173$		−	340.850i		−	0.149794i	−0.997191	−	0.0748970i	$-0.976137\pi$
$173$		−	340.850i		−	0.149794i	0.997191	−	0.0748970i	$-0.0238628\pi$
$174$	−1435.15			−0.625279
$175$		−	3791.26i		−	1.63767i
$176$		−	1226.00i		−	0.525076i
$177$			480.691i			0.204130i
$178$	892.842			0.375962
$179$	−1674.72			−0.699297			−0.349649	−	0.936881i	$-0.613699\pi$
$179$	−1674.72			−0.699297			−0.349649	+	0.936881i	$0.613699\pi$
$180$			333.578i			0.138130i
$181$		−	1178.76i		−	0.484071i	−0.970267	−	0.242035i	$-0.922185\pi$
$181$		−	1178.76i		−	0.484071i	0.970267	−	0.242035i	$-0.0778150\pi$
$182$		−	185.375i		−	0.0754997i
$183$	549.857			0.222113
$184$			4113.96i			1.64829i
$185$	−5064.96			−2.01288
$186$	533.261			0.210218
$187$	501.946	+	2122.86i	0.196289	+	0.830154i
$188$	−755.391			−0.293045
$189$	−2281.93			−0.878234
$190$			1291.20i			0.493020i
$191$	3686.60			1.39661			0.698306	−	0.715799i	$-0.253938\pi$
$191$	3686.60			1.39661			0.698306	+	0.715799i	$0.253938\pi$
$192$			2491.64i			0.936556i
$193$		−	1499.75i		−	0.559350i	−0.960095	−	0.279675i	$-0.909773\pi$
$193$		−	1499.75i		−	0.559350i	0.960095	−	0.279675i	$-0.0902267\pi$
$194$		−	719.202i		−	0.266163i
$195$	−450.436			−0.165417
$196$	−280.432			−0.102198
$197$		−	4359.97i		−	1.57683i	−0.615145	−	0.788414i	$-0.710902\pi$
$197$		−	4359.97i		−	1.57683i	0.615145	−	0.788414i	$-0.289098\pi$
$198$			534.056i			0.191685i
$199$		−	473.286i		−	0.168595i	−0.996441	−	0.0842974i	$-0.973135\pi$
$199$		−	473.286i		−	0.168595i	0.996441	−	0.0842974i	$-0.0268646\pi$
$200$	6222.10			2.19984
$201$		−	1084.03i		−	0.380407i
$202$	3522.18			1.22683
$203$	−2040.12			−0.705361
$204$	−170.108	−	719.431i	−0.0583822	−	0.246913i
$205$	3561.70			1.21346
$206$	−398.543			−0.134795
$207$		−	1209.43i		−	0.406091i
$208$	205.319			0.0684439
$209$		−	871.403i		−	0.288403i
$210$			3073.88i			1.01008i
$211$			4192.78i			1.36798i	0.729493	+	0.683988i	$0.239756\pi$
$211$			4192.78i			1.36798i	−0.729493	+	0.683988i	$0.760244\pi$
$212$	968.484			0.313753
$213$	−189.875			−0.0610798
$214$		−	2601.27i		−	0.830930i
$215$			6770.43i			2.14763i
$216$		−	3745.04i		−	1.17971i
$217$	758.049			0.237141
$218$			1964.29i			0.610269i
$219$	−3890.95			−1.20058
$220$	−1435.15			−0.439809
$221$	−355.516	+	84.0612i	−0.108211	+	0.0255863i
$222$	2748.11			0.830815
$223$	3017.07			0.906001			0.453001	−	0.891510i	$-0.350354\pi$
$223$	3017.07			0.906001			0.453001	+	0.891510i	$0.350354\pi$
$224$			1550.18i			0.462392i
$225$	−1829.18			−0.541979
$226$		−	4058.99i		−	1.19469i
$227$			535.758i			0.156650i	0.996928	+	0.0783250i	$0.0249572\pi$
$227$			535.758i			0.156650i	−0.996928	+	0.0783250i	$0.975043\pi$
$228$			295.316i			0.0857797i
$229$	−4029.45			−1.16277			−0.581383	−	0.813630i	$-0.697488\pi$
$229$	−4029.45			−1.16277			−0.581383	+	0.813630i	$0.697488\pi$
$230$	−7710.04			−2.21037
$231$		−	2074.49i		−	0.590871i
$232$		−	3348.18i		−	0.947496i
$233$		−	1415.69i		−	0.398047i	−0.979995	−	0.199024i	$-0.936223\pi$
$233$		−	1415.69i		−	0.398047i	0.979995	−	0.199024i	$-0.0637770\pi$
$234$	−89.4387			−0.0249863
$235$		−	6189.80i		−	1.71820i
$236$	−256.490			−0.0707460
$237$	−3336.91			−0.914580
$238$	573.653	+	2426.13i	0.156237	+	0.660766i
$239$	3584.18			0.970049			0.485024	−	0.874501i	$-0.338811\pi$
$239$	3584.18			0.970049			0.485024	+	0.874501i	$0.338811\pi$
$240$	−3404.58			−0.915688
$241$			6042.91i			1.61518i	0.589744	+	0.807590i	$0.299228\pi$
$241$			6042.91i			1.61518i	−0.589744	+	0.807590i	$0.700772\pi$
$242$	859.835			0.228398
$243$			1969.31i			0.519881i
$244$			293.396i			0.0769784i
$245$		−	2297.91i		−	0.599216i
$246$	−1932.48			−0.500855
$247$	145.934			0.0375934
$248$			1244.09i			0.318547i
$249$		−	2101.72i		−	0.534904i
$250$			5896.63i			1.49174i
$251$	5801.33			1.45887			0.729435	−	0.684050i	$-0.239783\pi$
$251$	5801.33			1.45887			0.729435	+	0.684050i	$0.239783\pi$
$252$		−	257.284i		−	0.0643149i
$253$	5203.32			1.29300
$254$	−2684.13			−0.663061
$255$	5895.14	−	1393.90i	1.44772	−	0.342310i
$256$	−3291.74			−0.803647
$257$	−2865.09			−0.695407			−0.347703	−	0.937605i	$-0.613038\pi$
$257$	−2865.09			−0.695407			−0.347703	+	0.937605i	$0.613038\pi$
$258$		−	3673.45i		−	0.886430i
$259$	3906.53			0.937220
$260$		−	240.346i		−	0.0573293i
$261$			984.303i			0.233436i
$262$		−	3618.71i		−	0.853300i
$263$	542.066			0.127092			0.0635460	−	0.997979i	$-0.479759\pi$
$263$	542.066			0.127092			0.0635460	+	0.997979i	$0.479759\pi$
$264$	3404.58			0.793703
$265$			7935.91i			1.83962i
$266$		−	995.889i		−	0.229556i
$267$			1673.29i			0.383534i
$268$	578.424			0.131839
$269$			1759.85i			0.398885i	0.979910	+	0.199442i	$0.0639131\pi$
$269$			1759.85i			0.398885i	−0.979910	+	0.199442i	$0.936087\pi$
$270$	7018.65			1.58201
$271$	−3596.70			−0.806215			−0.403107	−	0.915153i	$-0.632070\pi$
$271$	−3596.70			−0.806215			−0.403107	+	0.915153i	$0.632070\pi$
$272$	−2687.14	+	635.370i	−0.599015	+	0.141636i
$273$	347.415			0.0770202
$274$	1021.25			0.225169
$275$		−	7869.68i		−	1.72567i
$276$	−1763.39			−0.384578
$277$			4539.43i			0.984649i	0.870412	+	0.492325i	$0.163853\pi$
$277$			4539.43i			0.984649i	−0.870412	+	0.492325i	$0.836147\pi$
$278$		−	2547.67i		−	0.549638i
$279$		−	365.738i		−	0.0784809i
$280$	−7171.30			−1.53060
