LMFDB - Embedded newform 102.4.b.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [102,4,Mod(67,102)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("102.67"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(102, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	102.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.01819482059$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{569})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 285x^{2} + 20164 $ x^4 + 285*x^2 + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.1
Root			$11.4269i$ of defining polynomial
Character	$\chi$	$=$	102.67
Dual form			102.4.b.a.67.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -3.00000i q^{3} +4.00000 q^{4} -16.4269i q^{5} +6.00000i q^{6} +6.00000i q^{7} -8.00000 q^{8} -9.00000 q^{9} +32.8537i q^{10} +1.57314i q^{11} -12.0000i q^{12} -17.2806 q^{13} -12.0000i q^{14} -49.2806 q^{15} +16.0000 q^{16} +(-28.2806 - 64.1343i) q^{17} +18.0000 q^{18} -145.842 q^{19} -65.7074i q^{20} +18.0000 q^{21} -3.14628i q^{22} -30.9880i q^{23} +24.0000i q^{24} -144.842 q^{25} +34.5612 q^{26} +27.0000i q^{27} +24.0000i q^{28} -59.7074i q^{29} +98.5612 q^{30} +30.0000i q^{31} -32.0000 q^{32} +4.71942 q^{33} +(56.5612 + 128.269i) q^{34} +98.5612 q^{35} -36.0000 q^{36} +47.1223i q^{37} +291.683 q^{38} +51.8417i q^{39} +131.415i q^{40} -228.988i q^{41} -36.0000 q^{42} +376.086 q^{43} +6.29256i q^{44} +147.842i q^{45} +61.9760i q^{46} +456.806 q^{47} -48.0000i q^{48} +307.000 q^{49} +289.683 q^{50} +(-192.403 + 84.8417i) q^{51} -69.1223 q^{52} -563.122 q^{53} -54.0000i q^{54} +25.8417 q^{55} -48.0000i q^{56} +437.525i q^{57} +119.415i q^{58} -120.000 q^{59} -197.122 q^{60} +408.878i q^{61} -60.0000i q^{62} -54.0000i q^{63} +64.0000 q^{64} +283.866i q^{65} -9.43884 q^{66} +205.122 q^{67} +(-113.122 - 256.537i) q^{68} -92.9641 q^{69} -197.122 q^{70} -895.391i q^{71} +72.0000 q^{72} -1067.05i q^{73} -94.2447i q^{74} +434.525i q^{75} -583.367 q^{76} -9.43884 q^{77} -103.683i q^{78} -1038.81i q^{79} -262.830i q^{80} +81.0000 q^{81} +457.976i q^{82} +1099.68 q^{83} +72.0000 q^{84} +(-1053.53 + 464.561i) q^{85} -752.173 q^{86} -179.122 q^{87} -12.5851i q^{88} -794.489 q^{89} -295.683i q^{90} -103.683i q^{91} -123.952i q^{92} +90.0000 q^{93} -913.612 q^{94} +2395.72i q^{95} +96.0000i q^{96} -1006.24i q^{97} -614.000 q^{98} -14.1583i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 16 q^{4} - 32 q^{8} - 36 q^{9} + 74 q^{13} - 54 q^{15} + 64 q^{16} + 30 q^{17} + 72 q^{18} - 154 q^{19} + 72 q^{21} - 150 q^{25} - 148 q^{26} + 108 q^{30} - 128 q^{32} + 162 q^{33} - 60 q^{34}+ \cdots - 2456 q^{98}+O(q^{100}) $ 4 * q - 8 * q^2 + 16 * q^4 - 32 * q^8 - 36 * q^9 + 74 * q^13 - 54 * q^15 + 64 * q^16 + 30 * q^17 + 72 * q^18 - 154 * q^19 + 72 * q^21 - 150 * q^25 - 148 * q^26 + 108 * q^30 - 128 * q^32 + 162 * q^33 - 60 * q^34 + 108 * q^35 - 144 * q^36 + 308 * q^38 - 144 * q^42 - 70 * q^43 + 396 * q^47 + 1228 * q^49 + 300 * q^50 - 54 * q^51 + 296 * q^52 - 1680 * q^53 - 326 * q^55 - 480 * q^59 - 216 * q^60 + 256 * q^64 - 324 * q^66 + 248 * q^67 + 120 * q^68 + 630 * q^69 - 216 * q^70 + 288 * q^72 - 616 * q^76 - 324 * q^77 + 324 * q^81 + 3540 * q^83 + 288 * q^84 - 2926 * q^85 + 140 * q^86 - 144 * q^87 - 888 * q^89 + 360 * q^93 - 792 * q^94 - 2456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$-1$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	4.00000			0.500000
$5$		−	16.4269i		−	1.46926i	−0.678466	−	0.734632i	$-0.737355\pi$
$5$		−	16.4269i		−	1.46926i	0.678466	−	0.734632i	$-0.262645\pi$
$6$			6.00000i			0.408248i
$7$			6.00000i			0.323970i	0.986793	+	0.161985i	$0.0517895\pi$
$7$			6.00000i			0.323970i	−0.986793	+	0.161985i	$0.948210\pi$
$8$	−8.00000			−0.353553
$9$	−9.00000			−0.333333
$10$			32.8537i			1.03893i
$11$			1.57314i			0.0431199i	0.999768	+	0.0215600i	$0.00686328\pi$
$11$			1.57314i			0.0431199i	−0.999768	+	0.0215600i	$0.993137\pi$
$12$		−	12.0000i		−	0.288675i
$13$	−17.2806			−0.368675			−0.184337	−	0.982863i	$-0.559014\pi$
$13$	−17.2806			−0.368675			−0.184337	+	0.982863i	$0.559014\pi$
$14$		−	12.0000i		−	0.229081i
$15$	−49.2806			−0.848279
$16$	16.0000			0.250000
$17$	−28.2806	−	64.1343i	−0.403473	−	0.914991i
$17$	−28.2806	−	64.1343i	−0.403473	−	0.914991i
$18$	18.0000			0.235702
$19$	−145.842			−1.76097			−0.880484	−	0.474076i	$-0.842782\pi$
$19$	−145.842			−1.76097			−0.880484	+	0.474076i	$0.842782\pi$
$20$		−	65.7074i		−	0.734632i
$21$	18.0000			0.187044
$22$		−	3.14628i		−	0.0304904i
$23$		−	30.9880i		−	0.280933i	−0.990085	−	0.140466i	$-0.955140\pi$
$23$		−	30.9880i		−	0.280933i	0.990085	−	0.140466i	$-0.0448602\pi$
$24$			24.0000i			0.204124i
$25$	−144.842			−1.15873
$26$	34.5612			0.260692
$27$			27.0000i			0.192450i
$28$			24.0000i			0.161985i
$29$		−	59.7074i		−	0.382324i	−0.981559	−	0.191162i	$-0.938774\pi$
$29$		−	59.7074i		−	0.382324i	0.981559	−	0.191162i	$-0.0612256\pi$
$30$	98.5612			0.599824
$31$			30.0000i			0.173812i	0.996217	+	0.0869058i	$0.0276979\pi$
$31$			30.0000i			0.173812i	−0.996217	+	0.0869058i	$0.972302\pi$
$32$	−32.0000			−0.176777
$33$	4.71942			0.0248953
$34$	56.5612	+	128.269i	0.285299	+	0.646997i
$35$	98.5612			0.475996
$36$	−36.0000			−0.166667
$37$			47.1223i			0.209375i	0.994505	+	0.104687i	$0.0333842\pi$
$37$			47.1223i			0.209375i	−0.994505	+	0.104687i	$0.966616\pi$
$38$	291.683			1.24519
$39$			51.8417i			0.212854i
$40$			131.415i			0.519463i
$41$		−	228.988i		−	0.872242i	−0.899888	−	0.436121i	$-0.856352\pi$
$41$		−	228.988i		−	0.872242i	0.899888	−	0.436121i	$-0.143648\pi$
$42$	−36.0000			−0.132260
$43$	376.086			1.33378			0.666891	−	0.745155i	$-0.267625\pi$
$43$	376.086			1.33378			0.666891	+	0.745155i	$0.267625\pi$
$44$			6.29256i			0.0215600i
$45$			147.842i			0.489754i
$46$			61.9760i			0.198649i
$47$	456.806			1.41770			0.708851	−	0.705358i	$-0.249214\pi$
$47$	456.806			1.41770			0.708851	+	0.705358i	$0.249214\pi$
$48$		−	48.0000i		−	0.144338i
$49$	307.000			0.895044
$50$	289.683			0.819349
$51$	−192.403	+	84.8417i	−0.528271	+	0.232945i
$52$	−69.1223			−0.184337
$53$	−563.122			−1.45945			−0.729725	−	0.683741i	$-0.760352\pi$
$53$	−563.122			−1.45945			−0.729725	+	0.683741i	$0.760352\pi$
$54$		−	54.0000i		−	0.136083i
$55$	25.8417			0.0633545
$56$		−	48.0000i		−	0.114541i
$57$			437.525i			1.01670i
$58$			119.415i			0.270344i
$59$	−120.000			−0.264791			−0.132396	−	0.991197i	$-0.542267\pi$
$59$	−120.000			−0.264791			−0.132396	+	0.991197i	$0.542267\pi$
$60$	−197.122			−0.424140
$61$			408.878i			0.858220i	0.903252	+	0.429110i	$0.141173\pi$