$281$	1838.52			0.390309			0.195155	−	0.980772i	$-0.437479\pi$
$281$	1838.52			0.390309			0.195155	+	0.980772i	$0.437479\pi$
$282$			3358.42i			0.709187i
$283$		−	3934.41i		−	0.826418i	−0.910636	−	0.413209i	$-0.864408\pi$
$283$		−	3934.41i		−	0.826418i	0.910636	−	0.413209i	$-0.135592\pi$
$284$		−	101.314i		−	0.0211686i
$285$	−2419.87			−0.502950
$286$		−	384.792i		−	0.0795568i
$287$	−2747.09			−0.565002
$288$	747.920			0.153026
$289$	4392.74	−	2200.32i	0.894105	−	0.447858i
$290$	6274.89			1.27060
$291$	1347.87			0.271524
$292$		−	2076.15i		−	0.416088i
$293$	−4739.91			−0.945080			−0.472540	−	0.881309i	$-0.656663\pi$
$293$	−4739.91			−0.945080			−0.472540	+	0.881309i	$0.656663\pi$
$294$			1246.78i			0.247326i
$295$		−	2101.72i		−	0.414803i
$296$			6411.29i			1.25895i
$297$	−4736.72			−0.925428
$298$	−4321.26			−0.840014
$299$			871.403i			0.168544i
$300$			2667.02i			0.513267i
$301$		−	5221.94i		−	0.999959i
$302$	357.285			0.0680776
$303$			6600.97i			1.25154i
$304$	1103.03			0.208103
$305$	−2404.13			−0.451345
$306$	1170.54	−	276.772i	0.218678	−	0.0517059i
$307$	−4965.81			−0.923173			−0.461586	−	0.887095i	$-0.652720\pi$
$307$	−4965.81			−0.923173			−0.461586	+	0.887095i	$0.652720\pi$
$308$	1106.91			0.204780
$309$		−	746.917i		−	0.137510i
$310$	−2331.57			−0.427174
$311$			6039.28i			1.10114i	0.834787	+	0.550572i	$0.185591\pi$
$311$			6039.28i			1.10114i	−0.834787	+	0.550572i	$0.814409\pi$
$312$			570.168i			0.103460i
$313$		−	6495.68i		−	1.17303i	−0.809940	−	0.586513i	$-0.800500\pi$
$313$		−	6495.68i		−	1.17303i	0.809940	−	0.586513i	$-0.199500\pi$
$314$	3458.19			0.621519
$315$	2108.23			0.377096
$316$		−	1780.52i		−	0.316969i
$317$		−	3036.97i		−	0.538086i	−0.963128	−	0.269043i	$-0.913293\pi$
$317$		−	3036.97i		−	0.538086i	0.963128	−	0.269043i	$-0.0867074\pi$
$318$		−	4305.81i		−	0.759302i
$319$	−4234.77			−0.743265
$320$		−	10894.2i		−	1.90313i
$321$	4875.08			0.847665
$322$	5946.65			1.02917
$323$	−1909.93	+	451.601i	−0.329014	+	0.0777948i
$324$	1141.93			0.195804
$325$	1317.94			0.224942
$326$			6104.13i			1.03704i
$327$	−3681.31			−0.622560
$328$		−	4508.44i		−	0.758954i
$329$			4774.11i			0.800015i
$330$			6380.59i			1.06436i
$331$	−7769.51			−1.29018			−0.645092	−	0.764105i	$-0.723181\pi$
$331$	−7769.51			−1.29018			−0.645092	+	0.764105i	$0.723181\pi$
$332$	1121.44			0.185383
$333$		−	1884.80i		−	0.310169i
$334$			3709.02i			0.607630i
$335$			4739.70i			0.773008i
$336$	2625.91			0.426355
$337$			6053.47i			0.978498i	0.872144	+	0.489249i	$0.162729\pi$
$337$			6053.47i			0.978498i	−0.872144	+	0.489249i	$0.837271\pi$
$338$	−5147.46			−0.828358
$339$	7607.02			1.21875
$340$	743.761	+	3145.56i	0.118636	+	0.501740i
$341$	1573.52			0.249885
$342$	−480.490			−0.0759705
$343$			6914.92i			1.08854i
$344$	8570.10			1.34322
$345$		−	14449.5i		−	2.25489i
$346$		−	808.593i		−	0.125636i
$347$		−	336.418i		−	0.0520457i	−0.999661	−	0.0260228i	$-0.991716\pi$
$347$		−	336.418i		−	0.0520457i	0.999661	−	0.0260228i	$-0.00828426\pi$
$348$	1435.15			0.221070
$349$	8360.05			1.28224			0.641122	−	0.767439i	$-0.278469\pi$
$349$	8360.05			1.28224			0.641122	+	0.767439i	$0.278469\pi$
$350$		−	8993.93i		−	1.37356i
$351$		−	793.260i		−	0.120630i
$352$			3217.78i			0.487239i
$353$	2040.04			0.307593			0.153797	−	0.988103i	$-0.450850\pi$
$353$	2040.04			0.307593			0.153797	+	0.988103i	$0.450850\pi$
$354$			1140.34i			0.171209i
$355$	830.185			0.124117
$356$	−892.842			−0.132923
$357$	−4546.84	+	1075.09i	−0.674074	+	0.159384i
$358$	−3972.90			−0.586520
$359$	−594.357			−0.0873788			−0.0436894	−	0.999045i	$-0.513911\pi$
$359$	−594.357			−0.0873788			−0.0436894	+	0.999045i	$0.513911\pi$
$360$			3459.96i			0.506544i
$361$	−6075.00			−0.885698
$362$		−	2796.36i		−	0.406004i
$363$			1611.43i			0.232998i
$364$			185.375i			0.0266932i
$365$	17012.3			2.43964
$366$	1304.42			0.186292
$367$		−	11557.1i		−	1.64381i	−0.569628	−	0.821903i	$-0.692913\pi$
$367$		−	11557.1i		−	1.64381i	0.569628	−	0.821903i	$-0.307087\pi$
$368$			6586.43i			0.932993i
$369$			1325.40i			0.186985i
$370$	−12015.5			−1.68826
$371$		−	6120.86i		−	0.856548i
$372$	−533.261			−0.0743233
$373$	154.375			0.0214296			0.0107148	−	0.999943i	$-0.496589\pi$
$373$	154.375			0.0214296			0.0107148	+	0.999943i	$0.496589\pi$
$374$	1190.76	+	5036.02i	0.164633	+	0.696274i
$375$	−11051.0			−1.52179
$376$	−7835.13			−1.07464
$377$		−	709.199i		−	0.0968849i
$378$	−5413.39			−0.736600
$379$			8975.51i			1.21647i	0.793758	+	0.608234i	$0.208122\pi$
$379$			8975.51i			1.21647i	−0.793758	+	0.608234i	$0.791878\pi$
$380$		−	1291.20i		−	0.174309i
$381$		−	5030.38i		−	0.676415i
$382$	8745.65			1.17138
$383$	−14032.7			−1.87216			−0.936081	−	0.351784i	$-0.885575\pi$
$383$	−14032.7			−1.87216			−0.936081	+	0.351784i	$0.885575\pi$
$384$			2233.41i			0.296806i
$385$			9070.23i			1.20068i
$386$		−	3557.83i		−	0.469142i
$387$	−2519.45			−0.330932
$388$			719.202i			0.0941030i
$389$	−11432.1			−1.49006			−0.745029	−	0.667032i	$-0.767564\pi$
$389$	−11432.1			−1.49006			−0.745029	+	0.667032i	$0.767564\pi$
$390$	−1068.56			−0.138740
$391$	−2696.60	−	11404.6i	−0.348779	−	1.47508i
$392$	−2908.72			−0.374777
$393$	6781.88			0.870486
$394$		−	10343.1i		−	1.32253i
$395$	14589.9			1.85847
$396$		−	534.056i		−	0.0677710i
$397$		−	1261.59i		−	0.159490i	−0.996815	−	0.0797450i	$-0.974589\pi$
$397$		−	1261.59i		−	0.159490i	0.996815	−	0.0797450i	$-0.0254106\pi$
$398$		−	1122.77i		−	0.141405i
$399$	1866.41			0.234179
$400$	9961.55			1.24519
$401$			14316.4i			1.78286i	0.453158	+	0.891430i	$0.350297\pi$
$401$			14316.4i			1.78286i	−0.453158	+	0.891430i	$0.649703\pi$
$402$		−	2571.63i		−	0.319058i
$403$			263.518i			0.0325726i
$404$	−3522.18			−0.433750
$405$			9357.17i			1.14805i
$406$	−4839.74			−0.591606
$407$	8108.97			0.987584
$408$	−1764.41	−	7462.15i	−0.214096	−	0.905469i
$409$	6819.29			0.824431			0.412215	−	0.911086i	$-0.364755\pi$
$409$	6819.29			0.824431			0.412215	+	0.911086i	$0.364755\pi$
$410$	8449.34			1.01776
$411$			1913.95i			0.229704i
$412$	398.543			0.0476573
$413$			1621.03i			0.193137i
$414$		−	2869.10i		−	0.340600i
$415$			9189.30i			1.08695i
$416$	−538.883			−0.0635118
$417$	4774.64			0.560708
$418$		−	2067.21i		−	0.241892i
$419$		−	11987.4i		−	1.39767i	−0.715282	−	0.698836i	$-0.753702\pi$
$419$		−	11987.4i		−	1.39767i	0.715282	−	0.698836i	$-0.246298\pi$
$420$		−	3073.88i		−	0.357119i
$421$	8307.55			0.961722			0.480861	−	0.876797i	$-0.340324\pi$
$421$	8307.55			0.961722			0.480861	+	0.876797i	$0.340324\pi$
$422$			9946.45i			1.14736i
$423$	2303.38			0.264762
$424$	10045.4			1.15058
$425$	−17248.7	+	4078.43i	−1.96867	+	0.465489i
$426$	−450.436			−0.0512293
$427$	1854.27			0.210151
$428$			2601.27i			0.293778i
$429$	721.146			0.0811591
$430$			16061.4i			1.80127i
$431$		−	14582.2i		−	1.62970i	−0.579673	−	0.814849i	$-0.696820\pi$
$431$		−	14582.2i		−	1.62970i	0.579673	−	0.814849i	$-0.303180\pi$
$432$		−	5995.80i		−	0.667761i
$433$	14056.3			1.56006			0.780028	−	0.625744i	$-0.215205\pi$
$433$	14056.3			1.56006			0.780028	+	0.625744i	$0.215205\pi$
$434$	1798.30			0.198897
$435$			11759.9i			1.29619i
$436$		−	1964.29i		−	0.215763i
$437$			4681.42i			0.512455i
$438$	−9230.44			−1.00696
$439$		−	11386.3i		−	1.23790i	−0.785431	−	0.618950i	$-0.787559\pi$
$439$		−	11386.3i		−	1.23790i	0.785431	−	0.618950i	$-0.212441\pi$
$440$	−14885.8			−1.61285
$441$	855.108			0.0923343
$442$	−843.385	+	199.417i	−0.0907596	+	0.0214599i
$443$	−11695.6			−1.25435			−0.627173	−	0.778880i	$-0.715788\pi$
$443$	−11695.6			−1.25435			−0.627173	+	0.778880i	$0.715788\pi$
$444$	−2748.11			−0.293737
$445$		−	7316.09i		−	0.779362i
$446$	7157.35			0.759889
$447$		−	8098.55i		−	0.856932i
$448$			8402.52i			0.886120i
$449$		−	5124.39i		−	0.538608i	−0.963055	−	0.269304i	$-0.913206\pi$
$449$		−	5124.39i		−	0.538608i	0.963055	−	0.269304i	$-0.0867937\pi$
$450$	−4339.33			−0.454573
$451$	−5702.26			−0.595363
$452$			4058.99i			0.422387i
$453$			669.593i			0.0694486i
$454$			1270.97i			0.131387i
$455$	−1519.00			−0.156509
$456$			3063.10i			0.314568i
$457$	6346.71			0.649643			0.324821	−	0.945775i	$-0.394696\pi$
$457$	6346.71			0.649643			0.324821	+	0.945775i	$0.394696\pi$
$458$	−9558.99			−0.975245
$459$	2454.78	+	10381.9i	0.249628	+	1.05574i
$460$	7710.04			0.781484
$461$	−4564.08			−0.461107			−0.230553	−	0.973060i	$-0.574054\pi$
$461$	−4564.08			−0.461107			−0.230553	+	0.973060i	$0.574054\pi$
$462$		−	4921.26i		−	0.495580i
$463$	−13669.2			−1.37206			−0.686028	−	0.727575i	$-0.740647\pi$
$463$	−13669.2			−1.37206			−0.686028	+	0.727575i	$0.740647\pi$
$464$		−	5360.43i		−	0.536318i
$465$		−	4369.62i		−	0.435777i
$466$		−	3358.42i		−	0.333853i
$467$	7042.76			0.697859			0.348929	−	0.937149i	$-0.386545\pi$
$467$	7042.76			0.697859			0.348929	+	0.937149i	$0.386545\pi$
$468$	89.4387			0.00883398
$469$		−	3655.67i		−	0.359921i
$470$		−	14683.9i		−	1.44111i
$471$			6481.05i			0.634037i
$472$	−2660.38			−0.259436
$473$		−	10839.4i		−	1.05369i
$474$	−7916.08			−0.767084
$475$	7080.35			0.683934
$476$	−573.653	−	2426.13i	−0.0552381	−	0.233616i
$477$	−2953.15			−0.283471
$478$	8502.69			0.813607
$479$			6350.78i			0.605793i	0.953024	+	0.302896i	$0.0979536\pi$
$479$			6350.78i			0.605793i	−0.953024	+	0.302896i	$0.902046\pi$
$480$	8935.71			0.849703
$481$			1358.01i			0.128732i
$482$			14335.5i			1.35470i
$483$			11144.7i			1.04990i
$484$	−859.835			−0.0807508
$485$	−5893.26			−0.551751
$486$			4671.75i			0.436038i
$487$			10100.7i			0.939849i	0.882706	+	0.469925i	$0.155719\pi$
$487$			10100.7i			0.939849i	−0.882706	+	0.469925i	$0.844281\pi$
$488$			3043.18i			0.282292i
$489$	−11439.9			−1.05793
$490$		−	5451.28i		−	0.502579i
$491$	11896.0			1.09340			0.546699	−	0.837329i	$-0.315884\pi$
$491$	11896.0			1.09340			0.546699	+	0.837329i	$0.315884\pi$
$492$	1932.48			0.177079
$493$	2194.65	+	9281.74i	0.200491	+	0.847928i
$494$	346.197			0.0315307
$495$	4376.14			0.397360
$496$			1991.78i			0.180309i
$497$	−640.311			−0.0577904
$498$		−	4985.87i		−	0.448639i
$499$			19328.3i			1.73398i	0.498328	+	0.866989i	$0.333948\pi$
$499$			19328.3i			1.73398i	−0.498328	+	0.866989i	$0.666052\pi$
$500$		−	5896.63i		−	0.527411i
$501$	−6951.13			−0.619868
$502$	13762.4			1.22360
$503$		−	20998.4i		−	1.86138i	−0.365815	−	0.930688i	$-0.619210\pi$
$503$		−	20998.4i		−	1.86138i	0.365815	−	0.930688i	$-0.380790\pi$
$504$		−	2668.62i		−	0.235853i
$505$		−	28861.3i		−	2.54319i
$506$	12343.7			1.08448
$507$		−	9646.94i		−	0.845041i