$61$			408.878i			0.858220i	−0.903252	+	0.429110i	$0.858827\pi$
$62$		−	60.0000i		−	0.122903i
$63$		−	54.0000i		−	0.107990i
$64$	64.0000			0.125000
$65$			283.866i			0.541680i
$66$	−9.43884			−0.0176036
$67$	205.122			0.374025			0.187013	−	0.982358i	$-0.440119\pi$
$67$	205.122			0.374025			0.187013	+	0.982358i	$0.440119\pi$
$68$	−113.122	−	256.537i	−0.201737	−	0.457496i
$69$	−92.9641			−0.162197
$70$	−197.122			−0.336580
$71$		−	895.391i		−	1.49667i	−0.663323	−	0.748333i	$-0.730854\pi$
$71$		−	895.391i		−	1.49667i	0.663323	−	0.748333i	$-0.269146\pi$
$72$	72.0000			0.117851
$73$		−	1067.05i		−	1.71081i	−0.517963	−	0.855403i	$-0.673310\pi$
$73$		−	1067.05i		−	1.71081i	0.517963	−	0.855403i	$-0.326690\pi$
$74$		−	94.2447i		−	0.148050i
$75$			434.525i			0.668995i
$76$	−583.367			−0.880484
$77$	−9.43884			−0.0139695
$78$		−	103.683i		−	0.150511i
$79$		−	1038.81i		−	1.47943i	−0.672922	−	0.739714i	$-0.734961\pi$
$79$		−	1038.81i		−	1.47943i	0.672922	−	0.739714i	$-0.265039\pi$
$80$		−	262.830i		−	0.367316i
$81$	81.0000			0.111111
$82$			457.976i			0.616768i
$83$	1099.68			1.45429			0.727144	−	0.686485i	$-0.240847\pi$
$83$	1099.68			1.45429			0.727144	+	0.686485i	$0.240847\pi$
$84$	72.0000			0.0935220
$85$	−1053.53	+	464.561i	−1.34436	+	0.592809i
$86$	−752.173			−0.943126
$87$	−179.122			−0.220735
$88$		−	12.5851i		−	0.0152452i
$89$	−794.489			−0.946244			−0.473122	−	0.880997i	$-0.656873\pi$
$89$	−794.489			−0.946244			−0.473122	+	0.880997i	$0.656873\pi$
$90$		−	295.683i		−	0.346309i
$91$		−	103.683i		−	0.119439i
$92$		−	123.952i		−	0.140466i
$93$	90.0000			0.100350
$94$	−913.612			−1.00247
$95$			2395.72i			2.58733i
$96$			96.0000i			0.102062i
$97$		−	1006.24i		−	1.05329i	−0.850087	−	0.526643i	$-0.823451\pi$
$97$		−	1006.24i		−	1.05329i	0.850087	−	0.526643i	$-0.176549\pi$
$98$	−614.000			−0.632891
$99$		−	14.1583i		−	0.0143733i
$100$	−579.367			−0.579367
$101$	−394.173			−0.388333			−0.194167	−	0.980969i	$-0.562200\pi$
$101$	−394.173			−0.388333			−0.194167	+	0.980969i	$0.562200\pi$
$102$	384.806	−	169.683i	0.373544	−	0.164717i
$103$	748.892			0.716413			0.358207	−	0.933642i	$-0.383388\pi$
$103$	748.892			0.716413			0.358207	+	0.933642i	$0.383388\pi$
$104$	138.245			0.130346
$105$		−	295.683i		−	0.274817i
$106$	1126.24			1.03199
$107$			1200.48i			1.08462i	0.840177	+	0.542312i	$0.182451\pi$
$107$			1200.48i			1.08462i	−0.840177	+	0.542312i	$0.817549\pi$
$108$			108.000i			0.0962250i
$109$			1083.44i			0.952061i	0.879429	+	0.476030i	$0.157925\pi$
$109$			1083.44i			0.952061i	−0.879429	+	0.476030i	$0.842075\pi$
$110$	−51.6835			−0.0447984
$111$	141.367			0.120883
$112$			96.0000i			0.0809924i
$113$		−	1027.06i		−	0.855024i	−0.904010	−	0.427512i	$-0.859390\pi$
$113$		−	1027.06i		−	0.855024i	0.904010	−	0.427512i	$-0.140610\pi$
$114$		−	875.050i		−	0.718912i
$115$	−509.036			−0.412764
$116$		−	238.830i		−	0.191162i
$117$	155.525			0.122892
$118$	240.000			0.187236
$119$	384.806	−	169.683i	0.296429	−	0.130713i
$120$	394.245			0.299912
$121$	1328.53			0.998141
$122$		−	817.755i		−	0.606853i
$123$	−686.964			−0.503589
$124$			120.000i			0.0869058i
$125$			325.938i			0.233222i
$126$			108.000i			0.0763604i
$127$	2291.63			1.60117			0.800586	−	0.599217i	$-0.204521\pi$
$127$	2291.63			1.60117			0.800586	+	0.599217i	$0.204521\pi$
$128$	−128.000			−0.0883883
$129$		−	1128.26i		−	0.770060i
$130$		−	567.731i		−	0.383026i
$131$			1935.04i			1.29057i	0.763940	+	0.645287i	$0.223262\pi$
$131$			1935.04i			1.29057i	−0.763940	+	0.645287i	$0.776738\pi$
$132$	18.8777			0.0124477
$133$		−	875.050i		−	0.570500i
$134$	−410.245			−0.264476
$135$	443.525			0.282760
$136$	226.245	+	513.074i	0.142649	+	0.323498i
$137$	973.540			0.607118			0.303559	−	0.952813i	$-0.401825\pi$
$137$	973.540			0.607118			0.303559	+	0.952813i	$0.401825\pi$
$138$	185.928			0.114690
$139$		−	310.388i		−	0.189401i	−0.995506	−	0.0947007i	$-0.969811\pi$
$139$		−	310.388i		−	0.189401i	0.995506	−	0.0947007i	$-0.0301894\pi$
$140$	394.245			0.237998
$141$		−	1370.42i		−	0.818510i
$142$			1790.78i			1.05830i
$143$		−	27.1848i		−	0.0158972i
$144$	−144.000			−0.0833333
$145$	−980.806			−0.561734
$146$			2134.10i			1.20972i
$147$		−	921.000i		−	0.516754i
$148$			188.489i			0.104687i
$149$	−2680.76			−1.47394			−0.736969	−	0.675927i	$-0.763743\pi$
$149$	−2680.76			−1.47394			−0.736969	+	0.675927i	$0.763743\pi$
$150$		−	869.050i		−	0.473051i
$151$	−226.878			−0.122272			−0.0611359	−	0.998129i	$-0.519472\pi$
$151$	−226.878			−0.122272			−0.0611359	+	0.998129i	$0.519472\pi$
$152$	1166.73			0.622596
$153$	254.525	+	577.209i	0.134491	+	0.304997i
$154$	18.8777			0.00987796
$155$	492.806			0.255375
$156$			207.367i			0.106427i
$157$	353.108			0.179497			0.0897486	−	0.995964i	$-0.471394\pi$
$157$	353.108			0.179497			0.0897486	+	0.995964i	$0.471394\pi$
$158$			2077.61i			1.04611i
$159$			1689.37i			0.842613i
$160$			525.660i			0.259731i
$161$	185.928			0.0910136
$162$	−162.000			−0.0785674
$163$			1070.70i			0.514504i	0.966344	+	0.257252i	$0.0828170\pi$
$163$			1070.70i			0.514504i	−0.966344	+	0.257252i	$0.917183\pi$
$164$		−	915.952i		−	0.436121i
$165$		−	77.5252i		−	0.0365778i
$166$	−2199.37			−1.02834
$167$			744.408i			0.344934i	0.985015	+	0.172467i	$0.0551739\pi$
$167$			744.408i			0.344934i	−0.985015	+	0.172467i	$0.944826\pi$
$168$	−144.000			−0.0661300
$169$	−1898.38			−0.864079
$170$	2107.05	−	929.122i	0.950608	−	0.419179i
$171$	1312.58			0.586989
$172$	1504.35			0.666891
$173$		−	2870.53i		−	1.26152i	−0.775980	−	0.630758i	$-0.782744\pi$
$173$		−	2870.53i		−	1.26152i	0.775980	−	0.630758i	$-0.217256\pi$
$174$	358.245			0.156083
$175$		−	869.050i		−	0.375395i
$176$			25.1702i			0.0107800i
$177$			360.000i			0.152877i
$178$	1588.98			0.669095
$179$	−1144.03			−0.477702			−0.238851	−	0.971056i	$-0.576771\pi$
$179$	−1144.03			−0.477702			−0.238851	+	0.971056i	$0.576771\pi$
$180$			591.367i			0.244877i
$181$		−	3516.07i		−	1.44391i	−0.691940	−	0.721955i	$-0.743244\pi$
$181$		−	3516.07i		−	1.44391i	0.691940	−	0.721955i	$-0.256756\pi$
$182$			207.367i			0.0844564i
$183$	1226.63			0.495494
$184$			247.904i			0.0993247i
$185$	774.072			0.307626
$186$	−180.000			−0.0709583
$187$	100.892	−	44.4893i	0.0394544	−	0.0173978i
$188$	1827.22			0.708851
$189$	−162.000			−0.0623480
$190$		−	4791.44i		−	1.82952i
$191$	−4153.61			−1.57353			−0.786766	−	0.617251i	$-0.788246\pi$
$191$	−4153.61			−1.57353			−0.786766	+	0.617251i	$0.788246\pi$
$192$		−	192.000i		−	0.0721688i
$193$			4090.91i			1.52575i	0.646546	+	0.762875i	$0.276213\pi$
$193$			4090.91i			1.52575i	−0.646546	+	0.762875i	$0.723787\pi$
$194$			2012.49i			0.744785i
$195$	851.597			0.312739
$196$	1228.00			0.447522
$197$			4823.75i			1.74456i	0.489010	+	0.872278i	$0.337358\pi$
$197$			4823.75i			1.74456i	−0.489010	+	0.872278i	$0.662642\pi$
$198$			28.3165i			0.0101635i
$199$		−	2985.74i		−	1.06359i	−0.846874	−	0.531793i	$-0.821518\pi$
$199$		−	2985.74i		−	1.06359i	0.846874	−	0.531793i	$-0.178482\pi$
$200$	1158.73			0.409674
$201$		−	615.367i		−	0.215943i
$202$	788.346			0.274593
$203$	358.245			0.123861
$204$	−769.612	+	339.367i	−0.264135	+	0.116473i
$205$	−3761.55			−1.28155
$206$	−1497.78			−0.506581
$207$			278.892i			0.0936442i
$208$	−276.489			−0.0921687
$209$		−	229.429i		−	0.0759328i
$210$			591.367i			0.194325i
$211$			4387.40i			1.43147i	0.698370	+	0.715736i	$0.253909\pi$
$211$			4387.40i			1.43147i	−0.698370	+	0.715736i	$0.746091\pi$
$212$	−2252.49			−0.729725
$213$	−2686.17			−0.864101
$214$		−	2400.96i		−	0.766945i
$215$		−	6177.92i		−	1.95968i
$216$		−	216.000i		−	0.0680414i
$217$	−180.000			−0.0563097
$218$		−	2166.88i		−	0.673209i
$219$	−3201.15			−0.987734
$220$	103.367			0.0316773
$221$	488.705	+	1108.28i	0.148750	+	0.337334i
$222$	−282.734			−0.0854768
$223$	918.791			0.275905			0.137952	−	0.990439i	$-0.455948\pi$
$223$	918.791			0.275905			0.137952	+	0.990439i	$0.455948\pi$
$224$		−	192.000i		−	0.0572703i
$225$	1303.58			0.386245
$226$			2054.12i			0.604593i
$227$		−	1754.31i		−	0.512942i	−0.966552	−	0.256471i	$-0.917440\pi$
$227$		−	1754.31i		−	0.512942i	0.966552	−	0.256471i	$-0.0825598\pi$
$228$			1750.10i			0.508348i
$229$	−1859.18			−0.536498			−0.268249	−	0.963350i	$-0.586445\pi$
$229$	−1859.18			−0.536498			−0.268249	+	0.963350i	$0.586445\pi$
$230$	1018.07			0.291868
$231$			28.3165i			0.00806532i
$232$			477.660i			0.135172i
$233$			1537.43i			0.432276i	0.976363	+	0.216138i	$0.0693461\pi$
$233$			1537.43i			0.432276i	−0.976363	+	0.216138i	$0.930654\pi$
$234$	−311.050			−0.0868975
$235$		−	7503.89i		−	2.08298i
$236$	−480.000			−0.132396
$237$	−3116.42			−0.854148
$238$	−769.612	+	339.367i	−0.209607	+	0.0924281i
$239$	−3904.69			−1.05679			−0.528396	−	0.848998i	$-0.677206\pi$
$239$	−3904.69			−1.05679			−0.528396	+	0.848998i	$0.677206\pi$
$240$	−788.489			−0.212070
$241$			2369.64i			0.633369i	0.948531	+	0.316685i	$0.102570\pi$
$241$			2369.64i			0.633369i	−0.948531	+	0.316685i	$0.897430\pi$
$242$	−2657.05			−0.705792
$243$		−	243.000i		−	0.0641500i
$244$			1635.51i			0.429110i
$245$		−	5043.05i		−	1.31505i
$246$	1373.93			0.356091
$247$	2520.23			0.649224
$248$		−	240.000i		−	0.0614517i
$249$		−	3299.05i		−	0.839634i
$250$		−	651.875i		−	0.164913i
$251$	7356.23			1.84989			0.924943	−	0.380107i	$-0.124113\pi$
$251$	7356.23			1.84989			0.924943	+	0.380107i	$0.124113\pi$
$252$		−	216.000i		−	0.0539949i
$253$	48.7485			0.0121138
$254$	−4583.25			−1.13220
$255$	1393.68	+	3160.58i	0.342258	+	0.776168i
$256$	256.000			0.0625000
$257$	3415.32			0.828957			0.414479	−	0.910059i	$-0.363964\pi$
$257$	3415.32			0.828957			0.414479	+	0.910059i	$0.363964\pi$
$258$			2256.52i			0.544514i
$259$	−282.734			−0.0678310
$260$			1135.46i			0.270840i
$261$			537.367i			0.127441i
$262$		−	3870.08i		−	0.912574i
$263$	−3030.22			−0.710460			−0.355230	−	0.934779i	$-0.615598\pi$
$263$	−3030.22			−0.710460			−0.355230	+	0.934779i	$0.615598\pi$
$264$	−37.7553			−0.00880182
$265$			9250.33i			2.14431i
$266$			1750.10i			0.403404i
$267$			2383.47i			0.546314i
$268$	820.489			0.187013
$269$		−	5449.58i		−	1.23519i	−0.786496	−	0.617596i	$-0.788107\pi$
$269$		−	5449.58i		−	1.23519i	0.786496	−	0.617596i	$-0.211893\pi$
$270$	−887.050			−0.199941
$271$	2628.14			0.589109			0.294554	−	0.955635i	$-0.404829\pi$
$271$	2628.14			0.589109			0.294554	+	0.955635i	$0.404829\pi$
$272$	−452.489	−	1026.15i	−0.100868	−	0.228748i
$273$	−311.050			−0.0689584
$274$	−1947.08			−0.429297
$275$		−	227.856i		−	0.0499645i
$276$	−371.856			−0.0810983
$277$			7133.14i			1.54725i	0.633643	+	0.773626i	$0.281559\pi$
$277$			7133.14i			1.54725i	−0.633643	+	0.773626i	$0.718441\pi$
$278$			620.777i			0.133927i
$279$		−	270.000i		−	0.0579372i
$280$	−788.489			−0.168290
$281$	6010.26			1.27595			0.637975	−	0.770057i	$-0.279772\pi$
$281$	6010.26			1.27595			0.637975	+	0.770057i	$0.279772\pi$
$282$			2740.83i			0.578774i
$283$		−	1226.19i		−	0.257559i	−0.991673	−	0.128780i	$-0.958894\pi$
$283$		−	1226.19i		−	0.257559i	0.991673	−	0.128780i	$-0.0411060\pi$
$284$		−	3581.56i		−	0.748333i
$285$	7187.17			1.49379
$286$			54.3695i			0.0112410i
$287$	1373.93			0.282580
$288$	288.000			0.0589256
$289$	−3313.42	+	3627.51i	−0.674418	+	0.738349i
$290$	1961.61			0.397206
$291$	−3018.73			−0.608114
$292$		−	4268.20i		−	0.855403i
$293$	8459.73			1.68677			0.843383	−	0.537312i	$-0.180560\pi$
$293$	8459.73			1.68677			0.843383	+	0.537312i	$0.180560\pi$
$294$			1842.00i			0.365400i
$295$			1971.22i			0.389048i
$296$		−	376.979i		−	0.0740251i
$297$	−42.4748			−0.00829844
$298$	5361.53			1.04223
$299$			535.491i			0.103573i
$300$			1738.10i			0.334498i
$301$			2256.52i			0.432105i
$302$	453.755			0.0864592
$303$			1182.52i			0.224204i
$304$	−2333.47			−0.440242
$305$	6716.58			1.26095
$306$	−509.050	−	1154.42i	−0.0950996	−	0.215666i
$307$	−3384.78			−0.629249			−0.314624	−	0.949216i	$-0.601879\pi$
$307$	−3384.78			−0.629249			−0.314624	+	0.949216i	$0.601879\pi$
$308$	−37.7553			−0.00698477
$309$		−	2246.68i		−	0.413621i
$310$	−985.612			−0.180577
$311$		−	861.003i		−	0.156987i	−0.996915	−	0.0784935i	$-0.974989\pi$
$311$		−	861.003i		−	0.156987i	0.996915	−	0.0784935i	$-0.0250110\pi$
$312$		−	414.734i		−	0.0752554i
$313$			950.648i			0.171674i	0.996309	+	0.0858368i	$0.0273564\pi$
$313$			950.648i			0.171674i	−0.996309	+	0.0858368i	$0.972644\pi$
$314$	−706.216			−0.126924
$315$	−887.050			−0.158665
$316$		−	4155.22i		−	0.739714i
$317$		−	8401.18i		−	1.48851i	−0.667897	−	0.744254i	$-0.732805\pi$
$317$		−	8401.18i		−	1.48851i	0.667897	−	0.744254i	$-0.267195\pi$
$318$		−	3378.73i		−	0.595818i
$319$	93.9281			0.0164858
$320$		−	1051.32i		−	0.183658i
$321$	3601.44			0.626208
$322$	−371.856			−0.0643563
$323$	4124.49	+	9353.46i	0.710504	+	1.61127i
$324$	324.000			0.0555556
$325$	2502.95			0.427196
$326$		−	2141.41i		−	0.363809i
$327$	3250.32			0.549673
$328$			1831.90i			0.308384i
$329$			2740.83i			0.459292i
$330$			155.050i			0.0258644i
$331$	4128.20			0.685518			0.342759	−	0.939423i	$-0.388639\pi$
$331$	4128.20			0.685518			0.342759	+	0.939423i	$0.388639\pi$
$332$	4398.73			0.727144