$508$	2684.13			0.234427
$509$	−7644.91			−0.665727			−0.332863	−	0.942975i	$-0.608015\pi$
$509$	−7644.91			−0.665727			−0.332863	+	0.942975i	$0.608015\pi$
$510$	13984.9	−	3306.71i	1.21424	−	0.287105i
$511$	−13121.4			−1.13592
$512$	−11827.7			−1.02093
$513$		−	4261.62i		−	0.366774i
$514$	−6796.81			−0.583257
$515$			3265.73i			0.279428i
$516$			3673.45i			0.313400i
$517$			9909.84i			0.843006i
$518$	9267.39			0.786073
$519$	1515.40			0.128167
$520$		−	2492.93i		−	0.210235i
$521$			19875.7i			1.67134i	0.549229	+	0.835672i	$0.314922\pi$
$521$			19875.7i			1.67134i	−0.549229	+	0.835672i	$0.685078\pi$
$522$			2335.04i			0.195789i
$523$	12054.6			1.00786			0.503930	−	0.863744i	$-0.331887\pi$
$523$	12054.6			1.00786			0.503930	+	0.863744i	$0.331887\pi$
$524$			3618.71i			0.301687i
$525$	16855.7			1.40122
$526$	1285.93			0.106596
$527$	−815.468	−	3448.82i	−0.0674048	−	0.285072i
$528$	5450.72			0.449266
$529$	−15786.7			−1.29750
$530$			18826.2i			1.54294i
$531$	782.102			0.0639178
$532$			995.889i			0.0811603i
$533$		−	954.960i		−	0.0776058i
$534$			3969.51i			0.321681i
$535$	−21315.2			−1.72250
$536$	5999.58			0.483474
$537$		−	7445.68i		−	0.598333i
$538$			4174.86i			0.334556i
$539$			3678.94i			0.293994i
$540$	−7018.65			−0.559323
$541$		−	607.633i		−	0.0482887i	−0.999708	−	0.0241443i	$-0.992314\pi$
$541$		−	607.633i		−	0.0482887i	0.999708	−	0.0241443i	$-0.00768613\pi$
$542$	−8532.39			−0.676195
$543$	5240.70			0.414181
$544$	7052.71	−	1667.60i	0.555850	−	0.131430i
$545$	16095.7			1.26507
$546$	824.166			0.0645990
$547$		−	7671.62i		−	0.599662i	−0.953992	−	0.299831i	$-0.903070\pi$
$547$		−	7671.62i		−	0.599662i	0.953992	−	0.299831i	$-0.0969302\pi$
$548$	−1021.25			−0.0796092
$549$		−	894.637i		−	0.0695486i
$550$		−	18669.1i		−	1.44737i
$551$		−	3810.02i		−	0.294578i
$552$	−18290.4			−1.41031
$553$	−11253.0			−0.865327
$554$			10768.8i			0.825853i
$555$		−	22518.4i		−	1.72226i
$556$			2547.67i			0.194326i
$557$	6613.01			0.503056			0.251528	−	0.967850i	$-0.419067\pi$
$557$	6613.01			0.503056			0.251528	+	0.967850i	$0.419067\pi$
$558$		−	867.634i		−	0.0658241i
$559$	1815.28			0.137349
$560$	−11481.2			−0.866375
$561$	−9438.09	+	2231.62i	−0.710297	+	0.167948i
$562$	4361.49			0.327363
$563$	24867.1			1.86150			0.930750	−	0.365657i	$-0.119156\pi$
$563$	24867.1			1.86150			0.930750	+	0.365657i	$0.119156\pi$
$564$		−	3358.42i		−	0.250736i
$565$	−33260.0			−2.47657
$566$		−	9333.52i		−	0.693140i
$567$		−	7217.06i		−	0.534547i
$568$		−	1050.86i		−	0.0776286i
$569$	−11933.7			−0.879242			−0.439621	−	0.898183i	$-0.644887\pi$
$569$	−11933.7			−0.879242			−0.439621	+	0.898183i	$0.644887\pi$
$570$	−5740.61			−0.421838
$571$			8593.93i			0.629851i	0.949116	+	0.314925i	$0.101980\pi$
$571$			8593.93i			0.629851i	−0.949116	+	0.314925i	$0.898020\pi$
$572$			384.792i			0.0281276i
$573$			16390.4i			1.19497i
$574$	−6516.86			−0.473883
$575$			42278.2i			3.06630i
$576$	4053.99			0.293257
$577$	−2580.53			−0.186185			−0.0930927	−	0.995657i	$-0.529675\pi$
$577$	−2580.53			−0.186185			−0.0930927	+	0.995657i	$0.529675\pi$
$578$	10420.8	−	5219.79i	0.749911	−	0.375631i
$579$	6667.80			0.478591
$580$	−6274.89			−0.449225
$581$		−	7087.59i		−	0.506097i
$582$	3197.52			0.227735
$583$		−	12705.4i		−	0.902577i
$584$		−	21534.4i		−	1.52586i
$585$			732.875i			0.0517960i
$586$	−11244.4			−0.792665
$587$	−13533.0			−0.951560			−0.475780	−	0.879564i	$-0.657834\pi$
$587$	−13533.0			−0.951560			−0.475780	+	0.879564i	$0.657834\pi$
$588$		−	1246.78i		−	0.0874429i
$589$			1415.69i			0.0990366i
$590$		−	4985.87i		−	0.347907i
$591$	19384.1			1.34917
$592$			10264.4i			0.712611i
$593$	26998.2			1.86961			0.934807	−	0.355156i	$-0.115572\pi$
$593$	26998.2			1.86961			0.934807	+	0.355156i	$0.115572\pi$
$594$	−11236.8			−0.776183
$595$	19880.1	−	4700.61i	1.36975	−	0.323876i
$596$	4321.26			0.296990
$597$	2104.20			0.144253
$598$			2067.21i			0.141362i
$599$	26341.6			1.79681			0.898403	−	0.439172i	$-0.144728\pi$
$599$	26341.6			1.79681			0.898403	+	0.439172i	$0.144728\pi$
$600$			27663.0i			1.88223i
$601$		−	4099.87i		−	0.278265i	−0.990274	−	0.139133i	$-0.955569\pi$
$601$		−	4099.87i		−	0.278265i	0.990274	−	0.139133i	$-0.0444314\pi$
$602$		−	12387.9i		−	0.838694i
$603$	−1763.76			−0.119114
$604$	−357.285			−0.0240690
$605$		−	7045.63i		−	0.473464i
$606$			15659.4i			1.04970i
$607$			11101.4i			0.742328i	0.928567	+	0.371164i	$0.121041\pi$
$607$			11101.4i			0.742328i	−0.928567	+	0.371164i	$0.878959\pi$
$608$	−2895.03			−0.193107
$609$		−	9070.23i		−	0.603521i
$610$	−5703.28			−0.378556
$611$	−1659.61			−0.109886
$612$	−1170.54	+	276.772i	−0.0773142	+	0.0182808i
$613$	5421.00			0.357182			0.178591	−	0.983923i	$-0.442846\pi$
$613$	5421.00			0.357182			0.178591	+	0.983923i	$0.442846\pi$
$614$	−11780.3			−0.774291
$615$			15835.1i			1.03826i
$616$	11481.2			0.750960
$617$			7246.58i			0.472830i	0.971652	+	0.236415i	$0.0759725\pi$
$617$			7246.58i			0.472830i	−0.971652	+	0.236415i	$0.924027\pi$
$618$		−	1771.90i		−	0.115334i
$619$		−	18816.8i		−	1.22183i	−0.791697	−	0.610914i	$-0.790802\pi$
$619$		−	18816.8i		−	1.22183i	0.791697	−	0.610914i	$-0.209198\pi$
$620$	2331.57			0.151029
$621$	25447.0			1.64437
$622$			14326.9i			0.923561i