$333$		−	424.101i		−	0.0697916i
$334$		−	1488.82i		−	0.243905i
$335$		−	3369.52i		−	0.549541i
$336$	288.000			0.0467610
$337$		−	40.2293i		−	0.00650276i	−0.999995	−	0.00325138i	$-0.998965\pi$
$337$		−	40.2293i		−	0.00650276i	0.999995	−	0.00325138i	$-0.00103495\pi$
$338$	3796.76			0.610996
$339$	−3081.18			−0.493648
$340$	−4214.10	+	1858.24i	−0.672182	+	0.296404i
$341$	−47.1942			−0.00749475
$342$	−2625.15			−0.415064
$343$			3900.00i			0.613936i
$344$	−3008.69			−0.471563
$345$			1527.11i			0.238309i
$346$			5741.06i			0.892026i
$347$		−	1137.51i		−	0.175978i	−0.996121	−	0.0879892i	$-0.971956\pi$
$347$		−	1137.51i		−	0.175978i	0.996121	−	0.0879892i	$-0.0280441\pi$
$348$	−716.489			−0.110367
$349$	625.741			0.0959746			0.0479873	−	0.998848i	$-0.484719\pi$
$349$	625.741			0.0959746			0.0479873	+	0.998848i	$0.484719\pi$
$350$			1738.10i			0.265444i
$351$		−	466.576i		−	0.0709515i
$352$		−	50.3405i		−	0.00762260i
$353$	−6354.81			−0.958165			−0.479082	−	0.877770i	$-0.659031\pi$
$353$	−6354.81			−0.958165			−0.479082	+	0.877770i	$0.659031\pi$
$354$		−	720.000i		−	0.108100i
$355$	−14708.5			−2.19900
$356$	−3177.96			−0.473122
$357$	−509.050	−	1154.42i	−0.0754672	−	0.171144i
$358$	2288.06			0.337787
$359$	−10466.9			−1.53878			−0.769388	−	0.638781i	$-0.779439\pi$
$359$	−10466.9			−1.53878			−0.769388	+	0.638781i	$0.779439\pi$
$360$		−	1182.73i		−	0.173154i
$361$	14410.8			2.10101
$362$			7032.14i			1.02100i
$363$		−	3985.58i		−	0.576277i
$364$		−	414.734i		−	0.0597197i
$365$	−17528.3			−2.51362
$366$	−2453.27			−0.350367
$367$			8320.39i			1.18344i	0.806145	+	0.591718i	$0.201550\pi$
$367$			8320.39i			1.18344i	−0.806145	+	0.591718i	$0.798450\pi$
$368$		−	495.808i		−	0.0702331i
$369$			2060.89i			0.290747i
$370$	−1548.14			−0.217525
$371$		−	3378.73i		−	0.472817i
$372$	360.000			0.0501751
$373$	265.251			0.0368208			0.0184104	−	0.999831i	$-0.494139\pi$
$373$	265.251			0.0368208			0.0184104	+	0.999831i	$0.494139\pi$
$374$	−201.784	+	88.9786i	−0.0278985	+	0.0123021i
$375$	977.813			0.134651
$376$	−3654.45			−0.501233
$377$			1031.78i			0.140953i
$378$	324.000			0.0440867
$379$		−	10168.5i		−	1.37815i	−0.724688	−	0.689077i	$-0.758016\pi$
$379$		−	10168.5i		−	1.37815i	0.724688	−	0.689077i	$-0.241984\pi$
$380$			9582.89i			1.29366i
$381$		−	6874.88i		−	0.924438i
$382$	8307.22			1.11266
$383$	−1646.79			−0.219705			−0.109853	−	0.993948i	$-0.535038\pi$
$383$	−1646.79			−0.219705			−0.109853	+	0.993948i	$0.535038\pi$
$384$			384.000i			0.0510310i
$385$			155.050i			0.0205249i
$386$		−	8181.81i		−	1.07887i
$387$	−3384.78			−0.444594
$388$		−	4024.98i		−	0.526643i
$389$	6268.68			0.817055			0.408528	−	0.912746i	$-0.366042\pi$
$389$	6268.68			0.817055			0.408528	+	0.912746i	$0.366042\pi$
$390$	−1703.19			−0.221140
$391$	−1987.40	+	876.359i	−0.257051	+	0.113349i
$392$	−2456.00			−0.316446
$393$	5805.12			0.745114
$394$		−	9647.49i		−	1.23359i
$395$	−17064.3			−2.17367
$396$		−	56.6330i		−	0.00718666i
$397$		−	13537.7i		−	1.71143i	−0.517446	−	0.855716i	$-0.673117\pi$
$397$		−	13537.7i		−	1.71143i	0.517446	−	0.855716i	$-0.326883\pi$
$398$			5971.48i			0.752069i
$399$	−2625.15			−0.329378
$400$	−2317.47			−0.289683
$401$		−	6490.51i		−	0.808281i	−0.914697	−	0.404141i	$-0.867571\pi$
$401$		−	6490.51i		−	0.808281i	0.914697	−	0.404141i	$-0.132429\pi$
$402$			1230.73i			0.152695i
$403$		−	518.417i		−	0.0640799i
$404$	−1576.69			−0.194167
$405$		−	1330.58i		−	0.163251i
$406$	−716.489			−0.0875832
$407$	−74.1300			−0.00902822
$408$	1539.22	−	678.734i	0.186772	−	0.0823587i
$409$	−7733.80			−0.934992			−0.467496	−	0.883995i	$-0.654844\pi$
$409$	−7733.80			−0.934992			−0.467496	+	0.883995i	$0.654844\pi$
$410$	7523.11			0.906195
$411$		−	2920.62i		−	0.350520i
$412$	2995.57			0.358207
$413$		−	720.000i		−	0.0857842i
$414$		−	557.784i		−	0.0662164i
$415$		−	18064.3i		−	2.13673i
$416$	552.979			0.0651731
$417$	−931.165			−0.109351
$418$			458.859i			0.0536926i
$419$			8170.70i			0.952660i	0.879267	+	0.476330i	$0.158033\pi$
$419$			8170.70i			0.952660i	−0.879267	+	0.476330i	$0.841967\pi$
$420$		−	1182.73i		−	0.137408i
$421$	−13732.6			−1.58975			−0.794874	−	0.606774i	$-0.792463\pi$
$421$	−13732.6			−1.58975			−0.794874	+	0.606774i	$0.792463\pi$
$422$		−	8774.79i		−	1.01220i
$423$	−4111.25			−0.472567
$424$	4504.98			0.515993
$425$	4096.21	+	9289.32i	0.467518	+	1.06023i
$426$	5372.35			0.611012
$427$	−2453.27			−0.278037
$428$			4801.92i			0.542312i
$429$	−81.5543			−0.00917827
$430$			12355.8i			1.38570i
$431$			13075.7i			1.46133i	0.682734	+	0.730667i	$0.260791\pi$
$431$			13075.7i			1.46133i	−0.682734	+	0.730667i	$0.739209\pi$
$432$			432.000i			0.0481125i
$433$	16873.0			1.87266			0.936331	−	0.351118i	$-0.114198\pi$
$433$	16873.0			1.87266			0.936331	+	0.351118i	$0.114198\pi$
$434$	360.000			0.0398169
$435$			2942.42i			0.324318i
$436$			4333.76i			0.476030i
$437$			4519.35i			0.494713i
$438$	6402.30			0.698433
$439$		−	16207.3i		−	1.76203i	−0.473089	−	0.881014i	$-0.656861\pi$
$439$		−	16207.3i		−	1.76203i	0.473089	−	0.881014i	$-0.343139\pi$
$440$	−206.734			−0.0223992
$441$	−2763.00			−0.298348
$442$	−977.410	−	2216.56i	−0.105182	−	0.238531i
$443$	8022.65			0.860423			0.430212	−	0.902728i	$-0.358439\pi$
$443$	8022.65			0.860423			0.430212	+	0.902728i	$0.358439\pi$
$444$	565.468			0.0604413
$445$			13051.0i			1.39028i
$446$	−1837.58			−0.195094
$447$			8042.29i			0.850978i
$448$			384.000i			0.0404962i
$449$			4730.44i			0.497201i	0.968606	+	0.248600i	$0.0799706\pi$
$449$			4730.44i			0.497201i	−0.968606	+	0.248600i	$0.920029\pi$
$450$	−2607.15			−0.273116
$451$	360.230			0.0376110
$452$		−	4108.24i		−	0.427512i
$453$			680.633i			0.0705937i
$454$			3508.62i			0.362705i
$455$	−1703.19			−0.175488
$456$		−	3500.20i		−	0.359456i
$457$	840.447			0.0860273			0.0430136	−	0.999074i	$-0.486304\pi$
$457$	840.447			0.0860273			0.0430136	+	0.999074i	$0.486304\pi$
$458$	3718.36			0.379362
$459$	1731.63	−	763.576i	0.176090	−	0.0776485i
$460$	−2036.14			−0.206382
$461$	6788.88			0.685878			0.342939	−	0.939358i	$-0.388578\pi$
$461$	6788.88			0.685878			0.342939	+	0.939358i	$0.388578\pi$
$462$		−	56.6330i		−	0.00570304i
$463$	−11545.7			−1.15890			−0.579452	−	0.815006i	$-0.696733\pi$
$463$	−11545.7			−1.15890			−0.579452	+	0.815006i	$0.696733\pi$
$464$		−	955.319i		−	0.0955810i
$465$		−	1478.42i		−	0.147441i
$466$		−	3074.86i		−	0.305665i
$467$	174.303			0.0172715			0.00863573	−	0.999963i	$-0.497251\pi$
$467$	174.303			0.0172715			0.00863573	+	0.999963i	$0.497251\pi$
$468$	622.101			0.0614458