$623$			5642.80i			0.362880i
$624$			912.836i			0.0585620i
$625$	16709.3			1.06940
$626$		−	15409.6i		−	0.983850i
$627$	3874.20			0.246763
$628$	−3458.19			−0.219740
$629$	−4202.44	−	17773.2i	−0.266394	−	1.12665i
$630$	5001.31			0.316281
$631$	−17690.3			−1.11607			−0.558036	−	0.829817i	$-0.688445\pi$
$631$	−17690.3			−1.11607			−0.558036	+	0.829817i	$0.688445\pi$
$632$		−	18468.1i		−	1.16237i
$633$	−18640.8			−1.17047
$634$		−	7204.55i		−	0.451308i
$635$			21994.2i			1.37451i
$636$			4305.81i			0.268454i
$637$	−616.113			−0.0383223
$638$	−10046.1			−0.623397
$639$			308.933i			0.0191255i
$640$		−	9765.12i		−	0.603125i
$641$		−	8132.02i		−	0.501085i	−0.968106	−	0.250543i	$-0.919391\pi$
$641$		−	8132.02i		−	0.501085i	0.968106	−	0.250543i	$-0.0806090\pi$
$642$	11565.1			0.710960
$643$		−	2653.40i		−	0.162737i	−0.996684	−	0.0813684i	$-0.974071\pi$
$643$		−	2653.40i		−	0.162737i	0.996684	−	0.0813684i	$-0.0259290\pi$
$644$	−5946.65			−0.363868
$645$	−30100.9			−1.83755
$646$	−4530.90	+	1071.32i	−0.275953	+	0.0652487i
$647$	−12989.6			−0.789297			−0.394649	−	0.918832i	$-0.629134\pi$
$647$	−12989.6			−0.789297			−0.394649	+	0.918832i	$0.629134\pi$
$648$	11844.4			0.718045
$649$			3364.84i			0.203515i
$650$	3126.53			0.188665
$651$			3370.23i			0.202903i
$652$		−	6104.13i		−	0.366651i
$653$			20945.7i			1.25524i	0.778521	+	0.627618i	$0.215970\pi$
$653$			20945.7i			1.25524i	−0.778521	+	0.627618i	$0.784030\pi$
$654$	−8733.11			−0.522158
$655$	−29652.3			−1.76887
$656$		−	7217.99i		−	0.429596i
$657$			6330.72i			0.375928i
$658$			11325.5i			0.670995i
$659$	−5888.03			−0.348050			−0.174025	−	0.984741i	$-0.555677\pi$
$659$	−5888.03			−0.348050			−0.174025	+	0.984741i	$0.555677\pi$
$660$		−	6380.59i		−	0.376309i
$661$	−7987.91			−0.470036			−0.235018	−	0.971991i	$-0.575515\pi$
$661$	−7987.91			−0.470036			−0.235018	+	0.971991i	$0.575515\pi$
$662$	−18431.5			−1.08211
$663$	−373.730	−	1580.60i	−0.0218921	−	0.0925875i
$664$	11631.9			0.679830
$665$	−8160.48			−0.475864
$666$		−	4471.27i		−	0.260147i
$667$	22750.4			1.32069
$668$		−	3709.02i		−	0.214830i
$669$			13413.7i			0.775193i
$670$			11243.9i			0.648343i
$671$	3849.00			0.221444
$672$	−6891.99			−0.395632
$673$			16.7490i			0.000959325i	1.00000		0.000479662i	$0.000152681\pi$
$673$			16.7490i			0.000959325i	−1.00000		0.000479662i	$0.999847\pi$
$674$			14360.5i			0.820694i
$675$		−	38486.9i		−	2.19461i
$676$	5147.46			0.292869
$677$		−	28456.3i		−	1.61546i	−0.589556	−	0.807728i	$-0.700697\pi$
$677$		−	28456.3i		−	1.61546i	0.589556	−	0.807728i	$-0.299303\pi$
$678$	18046.0			1.02220
$679$	4545.39			0.256902
$680$	7714.50	+	32626.6i	0.435055	+	1.83996i
$681$	−2381.95			−0.134033
$682$	3732.82			0.209585
$683$			8066.90i			0.451935i	0.974135	+	0.225967i	$0.0725542\pi$
$683$			8066.90i			0.451935i	−0.974135	+	0.225967i	$0.927446\pi$
$684$	480.490			0.0268596
$685$		−	8368.33i		−	0.466770i
$686$			16404.1i			0.912992i
$687$		−	17914.7i		−	0.994887i
$688$	13720.7			0.760314
$689$	2127.77			0.117651
$690$		−	34278.3i		−	1.89124i
$691$		−	22083.7i		−	1.21578i	−0.794021	−	0.607890i	$-0.792016\pi$
$691$		−	22083.7i		−	1.21578i	0.794021	−	0.607890i	$-0.207984\pi$
$692$			808.593i			0.0444192i
$693$	−3375.26			−0.185015
$694$		−	798.078i		−	0.0436522i
$695$	−20876.1			−1.13939
$696$	14885.8			0.810697
$697$	2955.17	+	12498.2i	0.160595	+	0.679199i
$698$	19832.4			1.07545
$699$	6294.07			0.340577
$700$			8993.93i			0.485626i
$701$	276.484			0.0148968			0.00744839	−	0.999972i	$-0.497629\pi$
$701$	276.484			0.0148968			0.00744839	+	0.999972i	$0.497629\pi$
$702$		−	1881.84i		−	0.101176i
$703$			7295.63i			0.391408i
$704$			17441.5i			0.933737i
$705$	27519.4			1.47013
$706$	4839.55			0.257987
$707$			22260.3i			1.18414i
$708$		−	1140.34i		−	0.0605317i
$709$			24512.7i			1.29844i	0.760601	+	0.649219i	$0.224904\pi$
$709$			24512.7i			1.29844i	−0.760601	+	0.649219i	$0.775096\pi$
$710$	1969.43			0.104101
$711$			5429.27i			0.286376i
$712$	−9260.81			−0.487449
$713$	−8453.37			−0.444013
$714$	−10786.4	+	2550.42i	−0.565365	+	0.133679i
$715$	−3153.05			−0.164919
$716$	3972.90			0.207366
$717$			15935.0i			0.829993i
$718$	−1409.98			−0.0732870
$719$		−	10555.8i		−	0.547518i	−0.961798	−	0.273759i	$-0.911733\pi$
$719$		−	10555.8i		−	0.547518i	0.961798	−	0.273759i	$-0.0882670\pi$
$720$			5539.38i			0.286723i
$721$		−	2518.81i		−	0.130105i
$722$	−14411.6			−0.742859
$723$	−26866.4			−1.38198
$724$			2796.36i			0.143544i
$725$		−	34408.5i		−	1.76262i
$726$			3822.77i			0.195422i
$727$	26611.2			1.35757			0.678785	−	0.734337i	$-0.262507\pi$
$727$	26611.2			1.35757			0.678785	+	0.734337i	$0.262507\pi$
$728$			1922.77i			0.0978880i
$729$	−21752.2			−1.10513
$730$	40358.1			2.04619
$731$	−23757.8	+	5617.48i	−1.20207	+	0.284227i
$732$	−1304.42			−0.0658642
$733$	16288.7			0.820787			0.410393	−	0.911909i	$-0.365391\pi$
$733$	16288.7			0.820787			0.410393	+	0.911909i	$0.365391\pi$
$734$		−	27416.7i		−	1.37871i
$735$	10216.3			0.512701
$736$		−	17286.8i		−	0.865762i
$737$		−	7588.24i		−	0.379262i
$738$			3144.21i			0.156829i
$739$	−7901.82			−0.393333			−0.196667	−	0.980470i	$-0.563012\pi$
$739$	−7901.82			−0.393333			−0.196667	+	0.980470i	$0.563012\pi$
$740$	12015.5			0.596890