$469$			1230.73i			0.121173i
$470$			15007.8i			1.47289i
$471$		−	1059.32i		−	0.103633i
$472$	960.000			0.0936178
$473$			591.636i			0.0575126i
$474$	6232.83			0.603974
$475$	21124.0			2.04049
$476$	1539.22	−	678.734i	0.148215	−	0.0653566i
$477$	5068.10			0.486483
$478$	7809.38			0.747265
$479$			16182.7i			1.54365i	0.635837	+	0.771824i	$0.280655\pi$
$479$			16182.7i			1.54365i	−0.635837	+	0.771824i	$0.719345\pi$
$480$	1576.98			0.149956
$481$		−	814.301i		−	0.0771911i
$482$		−	4739.28i		−	0.447860i
$483$		−	557.784i		−	0.0525467i
$484$	5314.10			0.499070
$485$	−16529.4			−1.54755
$486$			486.000i			0.0453609i
$487$		−	17815.3i		−	1.65767i	−0.559491	−	0.828837i	$-0.689003\pi$
$487$		−	17815.3i		−	1.65767i	0.559491	−	0.828837i	$-0.310997\pi$
$488$		−	3271.02i		−	0.303427i
$489$	3212.11			0.297049
$490$			10086.1i			0.929884i
$491$	19445.2			1.78727			0.893635	−	0.448794i	$-0.148146\pi$
$491$	19445.2			1.78727			0.893635	+	0.448794i	$0.148146\pi$
$492$	−2747.86			−0.251795
$493$	−3829.30	+	1688.56i	−0.349823	+	0.154258i
$494$	−5040.46			−0.459071
$495$	−232.576			−0.0211182
$496$			480.000i			0.0434529i
$497$	5372.35			0.484875
$498$			6598.10i			0.593711i
$499$		−	9524.72i		−	0.854479i	−0.904138	−	0.427240i	$-0.859486\pi$
$499$		−	9524.72i		−	0.854479i	0.904138	−	0.427240i	$-0.140514\pi$
$500$			1303.75i			0.116611i
$501$	2233.22			0.199148
$502$	−14712.5			−1.30807
$503$		−	1592.37i		−	0.141154i	−0.997506	−	0.0705768i	$-0.977516\pi$
$503$		−	1592.37i		−	0.141154i	0.997506	−	0.0705768i	$-0.0224840\pi$
$504$			432.000i			0.0381802i
$505$			6475.02i			0.570564i
$506$	−97.4970			−0.00856575
$507$			5695.14i			0.498876i
$508$	9166.50			0.800586
$509$	−14893.7			−1.29696			−0.648480	−	0.761232i	$-0.724595\pi$
$509$	−14893.7			−1.29696			−0.648480	+	0.761232i	$0.724595\pi$
$510$	−2787.37	−	6321.15i	−0.242013	−	0.548834i
$511$	6402.30			0.554249
$512$	−512.000			−0.0441942
$513$		−	3937.73i		−	0.338898i
$514$	−6830.65			−0.586161
$515$		−	12301.9i		−	1.05260i
$516$		−	4513.04i		−	0.385030i
$517$			718.619i			0.0611312i
$518$	565.468			0.0479638
$519$	−8611.58			−0.728336
$520$		−	2270.93i		−	0.191513i
$521$		−	4403.38i		−	0.370279i	−0.982712	−	0.185140i	$-0.940726\pi$
$521$		−	4403.38i		−	0.370279i	0.982712	−	0.185140i	$-0.0592737\pi$
$522$		−	1074.73i		−	0.0901146i
$523$	−6728.23			−0.562533			−0.281267	−	0.959630i	$-0.590755\pi$
$523$	−6728.23			−0.562533			−0.281267	+	0.959630i	$0.590755\pi$
$524$			7740.16i			0.645287i
$525$	−2607.15			−0.216734
$526$	6060.43			0.502371
$527$	1924.03	−	848.417i	0.159036	−	0.0701284i
$528$	75.5107			0.00622383
$529$	11206.7			0.921077
$530$		−	18500.7i		−	1.51626i
$531$	1080.00			0.0882637
$532$		−	3500.20i		−	0.285250i
$533$			3957.05i			0.321574i
$534$		−	4766.94i		−	0.386302i
$535$	19720.1			1.59360
$536$	−1640.98			−0.132238
$537$			3432.09i			0.275802i
$538$			10899.2i			0.873413i
$539$			482.954i			0.0385942i
$540$	1774.10			0.141380
$541$			13624.4i			1.08273i	0.840787	+	0.541366i	$0.182093\pi$
$541$			13624.4i			1.08273i	−0.840787	+	0.541366i	$0.817907\pi$
$542$	−5256.29			−0.416563
$543$	−10548.2			−0.833641
$544$	904.979	+	2052.30i	0.0713247	+	0.161749i
$545$	17797.5			1.39883
$546$	622.101			0.0487609
$547$			3158.10i			0.246857i	0.992353	+	0.123428i	$0.0393889\pi$
$547$			3158.10i			0.246857i	−0.992353	+	0.123428i	$0.960611\pi$
$548$	3894.16			0.303559
$549$		−	3679.90i		−	0.286073i
$550$			455.713i			0.0353303i
$551$			8707.84i			0.673260i
$552$	743.713			0.0573451
$553$	6232.83			0.479290
$554$		−	14266.3i		−	1.09407i
$555$		−	2322.22i		−	0.177608i
$556$		−	1241.55i		−	0.0947007i
$557$	−5831.35			−0.443595			−0.221797	−	0.975093i	$-0.571192\pi$
$557$	−5831.35			−0.443595			−0.221797	+	0.975093i	$0.571192\pi$
$558$			540.000i			0.0409678i
$559$	−6498.99			−0.491732
$560$	1576.98			0.118999
$561$	−133.468	−	302.677i	−0.0100446	−	0.0227790i
$562$	−12020.5			−0.902233
$563$	−12511.5			−0.936587			−0.468294	−	0.883573i	$-0.655131\pi$
$563$	−12511.5			−0.936587			−0.468294	+	0.883573i	$0.655131\pi$
$564$		−	5481.67i		−	0.409255i
$565$	−16871.4			−1.25625
$566$			2452.37i			0.182122i
$567$			486.000i			0.0359966i
$568$			7163.13i			0.529152i
$569$	−8469.14			−0.623980			−0.311990	−	0.950085i	$-0.600996\pi$
$569$	−8469.14			−0.623980			−0.311990	+	0.950085i	$0.600996\pi$
$570$	−14374.3			−1.05627
$571$			5857.64i			0.429308i	0.976690	+	0.214654i	$0.0688623\pi$
$571$			5857.64i			0.429308i	−0.976690	+	0.214654i	$0.931138\pi$
$572$		−	108.739i		−	0.00794862i
$573$			12460.8i			0.908480i
$574$	−2747.86			−0.199814
$575$			4488.36i			0.325526i
$576$	−576.000			−0.0416667
$577$	15537.9			1.12106			0.560528	−	0.828135i	$-0.310598\pi$
$577$	15537.9			1.12106			0.560528	+	0.828135i	$0.310598\pi$
$578$	6626.83	−	7255.02i	0.476886	−	0.522092i
$579$	12272.7			0.880893
$580$	−3923.22			−0.280867
$581$			6598.10i			0.471145i
$582$	6037.47			0.430002
$583$		−	885.870i		−	0.0629314i
$584$			8536.40i			0.604861i
$585$		−	2554.79i		−	0.180560i
$586$	−16919.5			−1.19272
$587$	1491.54			0.104876			0.0524382	−	0.998624i	$-0.483301\pi$
$587$	1491.54			0.104876			0.0524382	+	0.998624i	$0.483301\pi$
$588$		−	3684.00i		−	0.258377i
$589$		−	4375.25i		−	0.306077i
$590$		−	3942.45i		−	0.275098i
$591$	14471.2			1.00722
$592$			753.957i			0.0523437i
$593$	14418.0			0.998442			0.499221	−	0.866475i	$-0.333620\pi$
$593$	14418.0			0.998442			0.499221	+	0.866475i	$0.333620\pi$
$594$	84.9495			0.00586788
$595$	−2787.37	−	6321.15i	−0.192052	−	0.435533i
$596$	−10723.1			−0.736969
$597$	−8957.22			−0.614062
$598$		−	1070.98i		−	0.0732370i
$599$	3644.49			0.248597			0.124299	−	0.992245i	$-0.460332\pi$
$599$	3644.49			0.248597			0.124299	+	0.992245i	$0.460332\pi$
$600$		−	3476.20i		−	0.236526i
$601$		−	6984.34i		−	0.474039i	−0.971505	−	0.237019i	$-0.923829\pi$
$601$		−	6984.34i		−	0.474039i	0.971505	−	0.237019i	$-0.0761705\pi$
$602$		−	4513.04i		−	0.305544i
$603$	−1846.10			−0.124675
$604$	−907.511			−0.0611359
$605$		−	21823.5i		−	1.46653i
$606$		−	2365.04i		−	0.158536i
$607$			14362.8i			0.960407i	0.877157	+	0.480204i	$0.159437\pi$
$607$			14362.8i			0.960407i	−0.877157	+	0.480204i	$0.840563\pi$
$608$	4666.94			0.311298
$609$		−	1074.73i		−	0.0715114i
$610$	−13433.2			−0.891627
$611$	−7893.87			−0.522671
$612$	1018.10	+	2308.83i	0.0672456	+	0.152499i
$613$	−8703.81			−0.573481			−0.286740	−	0.958008i	$-0.592572\pi$
$613$	−8703.81			−0.573481			−0.286740	+	0.958008i	$0.592572\pi$
$614$	6769.55			0.444946
$615$			11284.7i			0.739905i
$616$	75.5107			0.00493898
$617$		−	26903.7i		−	1.75543i	−0.479182	−	0.877715i	$-0.659067\pi$
$617$		−	26903.7i		−	1.75543i	0.479182	−	0.877715i	$-0.340933\pi$
$618$			4493.35i			0.292474i
$619$			8641.76i			0.561133i	0.959835	+	0.280567i	$0.0905224\pi$
$619$			8641.76i			0.561133i	−0.959835	+	0.280567i	$0.909478\pi$
$620$	1971.22			0.127687
$621$	836.677			0.0540655
$622$			1722.01i			0.111007i
$623$		−	4766.94i		−	0.306554i
$624$			829.468i			0.0532136i
$625$	−12751.1			−0.816070
$626$		−	1901.30i		−	0.121392i
$627$	−688.288			−0.0438398
$628$	1412.43			0.0897486
$629$	3022.16	−	1332.65i	0.191576	−	0.0844771i
$630$	1774.10			0.112193
$631$	−10472.0			−0.660672			−0.330336	−	0.943863i	$-0.607162\pi$
$631$	−10472.0			−0.660672			−0.330336	+	0.943863i	$0.607162\pi$
$632$			8310.45i			0.523057i
$633$	13162.2			0.826461
$634$			16802.4i			1.05253i
$635$		−	37644.2i		−	2.35254i
$636$			6757.47i			0.421307i
$637$	−5305.14			−0.329980
$638$	−187.856			−0.0116572
$639$			8058.52i			0.498889i
$640$			2102.64i			0.129866i
$641$			9806.52i			0.604266i	0.953266	+	0.302133i	$0.0976986\pi$
$641$			9806.52i			0.604266i	−0.953266	+	0.302133i	$0.902301\pi$
$642$	−7202.88			−0.442796
$643$			13782.6i			0.845307i	0.906291	+	0.422653i	$0.138901\pi$
$643$			13782.6i			0.845307i	−0.906291	+	0.422653i	$0.861099\pi$
$644$	743.713			0.0455068
$645$	−18533.8			−1.13142
$646$	−8248.98	−	18706.9i	−0.502402	−	1.13934i
$647$	13972.3			0.849005			0.424502	−	0.905427i	$-0.360449\pi$
$647$	13972.3			0.849005			0.424502	+	0.905427i	$0.360449\pi$
$648$	−648.000			−0.0392837
$649$		−	188.777i		−	0.0114178i
$650$	−5005.90			−0.302073
$651$			540.000i			0.0325104i
$652$			4282.82i			0.257252i
$653$		−	469.753i		−	0.0281514i	−0.999901	−	0.0140757i	$-0.995519\pi$
$653$		−	469.753i		−	0.0281514i	0.999901	−	0.0140757i	$-0.00448058\pi$
$654$	−6500.63			−0.388677
$655$	31786.6			1.89619
$656$		−	3663.81i		−	0.218060i
$657$			9603.45i			0.570269i
$658$		−	5481.67i		−	0.324769i
$659$	6126.73			0.362160			0.181080	−	0.983468i	$-0.442041\pi$
$659$	6126.73			0.362160			0.181080	+	0.983468i	$0.442041\pi$
$660$		−	310.101i		−	0.0182889i
$661$	−19862.7			−1.16879			−0.584393	−	0.811471i	$-0.698667\pi$
$661$	−19862.7			−1.16879			−0.584393	+	0.811471i	$0.698667\pi$
$662$	−8256.40			−0.484734
$663$	3324.83	−	1466.11i	0.194760	−	0.0858811i
$664$	−8797.47			−0.514169
$665$	−14374.3			−0.838215
$666$			848.202i			0.0493501i
$667$	−1850.22			−0.107407
$668$			2977.63i			0.172467i
$669$		−	2756.37i		−	0.159294i
$670$			6739.03i			0.388584i
$671$	−643.222			−0.0370064
$672$	−576.000			−0.0330650
$673$		−	29895.9i		−	1.71234i	−0.516697	−	0.856169i	$-0.672838\pi$
$673$		−	29895.9i		−	1.71234i	0.516697	−	0.856169i	$-0.327162\pi$
$674$			80.4586i			0.00459815i
$675$		−	3910.73i		−	0.222998i
$676$	−7593.53			−0.432039
$677$			3689.27i			0.209439i	0.994502	+	0.104719i	$0.0333945\pi$
$677$			3689.27i			0.209439i	−0.994502	+	0.104719i	$0.966606\pi$
$678$	6162.36			0.349062
$679$	6037.47			0.341232
$680$	8428.20	−	3716.49i	0.475304	−	0.209589i
$681$	−5262.94			−0.296147
$682$	94.3884			0.00529959
$683$			14206.2i			0.795879i	0.917412	+	0.397940i	$0.130275\pi$
$683$			14206.2i			0.795879i	−0.917412	+	0.397940i	$0.869725\pi$
$684$	5250.30			0.293495
$685$		−	15992.2i		−	0.892016i
$686$		−	7800.00i		−	0.434119i
$687$			5577.54i			0.309747i
$688$	6017.38			0.333446
$689$	9731.08			0.538062
$690$		−	3054.22i		−	0.168510i
$691$			36094.2i			1.98710i	0.113391	+	0.993550i	$0.463829\pi$
$691$			36094.2i			1.98710i	−0.113391	+	0.993550i	$0.536171\pi$
$692$		−	11482.1i		−	0.630758i
$693$	84.9495			0.00465652
$694$			2275.01i			0.124436i
$695$	−5098.71			−0.278281
$696$	1432.98			0.0780415
$697$	−14686.0	+	6475.91i	−0.798094	+	0.351926i
$698$	−1251.48			−0.0678643
$699$	4612.29			0.249575
$700$		−	3476.20i		−	0.187697i
$701$	17089.4			0.920767			0.460383	−	0.887720i	$-0.347712\pi$
$701$	17089.4			0.920767			0.460383	+	0.887720i	$0.347712\pi$
$702$			933.151i			0.0501703i
$703$		−	6872.40i		−	0.368702i
$704$			100.681i			0.00538999i
$705$	−22511.7			−1.20261
$706$	12709.6			0.677525
$707$		−	2365.04i		−	0.125808i
$708$			1440.00i			0.0764386i
$709$		−	17325.6i		−	0.917737i	−0.888504	−	0.458868i	$-0.848255\pi$
$709$		−	17325.6i		−	0.917737i	0.888504	−	0.458868i	$-0.151745\pi$
$710$	29416.9			1.55493
$711$			9349.25i			0.493143i
$712$	6355.91			0.334548
$713$	929.641			0.0488293
$714$	1018.10	+	2308.83i	0.0533634	+	0.121017i
$715$	−446.560			−0.0233572
$716$	−4576.12			−0.238851
$717$			11714.1i			0.610140i
$718$	20933.8			1.08808
$719$			3861.73i			0.200304i	0.994972	+	0.100152i	$0.0319329\pi$
$719$			3861.73i			0.200304i	−0.994972	+	0.100152i	$0.968067\pi$
$720$			2365.47i			0.122439i
$721$			4493.35i			0.232096i
$722$	−28821.6			−1.48564
$723$	7108.92			0.365676
$724$		−	14064.3i		−	0.721955i
$725$			8648.13i			0.443012i
$726$			7971.15i			0.407489i
$727$	3016.23			0.153873			0.0769366	−	0.997036i	$-0.475486\pi$
$727$	3016.23			0.153873			0.0769366	+	0.997036i	$0.475486\pi$
$728$			829.468i			0.0422282i
$729$	−729.000			−0.0370370
$730$	35056.6			1.77740
$731$	−10635.9	−	24120.0i	−0.538146	−	1.22040i
$732$	4906.53			0.247747
$733$	−6778.92			−0.341590			−0.170795	−	0.985307i	$-0.554634\pi$
$733$	−6778.92			−0.341590			−0.170795	+	0.985307i	$0.554634\pi$
$734$		−	16640.8i		−	0.836815i
$735$	−15129.1			−0.759247
$736$			991.617i			0.0496623i
$737$			322.686i			0.0161279i
$738$		−	4121.78i		−	0.205589i
$739$	25629.9			1.27579			0.637896	−	0.770123i	$-0.279805\pi$
$739$	25629.9			1.27579			0.637896	+	0.770123i	$0.279805\pi$
$740$	3096.29			0.153813
$741$		−	7560.69i		−	0.374830i
$742$			6757.47i			0.334332i
$743$			8981.07i			0.443450i	0.975109	+	0.221725i	$0.0711688\pi$
$743$			8981.07i			0.443450i	−0.975109	+	0.221725i	$0.928831\pi$
$744$	−720.000			−0.0354791
$745$			44036.5i			2.16560i
$746$	−530.501			−0.0260362
$747$	−9897.15			−0.484763
$748$	403.569	−	177.957i	0.0197272	−	0.00869888i
$749$	−7202.88			−0.351385
$750$	−1955.63			−0.0952125
$751$			4198.37i			0.203996i	0.994785	+	0.101998i	$0.0325235\pi$
$751$			4198.37i			0.203996i	−0.994785	+	0.101998i	$0.967477\pi$
$752$	7308.89			0.354425
$753$		−	22068.7i		−	1.06803i
$754$		−	2063.56i		−	0.0996689i
$755$			3726.89i			0.179649i
$756$	−648.000			−0.0311740
$757$	11693.1			0.561418			0.280709	−	0.959793i	$-0.409430\pi$
$757$	11693.1			0.561418			0.280709	+	0.959793i	$0.409430\pi$
$758$			20337.0i			0.974502i
$759$		−	146.245i		−	0.00699390i
$760$		−	19165.8i		−	0.914758i