$741$			648.814i			0.0321657i
$742$		−	14520.4i		−	0.718411i
$743$		−	28240.7i		−	1.39441i	−0.716870	−	0.697207i	$-0.754426\pi$
$743$		−	28240.7i		−	1.39441i	0.716870	−	0.697207i	$-0.245574\pi$
$744$	−5531.13			−0.272555
$745$			35409.2i			1.74133i
$746$	366.222			0.0179736
$747$	−3419.57			−0.167491
$748$	−1190.76	−	5036.02i	−0.0582064	−	0.246170i
$749$	16440.1			0.802016
$750$	−26216.0			−1.27637
$751$			520.691i			0.0253000i	0.999920	+	0.0126500i	$0.00402673\pi$
$751$			520.691i			0.0253000i	−0.999920	+	0.0126500i	$0.995973\pi$
$752$	−12544.0			−0.608288
$753$			25792.3i			1.24824i
$754$		−	1682.42i		−	0.0812601i
$755$		−	2927.65i		−	0.141123i
$756$	5413.39			0.260427
$757$	26471.9			1.27099			0.635495	−	0.772105i	$-0.280796\pi$
$757$	26471.9			1.27099			0.635495	+	0.772105i	$0.280796\pi$
$758$			21292.4i			1.02029i
$759$			23133.6i			1.10632i
$760$		−	13392.7i		−	0.639218i
$761$	−8204.72			−0.390829			−0.195415	−	0.980721i	$-0.562605\pi$
$761$	−8204.72			−0.390829			−0.195415	+	0.980721i	$0.562605\pi$
$762$		−	11933.5i		−	0.567328i
$763$	−12414.4			−0.589033
$764$	−8745.65			−0.414145
$765$	−2267.92	−	9591.60i	−0.107185	−	0.453314i
$766$	−33289.6			−1.57024
$767$	−563.512			−0.0265283
$768$		−	14634.9i		−	0.687617i
$769$	−930.048			−0.0436130			−0.0218065	−	0.999762i	$-0.506942\pi$
$769$	−930.048			−0.0436130			−0.0218065	+	0.999762i	$0.506942\pi$
$770$			21517.1i			1.00704i
$771$		−	12738.0i		−	0.595004i
$772$			3557.83i			0.165867i
$773$	24346.7			1.13285			0.566423	−	0.824114i	$-0.308327\pi$
$773$	24346.7			1.13285			0.566423	+	0.824114i	$0.308327\pi$
$774$	−5976.83			−0.277562
$775$			12785.2i			0.592590i
$776$			7459.77i			0.345090i
$777$			17368.2i			0.801904i
$778$	−27120.3			−1.24975
$779$		−	5130.31i		−	0.235960i
$780$	1068.56			0.0490521
$781$	−1329.12			−0.0608959
$782$	−6397.09	−	27054.9i	−0.292531	−	1.23719i
$783$	−20710.3			−0.945242
$784$	−4656.84			−0.212138
$785$		−	28337.0i		−	1.28840i
$786$	16088.5			0.730101
$787$			3683.89i			0.166857i	0.996514	+	0.0834286i	$0.0265870\pi$
$787$			3683.89i			0.166857i	−0.996514	+	0.0834286i	$0.973413\pi$
$788$			10343.1i			0.467585i
$789$			2409.99i			0.108742i
$790$	34611.3			1.55875
$791$	25653.0			1.15312
$792$		−	5539.38i		−	0.248527i
$793$			644.594i			0.0288653i
$794$		−	2992.85i		−	0.133769i
$795$	−35282.5			−1.57402
$796$			1122.77i			0.0499943i
$797$	10785.2			0.479336			0.239668	−	0.970855i	$-0.422961\pi$
$797$	10785.2			0.479336			0.239668	+	0.970855i	$0.422961\pi$
$798$	4427.65			0.196413
$799$	21720.3	−	5135.73i	0.961714	−	0.227396i
$800$	−26145.2			−1.15547
$801$	2722.50			0.120093
$802$			33962.5i			1.49534i
$803$	−27236.7			−1.19696
$804$			2571.63i			0.112804i
$805$		−	48727.8i		−	2.13345i
$806$			625.138i			0.0273195i
$807$	−7824.18			−0.341294
$808$	−36533.0			−1.59063
$809$		−	5287.10i		−	0.229771i	−0.993379	−	0.114885i	$-0.963350\pi$
$809$		−	5287.10i		−	0.229771i	0.993379	−	0.114885i	$-0.0366501\pi$
$810$			22197.8i			0.962905i
$811$			34185.5i			1.48017i	0.672515	+	0.740084i	$0.265214\pi$
$811$			34185.5i			1.48017i	−0.672515	+	0.740084i	$0.734786\pi$
$812$	4839.74			0.209164
$813$		−	15990.7i		−	0.689814i
$814$	19236.8			0.828314
$815$	50018.3			2.14977
$816$	−2824.81	−	11946.9i	−0.121187	−	0.512529i
$817$	9752.21			0.417609
$818$	16177.3			0.691473
$819$		−	565.257i		−	0.0241168i
$820$	−8449.34			−0.359834
$821$			13283.1i			0.564655i	0.959318	+	0.282327i	$0.0911065\pi$
$821$			13283.1i			0.564655i	−0.959318	+	0.282327i	$0.908894\pi$
$822$			4540.43i			0.192659i
$823$		−	37925.7i		−	1.60633i	−0.595759	−	0.803164i	$-0.703149\pi$
$823$		−	37925.7i		−	1.60633i	0.595759	−	0.803164i	$-0.296851\pi$
$824$	4133.80			0.174767
$825$	34988.1			1.47652
$826$			3845.53i			0.161989i
$827$			29268.3i			1.23066i	0.788269	+	0.615331i	$0.210978\pi$
$827$			29268.3i			1.23066i	−0.788269	+	0.615331i	$0.789022\pi$
$828$			2869.10i			0.120420i
$829$	−13301.0			−0.557252			−0.278626	−	0.960400i	$-0.589879\pi$
$829$	−13301.0			−0.557252			−0.278626	+	0.960400i	$0.589879\pi$
$830$			21799.6i			0.911657i
$831$	−20182.0			−0.842486
$832$	−2920.94			−0.121713
$833$	8063.47	−	1906.59i	0.335393	−	0.0793031i
$834$	11326.8			0.470281
$835$	30392.3			1.25960
$836$			2067.21i			0.0855216i
$837$	7695.32			0.317789
$838$		−	28437.6i		−	1.17227i
$839$		−	10311.1i		−	0.424288i	−0.977238	−	0.212144i	$-0.931955\pi$
$839$		−	10311.1i		−	0.424288i	0.977238	−	0.212144i	$-0.0680446\pi$
$840$		−	31883.1i		−	1.30961i
$841$	5873.39			0.240821
$842$	19707.8			0.806623
$843$			8173.94i			0.333956i
$844$		−	9946.45i		−	0.405653i
$845$			42179.1i			1.71717i
$846$	5464.26			0.222063
$847$			5434.20i			0.220450i
$848$	16082.6			0.651272
$849$	17492.1			0.707100
$850$	−40918.8	+	9675.18i	−1.65118	+	0.390419i
$851$	−43563.7			−1.75481
$852$	450.436			0.0181123
$853$		−	2240.96i		−	0.0899518i	−0.998988	−	0.0449759i	$-0.985679\pi$
$853$		−	2240.96i		−	0.0899518i	0.998988	−	0.0449759i	$-0.0143211\pi$
$854$	4398.86			0.176260
$855$			3937.21i			0.157485i
$856$			26981.1i			1.07733i
$857$			31870.7i			1.27034i	0.772371	+	0.635171i	$0.219070\pi$
$857$			31870.7i			1.27034i	−0.772371	+	0.635171i	$0.780930\pi$
$858$	1710.76			0.0680704
$859$	36917.9			1.46638			0.733191	−	0.680022i	$-0.238030\pi$
$859$	36917.9			1.46638			0.733191	+	0.680022i	$0.238030\pi$
$860$		−	16061.4i		−	0.636846i
$861$		−	12213.4i		−	0.483427i
$862$		−	34593.1i		−	1.36687i
$863$	−45364.1			−1.78936			−0.894678	−	0.446712i	$-0.852595\pi$
$863$	−45364.1			−1.78936			−0.894678	+	0.446712i	$0.852595\pi$
$864$			15736.6i			0.619643i
$865$	−6625.74			−0.260442
$866$	33345.6			1.30846
$867$	9782.50	+	19529.8i	0.383196	+	0.765014i
$868$	−1798.30			−0.0703208
$869$	−23358.4			−0.911827
$870$			27897.7i			1.08715i
$871$	1270.81			0.0494370
$872$		−	20374.2i		−	0.791235i
$873$		−	2193.03i		−	0.0850204i
$874$			11105.6i			0.429810i
$875$	−37267.0			−1.43983
$876$	9230.44			0.356013
$877$		−	37081.4i		−	1.42776i	−0.700266	−	0.713882i	$-0.746935\pi$
$877$		−	37081.4i		−	1.42776i	0.700266	−	0.713882i	$-0.253065\pi$
$878$		−	27011.5i		−	1.03826i
$879$		−	21073.3i		−	0.808630i
$880$	−23832.1			−0.912932
$881$		−	7501.20i		−	0.286858i	−0.989661	−	0.143429i	$-0.954187\pi$
$881$		−	7501.20i		−	0.286858i	0.989661	−	0.143429i	$-0.0458129\pi$
$882$	2028.56			0.0774434
$883$	−24875.8			−0.948059			−0.474029	−	0.880509i	$-0.657201\pi$
$883$	−24875.8			−0.948059			−0.474029	+	0.880509i	$0.657201\pi$
$884$	843.385	−	199.417i	0.0320884	−	0.00758723i
$885$	9344.10			0.354913
$886$	−27745.3			−1.05205
$887$			6729.37i			0.254735i	0.991856	+	0.127368i	$0.0406528\pi$
$887$			6729.37i			0.254735i	−0.991856	+	0.127368i	$0.959347\pi$
$888$	−28504.1			−1.07718
$889$		−	16963.8i		−	0.639988i
$890$		−	17355.8i		−	0.653673i
$891$		−	14980.8i		−	0.563272i
$892$	−7157.35			−0.268661
$893$	−8915.87			−0.334108
$894$		−	19212.0i		−	0.718733i
$895$			32554.6i			1.21584i
$896$			7531.70i			0.280822i
$897$	−3874.20			−0.144209
$898$		−	12156.5i		−	0.451746i
$899$	6879.86			0.255235
$900$	4339.33			0.160716
$901$	−27847.5	+	6584.50i	−1.02967	+	0.243464i
$902$	−13527.4			−0.499348
$903$	23216.4			0.855585
$904$			42101.0i			1.54896i
$905$	−22913.8			−0.841637
$906$			1588.46i			0.0582485i
$907$			25375.5i			0.928976i	0.885580	+	0.464488i	$0.153762\pi$
$907$			25375.5i			0.928976i	−0.885580	+	0.464488i	$0.846238\pi$
$908$		−	1270.97i		−	0.0464522i
$909$	10740.0			0.391885
$910$	−3603.49			−0.131269
$911$		−	34073.4i		−	1.23919i	−0.784922	−	0.619595i	$-0.787297\pi$
$911$		−	34073.4i		−	1.23919i	0.784922	−	0.619595i	$-0.212703\pi$
$912$			4904.01i			0.178057i
$913$		−	14712.0i		−	0.533294i
$914$	15056.2			0.544873
$915$		−	10688.6i		−	0.386180i
$916$	9558.99			0.344801
$917$	22870.4			0.823607
$918$	5823.43	+	24628.8i	0.209370	+	0.885481i
$919$	2927.25			0.105072			0.0525360	−	0.998619i	$-0.483270\pi$
$919$	2927.25			0.105072			0.0525360	+	0.998619i	$0.483270\pi$
$920$	79970.7			2.86582
$921$		−	22077.7i		−	0.789885i
$922$	−10827.3			−0.386743
$923$		−	222.589i		−	0.00793781i
$924$			4921.26i			0.175214i
$925$			65887.2i			2.34201i
$926$	−32427.2			−1.15078
$927$	−1215.26			−0.0430576
$928$			14069.0i			0.497671i
$929$			10239.9i			0.361637i	0.983516	+	0.180819i	$0.0578747\pi$
$929$			10239.9i			0.361637i	−0.983516	+	0.180819i	$0.942125\pi$
$930$		−	10366.0i		−	0.365499i
$931$	−3309.93			−0.116518
$932$			3358.42i			0.118035i
$933$	−26850.2			−0.942162
$934$	16707.4			0.585314
$935$	41266.0	−	9757.27i	1.44336	−	0.341280i
$936$	927.683			0.0323956
$937$	−23319.4			−0.813031			−0.406516	−	0.913644i	$-0.633256\pi$
$937$	−23319.4			−0.813031			−0.406516	+	0.913644i	$0.633256\pi$
$938$		−	8672.27i		−	0.301876i
$939$	28879.3			1.00366
$940$			14683.9i			0.509508i
$941$			11650.7i			0.403617i	0.979425	+	0.201808i	$0.0646818\pi$
$941$			11650.7i			0.403617i	−0.979425	+	0.201808i	$0.935318\pi$
$942$			15374.9i			0.531784i
$943$	30634.1			1.05788
$944$	−4259.26			−0.146851
$945$			44358.2i			1.52696i
$946$		−	25714.2i		−	0.883762i
$947$		−	37562.0i		−	1.28891i	−0.764641	−	0.644456i	$-0.777084\pi$
$947$		−	37562.0i		−	1.28891i	0.764641	−	0.644456i	$-0.222916\pi$
$948$	7916.08			0.271205
$949$		−	4561.34i		−	0.156025i
$950$	16796.6			0.573635
$951$	13502.2			0.460397
$952$	−5950.09	−	25164.5i	−0.202567	−	0.856707i
$953$	23737.8			0.806864			0.403432	−	0.915010i	$-0.367817\pi$
$953$	23737.8			0.806864			0.403432	+	0.915010i	$0.367817\pi$
$954$	−7005.71			−0.237755
$955$		−	71663.3i		−	2.42824i
$956$	−8502.69			−0.287654
$957$		−	18827.5i		−	0.635953i
$958$			15065.8i			0.508095i
$959$			6454.38i			0.217333i
$960$	48434.7			1.62836
$961$	27234.6			0.914190
$962$			3221.59i			0.107971i
$963$		−	7931.93i		−	0.265423i
$964$		−	14335.5i		−	0.478958i
$965$	−29153.5			−0.972522
$966$			26438.4i			0.880581i
$967$	−5987.71			−0.199123			−0.0995614	−	0.995031i	$-0.531744\pi$
$967$	−5987.71			−0.199123			−0.0995614	+	0.995031i	$0.531744\pi$
$968$	−8918.45			−0.296126
$969$	−2007.79	−	8491.44i	−0.0665628	−	0.281511i
$970$	−13980.5			−0.462769
$971$	−49295.6			−1.62922			−0.814609	−	0.580011i	$-0.803048\pi$
$971$	−49295.6			−1.62922			−0.814609	+	0.580011i	$0.803048\pi$
$972$		−	4671.75i		−	0.154163i
$973$	16101.4			0.530512
$974$			23961.7i			0.788278i
$975$			5859.47i			0.192465i
$976$			4872.12i			0.159788i
$977$	−14932.5			−0.488979			−0.244490	−	0.969652i	$-0.578620\pi$
$977$	−14932.5			−0.488979			−0.244490	+	0.969652i	$0.578620\pi$