$761$	13505.6			0.643333			0.321667	−	0.946853i	$-0.395757\pi$
$761$	13505.6			0.643333			0.321667	+	0.946853i	$0.395757\pi$
$762$			13749.8i			0.653676i
$763$	−6500.63			−0.308439
$764$	−16614.4			−0.786766
$765$	9481.73	−	4181.05i	0.448121	−	0.197603i
$766$	3293.58			0.155355
$767$	2073.67			0.0976217
$768$		−	768.000i		−	0.0360844i
$769$	15256.1			0.715407			0.357704	−	0.933835i	$-0.383560\pi$
$769$	15256.1			0.715407			0.357704	+	0.933835i	$0.383560\pi$
$770$		−	310.101i		−	0.0145133i
$771$		−	10246.0i		−	0.478599i
$772$			16363.6i			0.762875i
$773$	−16038.3			−0.746256			−0.373128	−	0.927780i	$-0.621715\pi$
$773$	−16038.3			−0.746256			−0.373128	+	0.927780i	$0.621715\pi$
$774$	6769.56			0.314375
$775$		−	4345.25i		−	0.201401i
$776$			8049.96i			0.372393i
$777$			848.202i			0.0391623i
$778$	−12537.4			−0.577745
$779$			33396.0i			1.53599i
$780$	3406.39			0.156370
$781$	1408.57			0.0645362
$782$	3974.79	−	1752.72i	0.181762	−	0.0801497i
$783$	1612.10			0.0735783
$784$	4912.00			0.223761
$785$		−	5800.45i		−	0.263729i
$786$	−11610.2			−0.526875
$787$		−	26105.8i		−	1.18243i	−0.806514	−	0.591215i	$-0.798648\pi$
$787$		−	26105.8i		−	1.18243i	0.806514	−	0.591215i	$-0.201352\pi$
$788$			19295.0i			0.872278i
$789$			9090.65i			0.410185i
$790$	34128.6			1.53702
$791$	6162.36			0.277002
$792$			113.266i			0.00508173i
$793$		−	7065.64i		−	0.316404i
$794$			27075.4i			1.21016i
$795$	27751.0			1.23802
$796$		−	11943.0i		−	0.531793i
$797$	5988.53			0.266154			0.133077	−	0.991106i	$-0.457514\pi$
$797$	5988.53			0.266154			0.133077	+	0.991106i	$0.457514\pi$
$798$	5250.30			0.232906
$799$	−12918.7	−	29296.9i	−0.572005	−	1.29718i
$800$	4634.94			0.204837
$801$	7150.40			0.315415
$802$			12981.0i			0.571541i
$803$	1678.62			0.0737698
$804$		−	2461.47i		−	0.107972i
$805$		−	3054.22i		−	0.133723i
$806$			1036.83i			0.0453114i
$807$	−16348.7			−0.713138
$808$	3153.38			0.137297
$809$			44380.7i			1.92873i	0.264577	+	0.964365i	$0.414768\pi$
$809$			44380.7i			1.92873i	−0.264577	+	0.964365i	$0.585232\pi$
$810$			2661.15i			0.115436i
$811$			33546.5i			1.45250i	0.687432	+	0.726249i	$0.258738\pi$
$811$			33546.5i			1.45250i	−0.687432	+	0.726249i	$0.741262\pi$
$812$	1432.98			0.0619307
$813$		−	7884.43i		−	0.340122i
$814$	148.260			0.00638392
$815$	17588.3			0.755941
$816$	−3078.45	+	1357.47i	−0.132068	+	0.0582364i
$817$	−54849.1			−2.34875
$818$	15467.6			0.661139
$819$			933.151i			0.0398131i
$820$	−15046.2			−0.640776
$821$		−	13701.7i		−	0.582451i	−0.956654	−	0.291226i	$-0.905937\pi$
$821$		−	13701.7i		−	0.582451i	0.956654	−	0.291226i	$-0.0940630\pi$
$822$			5841.24i			0.247855i
$823$		−	4440.76i		−	0.188087i	−0.995568	−	0.0940433i	$-0.970021\pi$
$823$		−	4440.76i		−	0.188087i	0.995568	−	0.0940433i	$-0.0299792\pi$
$824$	−5991.14			−0.253290
$825$	−683.569			−0.0288470
$826$			1440.00i			0.0606586i
$827$		−	8705.42i		−	0.366043i	−0.983109	−	0.183021i	$-0.941412\pi$
$827$		−	8705.42i		−	0.366043i	0.983109	−	0.183021i	$-0.0585877\pi$
$828$			1115.57i			0.0468221i
$829$	5755.30			0.241121			0.120561	−	0.992706i	$-0.461531\pi$
$829$	5755.30			0.241121			0.120561	+	0.992706i	$0.461531\pi$
$830$			36128.7i			1.51090i
$831$	21399.4			0.893306
$832$	−1105.96			−0.0460843
$833$	−8682.14	−	19689.2i	−0.361126	−	0.818957i
$834$	1862.33			0.0773228
$835$	12228.3			0.506799
$836$		−	917.718i		−	0.0379664i
$837$	−810.000			−0.0334501
$838$		−	16341.4i		−	0.673633i
$839$		−	29272.2i		−	1.20451i	−0.798302	−	0.602257i	$-0.794268\pi$
$839$		−	29272.2i		−	1.20451i	0.798302	−	0.602257i	$-0.205732\pi$
$840$			2365.47i			0.0971624i
$841$	20824.0			0.853828
$842$	27465.1			1.12412
$843$		−	18030.8i		−	0.736670i
$844$			17549.6i			0.715736i
$845$			31184.4i			1.26956i
$846$	8222.50			0.334155
$847$			7971.15i			0.323367i
$848$	−9009.96			−0.364862
$849$	−3678.56			−0.148702
$850$	−8192.42	−	18578.6i	−0.330585	−	0.749697i
$851$	1460.23			0.0588202
$852$	−10744.7			−0.432051
$853$		−	45569.0i		−	1.82913i	−0.404434	−	0.914567i	$-0.632531\pi$
$853$		−	45569.0i		−	1.82913i	0.404434	−	0.914567i	$-0.367469\pi$
$854$	4906.53			0.196602
$855$		−	21561.5i		−	0.862442i
$856$		−	9603.84i		−	0.383473i
$857$		−	33462.5i		−	1.33379i	−0.745151	−	0.666895i	$-0.767623\pi$
$857$		−	33462.5i		−	1.33379i	0.745151	−	0.666895i	$-0.232377\pi$
$858$	163.109			0.00649002
$859$	7859.19			0.312168			0.156084	−	0.987744i	$-0.450113\pi$
$859$	7859.19			0.312168			0.156084	+	0.987744i	$0.450113\pi$
$860$		−	24711.7i		−	0.979839i
$861$		−	4121.78i		−	0.163148i
$862$		−	26151.4i		−	1.03332i
$863$	−17613.4			−0.694746			−0.347373	−	0.937727i	$-0.612926\pi$
$863$	−17613.4			−0.694746			−0.347373	+	0.937727i	$0.612926\pi$
$864$		−	864.000i		−	0.0340207i
$865$	−47153.8			−1.85350
$866$	−33745.9			−1.32417
$867$	10882.5	+	9940.25i	0.426286	+	0.389376i
$868$	−720.000			−0.0281548
$869$	1634.19			0.0637928
$870$		−	5884.83i		−	0.229327i
$871$	−3544.63			−0.137894
$872$		−	8667.51i		−	0.336604i
$873$			9056.20i			0.351095i
$874$		−	9038.69i		−	0.349815i
$875$	−1955.63			−0.0755568
$876$	−12804.6			−0.493867
$877$		−	38660.0i		−	1.48855i	−0.667874	−	0.744274i	$-0.732796\pi$
$877$		−	38660.0i		−	1.48855i	0.667874	−	0.744274i	$-0.267204\pi$
$878$			32414.5i			1.24594i
$879$		−	25379.2i		−	0.973855i
$880$	413.468			0.0158386
$881$			15647.5i			0.598384i	0.954193	+	0.299192i	$0.0967172\pi$
$881$			15647.5i			0.598384i	−0.954193	+	0.299192i	$0.903283\pi$
$882$	5526.00			0.210964
$883$	−12759.6			−0.486291			−0.243145	−	0.969990i	$-0.578179\pi$
$883$	−12759.6			−0.486291			−0.243145	+	0.969990i	$0.578179\pi$
$884$	1954.82	+	4433.11i	0.0743752	+	0.168667i
$885$	5913.67			0.224617
$886$	−16045.3			−0.608411
$887$			18022.4i			0.682225i	0.940022	+	0.341113i	$0.110804\pi$
$887$			18022.4i			0.682225i	−0.940022	+	0.341113i	$0.889196\pi$
$888$	−1130.94			−0.0427384
$889$			13749.8i			0.518731i
$890$		−	26101.9i		−	0.983077i
$891$			127.424i			0.00479111i
$892$	3675.17			0.137952
$893$	−66621.4			−2.49653
$894$		−	16084.6i		−	0.601732i
$895$			18792.8i			0.701871i
$896$		−	768.000i		−	0.0286351i
$897$	1606.47			0.0597977
$898$		−	9460.88i		−	0.351574i
$899$	1791.22			0.0664523
$900$	5214.30			0.193122
$901$	15925.4	+	36115.5i	0.588849	+	1.33538i
$902$	−720.460			−0.0265950
$903$	6769.56			0.249476
$904$			8216.48i			0.302296i
$905$	−57758.0			−2.12148
$906$		−	1361.27i		−	0.0499173i
$907$			51434.0i			1.88295i	0.337078	+	0.941477i	$0.390561\pi$
$907$			51434.0i			1.88295i	−0.337078	+	0.941477i	$0.609439\pi$
$908$		−	7017.25i		−	0.256471i
$909$	3547.56			0.129444