$978$	−27138.6			−0.887316
$979$			11713.0i			0.382380i
$980$			5451.28i			0.177689i
$981$			5989.63i			0.194938i
$982$	28220.6			0.917064
$983$			10738.5i			0.348427i	0.984708	+	0.174213i	$0.0557383\pi$
$983$			10738.5i			0.348427i	−0.984708	+	0.174213i	$0.944262\pi$
$984$	20044.2			0.649376
$985$	−84752.9			−2.74158
$986$	5206.33	+	22018.9i	0.168157	+	0.711181i
$987$	−21225.4			−0.684509
$988$	−346.197			−0.0111478
$989$			58232.4i			1.87228i
$990$	10381.4			0.333277
$991$			27948.6i			0.895878i	0.894064	+	0.447939i	$0.147842\pi$
$991$			27948.6i			0.895878i	−0.894064	+	0.447939i	$0.852158\pi$
$992$		−	5227.64i		−	0.167316i
$993$		−	34542.7i		−	1.10391i
$994$	−1519.00			−0.0484705
$995$	−9200.14			−0.293130
$996$			4985.87i			0.158618i
$997$		−	28711.8i		−	0.912049i	−0.889967	−	0.456025i	$-0.849273\pi$
$997$		−	28711.8i		−	0.912049i	0.889967	−	0.456025i	$-0.150727\pi$
$998$			45852.2i			1.45434i
$999$	39657.1			1.25595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.b.a.16.4	yes	4
3.2	odd	2		153.4.d.b.118.2		4
4.3	odd	2		272.4.b.d.33.2		4
5.2	odd	4		425.4.c.c.424.6		8
5.3	odd	4		425.4.c.c.424.3		8
5.4	even	2		425.4.d.c.101.1		4
17.4	even	4		289.4.a.e.1.2		4
17.13	even	4		289.4.a.e.1.1		4
17.16	even	2	inner	17.4.b.a.16.3	✓	4
51.50	odd	2		153.4.d.b.118.1		4
68.67	odd	2		272.4.b.d.33.3		4
85.33	odd	4		425.4.c.c.424.4		8
85.67	odd	4		425.4.c.c.424.5		8
85.84	even	2		425.4.d.c.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.b.a.16.3	✓	4	17.16	even	2	inner
17.4.b.a.16.4	yes	4	1.1	even	1	trivial
153.4.d.b.118.1		4	51.50	odd	2
153.4.d.b.118.2		4	3.2	odd	2
272.4.b.d.33.2		4	4.3	odd	2
272.4.b.d.33.3		4	68.67	odd	2
289.4.a.e.1.1		4	17.13	even	4
289.4.a.e.1.2		4	17.4	even	4
425.4.c.c.424.3		8	5.3	odd	4
425.4.c.c.424.4		8	85.33	odd	4
425.4.c.c.424.5		8	85.67	odd	4
425.4.c.c.424.6		8	5.2	odd	4
425.4.d.c.101.1		4	5.4	even	2
425.4.d.c.101.2		4	85.84	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.37228 q^{2} +4.44593i q^{3} -2.37228 q^{4} -19.4389i q^{5} +10.5470i q^{6} +14.9929i q^{7} -24.6060 q^{8} +7.23369 q^{9} +O(q^{10})\)	\(q+2.37228 q^{2} +4.44593i q^{3} -2.37228 q^{4} -19.4389i q^{5} +10.5470i q^{6} +14.9929i q^{7} -24.6060 q^{8} +7.23369 q^{9} -46.1145i q^{10} +31.1215i q^{11} -10.5470i q^{12} -5.21194 q^{13} +35.5675i q^{14} +86.4239 q^{15} -39.3940 q^{16} +(68.2119 - 16.1286i) q^{17} +17.1603 q^{18} -28.0000 q^{19} +46.1145i q^{20} -66.6576 q^{21} +73.8290i q^{22} -167.194i q^{23} -109.396i q^{24} -252.870 q^{25} -12.3642 q^{26} +152.201i q^{27} -35.5675i q^{28} +136.072i q^{29} +205.022 q^{30} -50.5604i q^{31} +103.394 q^{32} -138.364 q^{33} +(161.818 - 38.2616i) q^{34} +291.446 q^{35} -17.1603 q^{36} -260.558i q^{37} -66.4239 q^{38} -23.1719i q^{39} +478.312i q^{40} +183.225i q^{41} -158.130 q^{42} -348.293 q^{43} -73.8290i q^{44} -140.615i q^{45} -396.630i q^{46} +318.424 q^{47} -175.143i q^{48} +118.212 q^{49} -599.878 q^{50} +(71.7066 + 303.266i) q^{51} +12.3642 q^{52} -408.250 q^{53} +361.063i q^{54} +604.967 q^{55} -368.916i q^{56} -124.486i q^{57} +322.801i q^{58} +108.119 q^{59} -205.022 q^{60} -123.677i q^{61} -119.943i q^{62} +108.454i q^{63} +560.432 q^{64} +101.314i q^{65} -328.239 q^{66} -243.826 q^{67} +(-161.818 + 38.2616i) q^{68} +743.331 q^{69} +691.391 q^{70} +42.7075i q^{71} -177.992 q^{72} +875.172i q^{73} -618.117i q^{74} -1124.24i q^{75} +66.4239 q^{76} -466.603 q^{77} -54.9703i q^{78} +750.553i q^{79} +765.775i q^{80} -481.364 q^{81} +434.662i q^{82} -472.728 q^{83} +158.130 q^{84} +(-313.522 - 1325.96i) q^{85} -826.250 q^{86} -604.967 q^{87} -765.775i q^{88} +376.364 q^{89} -333.578i q^{90} -78.1422i q^{91} +396.630i q^{92} +224.788 q^{93} +755.391 q^{94} +544.288i q^{95} +459.683i q^{96} -303.169i q^{97} +280.432 q^{98} +225.123i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9	\( 4 q - 2 q^{2} + 2 q^{4} - 18 q^{8} - 40 q^{9} + 140 q^{13} + 24 q^{15} - 238 q^{16} + 112 q^{17} + 218 q^{18} - 112 q^{19} + 124 q^{21} - 460 q^{25} - 532 q^{26} + 912 q^{30} + 494 q^{32} - 1036 q^{33} + 406 q^{34} + 936 q^{35} - 218 q^{36} + 56 q^{38} - 1184 q^{42} - 520 q^{43} + 952 q^{47} + 312 q^{49} - 1354 q^{50} + 1160 q^{51} + 532 q^{52} - 576 q^{53} + 168 q^{55} - 1176 q^{59} - 912 q^{60} + 1426 q^{64} + 1904 q^{66} - 240 q^{67} - 406 q^{68} + 1204 q^{69} + 192 q^{70} - 1206 q^{72} - 56 q^{76} + 868 q^{77} - 2408 q^{81} - 2856 q^{83} + 1184 q^{84} + 768 q^{85} - 2248 q^{86} - 168 q^{87} + 1988 q^{89} + 1060 q^{93} + 448 q^{94} + 306 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^4 - 18 * q^8 - 40 * q^9 + 140 * q^13 + 24 * q^15 - 238 * q^16 + 112 * q^17 + 218 * q^18 - 112 * q^19 + 124 * q^21 - 460 * q^25 - 532 * q^26 + 912 * q^30 + 494 * q^32 - 1036 * q^33 + 406 * q^34 + 936 * q^35 - 218 * q^36 + 56 * q^38 - 1184 * q^42 - 520 * q^43 + 952 * q^47 + 312 * q^49 - 1354 * q^50 + 1160 * q^51 + 532 * q^52 - 576 * q^53 + 168 * q^55 - 1176 * q^59 - 912 * q^60 + 1426 * q^64 + 1904 * q^66 - 240 * q^67 - 406 * q^68 + 1204 * q^69 + 192 * q^70 - 1206 * q^72 - 56 * q^76 + 868 * q^77 - 2408 * q^81 - 2856 * q^83 + 1184 * q^84 + 768 * q^85 - 2248 * q^86 - 168 * q^87 + 1988 * q^89 + 1060 * q^93 + 448 * q^94 + 306 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more