$910$	3406.39			0.124089
$911$			7890.19i			0.286953i	0.989654	+	0.143476i	$0.0458281\pi$
$911$			7890.19i			0.286953i	−0.989654	+	0.143476i	$0.954172\pi$
$912$			7000.40i			0.254174i
$913$			1729.96i			0.0627088i
$914$	−1680.89			−0.0608305
$915$		−	20149.7i		−	0.728010i
$916$	−7436.72			−0.268249
$917$	−11610.2			−0.418107
$918$	−3463.25	+	1527.15i	−0.124515	+	0.0549058i
$919$	−46068.0			−1.65358			−0.826792	−	0.562507i	$-0.809837\pi$
$919$	−46068.0			−1.65358			−0.826792	+	0.562507i	$0.809837\pi$
$920$	4072.29			0.145934
$921$			10154.3i			0.363297i
$922$	−13577.8			−0.484989
$923$			15472.9i			0.551783i
$924$			113.266i			0.00403266i
$925$		−	6825.28i		−	0.242610i
$926$	23091.3			0.819469
$927$	−6740.03			−0.238804
$928$			1910.64i			0.0675860i
$929$			28007.0i			0.989106i	0.869147	+	0.494553i	$0.164668\pi$
$929$			28007.0i			0.989106i	−0.869147	+	0.494553i	$0.835332\pi$
$930$			2956.83i			0.104256i
$931$	−44773.4			−1.57614
$932$			6149.72i			0.216138i
$933$	−2583.01			−0.0906365
$934$	−348.606			−0.0122128
$935$	−730.820	−	1657.34i	−0.0255619	−	0.0579689i
$936$	−1244.20			−0.0434487
$937$	42032.8			1.46548			0.732738	−	0.680511i	$-0.238242\pi$
$937$	42032.8			1.46548			0.732738	+	0.680511i	$0.238242\pi$
$938$		−	2461.47i		−	0.0856821i
$939$	2851.95			0.0991158
$940$		−	30015.5i		−	1.04149i
$941$		−	31863.4i		−	1.10384i	−0.833896	−	0.551922i	$-0.813895\pi$
$941$		−	31863.4i		−	1.10384i	0.833896	−	0.551922i	$-0.186105\pi$
$942$			2118.65i			0.0732794i
$943$	−7095.89			−0.245041
$944$	−1920.00			−0.0661978
$945$			2661.15i			0.0916056i
$946$		−	1183.27i		−	0.0406676i
$947$		−	42612.1i		−	1.46220i	−0.682269	−	0.731102i	$-0.739007\pi$
$947$		−	42612.1i		−	1.46220i	0.682269	−	0.731102i	$-0.260993\pi$
$948$	−12465.7			−0.427074
$949$			18439.3i			0.630731i
$950$	−42247.9			−1.44285
$951$	−25203.5			−0.859390
$952$	−3078.45	+	1357.47i	−0.104804	+	0.0462141i
$953$	−6529.28			−0.221935			−0.110968	−	0.993824i	$-0.535395\pi$
$953$	−6529.28			−0.221935			−0.110968	+	0.993824i	$0.535395\pi$
$954$	−10136.2			−0.343995
$955$			68230.8i			2.31193i
$956$	−15618.8			−0.528396
$957$		−	281.784i		−	0.00951807i
$958$		−	32365.4i		−	1.09152i
$959$			5841.24i			0.196688i
$960$	−3153.96			−0.106035
$961$	28891.0			0.969790
$962$			1628.60i			0.0545824i
$963$		−	10804.3i		−	0.361541i
$964$			9478.56i			0.316685i
$965$	67200.8			2.24173
$966$			1115.57i			0.0371561i
$967$	21784.1			0.724436			0.362218	−	0.932093i	$-0.382020\pi$
$967$	21784.1			0.724436			0.362218	+	0.932093i	$0.382020\pi$
$968$	−10628.2			−0.352896
$969$	28060.4	−	12373.5i	0.930267	−	0.410210i
$970$	33058.9			1.09429
$971$	−293.579			−0.00970279			−0.00485140	−	0.999988i	$-0.501544\pi$
$971$	−293.579			−0.00970279			−0.00485140	+	0.999988i	$0.501544\pi$
$972$		−	972.000i		−	0.0320750i
$973$	1862.33			0.0613603
$974$			35630.5i			1.17215i
$975$		−	7508.85i		−	0.246642i
$976$			6542.04i			0.214555i
$977$	42000.5			1.37535			0.687673	−	0.726020i	$-0.258632\pi$
$977$	42000.5			1.37535			0.687673	+	0.726020i	$0.258632\pi$
$978$	−6424.23			−0.210045
$979$		−	1249.84i		−	0.0408020i
$980$		−	20172.2i		−	0.657527i
$981$		−	9750.95i		−	0.317354i
$982$	−38890.4			−1.26379
$983$			4754.22i			0.154258i	0.997021	+	0.0771292i	$0.0245754\pi$
$983$			4754.22i			0.154258i	−0.997021	+	0.0771292i	$0.975425\pi$
$984$	5495.71			0.178046
$985$	79239.0			2.56321
$986$	7658.59	−	3377.12i	0.247362	−	0.109077i
$987$	8222.50			0.265172
$988$	10080.9			0.324612
$989$		−	11654.2i		−	0.374703i
$990$	465.151			0.0149328
$991$		−	44080.5i		−	1.41298i	−0.707722	−	0.706491i	$-0.750277\pi$
$991$		−	44080.5i		−	1.41298i	0.707722	−	0.706491i	$-0.249723\pi$
$992$		−	960.000i		−	0.0307258i
$993$		−	12384.6i		−	0.395784i
$994$	−10744.7			−0.342858
$995$	−49046.4			−1.56269
$996$		−	13196.2i		−	0.419817i
$997$			6073.28i			0.192922i	0.995337	+	0.0964608i	$0.0307522\pi$
$997$			6073.28i			0.192922i	−0.995337	+	0.0964608i	$0.969248\pi$
$998$			19049.4i			0.604208i
$999$	−1272.30			−0.0402942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.4.b.a.67.1	✓	4
3.2	odd	2		306.4.b.e.271.4		4
4.3	odd	2		816.4.c.b.577.3		4
17.4	even	4		1734.4.a.m.1.1		2
17.13	even	4		1734.4.a.s.1.2		2
17.16	even	2	inner	102.4.b.a.67.4	yes	4
51.50	odd	2		306.4.b.e.271.1		4
68.67	odd	2		816.4.c.b.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.b.a.67.1	✓	4	1.1	even	1	trivial
102.4.b.a.67.4	yes	4	17.16	even	2	inner
306.4.b.e.271.1		4	51.50	odd	2
306.4.b.e.271.4		4	3.2	odd	2
816.4.c.b.577.2		4	68.67	odd	2
816.4.c.b.577.3		4	4.3	odd	2
1734.4.a.m.1.1		2	17.4	even	4
1734.4.a.s.1.2		2	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	102.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000i q^{3} +4.00000 q^{4} -16.4269i q^{5} +6.00000i q^{6} +6.00000i q^{7} -8.00000 q^{8} -9.00000 q^{9} +32.8537i q^{10} +1.57314i q^{11} -12.0000i q^{12} -17.2806 q^{13} -12.0000i q^{14} -49.2806 q^{15} +16.0000 q^{16} +(-28.2806 - 64.1343i) q^{17} +18.0000 q^{18} -145.842 q^{19} -65.7074i q^{20} +18.0000 q^{21} -3.14628i q^{22} -30.9880i q^{23} +24.0000i q^{24} -144.842 q^{25} +34.5612 q^{26} +27.0000i q^{27} +24.0000i q^{28} -59.7074i q^{29} +98.5612 q^{30} +30.0000i q^{31} -32.0000 q^{32} +4.71942 q^{33} +(56.5612 + 128.269i) q^{34} +98.5612 q^{35} -36.0000 q^{36} +47.1223i q^{37} +291.683 q^{38} +51.8417i q^{39} +131.415i q^{40} -228.988i q^{41} -36.0000 q^{42} +376.086 q^{43} +6.29256i q^{44} +147.842i q^{45} +61.9760i q^{46} +456.806 q^{47} -48.0000i q^{48} +307.000 q^{49} +289.683 q^{50} +(-192.403 + 84.8417i) q^{51} -69.1223 q^{52} -563.122 q^{53} -54.0000i q^{54} +25.8417 q^{55} -48.0000i q^{56} +437.525i q^{57} +119.415i q^{58} -120.000 q^{59} -197.122 q^{60} +408.878i q^{61} -60.0000i q^{62} -54.0000i q^{63} +64.0000 q^{64} +283.866i q^{65} -9.43884 q^{66} +205.122 q^{67} +(-113.122 - 256.537i) q^{68} -92.9641 q^{69} -197.122 q^{70} -895.391i q^{71} +72.0000 q^{72} -1067.05i q^{73} -94.2447i q^{74} +434.525i q^{75} -583.367 q^{76} -9.43884 q^{77} -103.683i q^{78} -1038.81i q^{79} -262.830i q^{80} +81.0000 q^{81} +457.976i q^{82} +1099.68 q^{83} +72.0000 q^{84} +(-1053.53 + 464.561i) q^{85} -752.173 q^{86} -179.122 q^{87} -12.5851i q^{88} -794.489 q^{89} -295.683i q^{90} -103.683i q^{91} -123.952i q^{92} +90.0000 q^{93} -913.612 q^{94} +2395.72i q^{95} +96.0000i q^{96} -1006.24i q^{97} -614.000 q^{98} -14.1583i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 16 q^{4} - 32 q^{8} - 36 q^{9} + 74 q^{13} - 54 q^{15} + 64 q^{16} + 30 q^{17} + 72 q^{18} - 154 q^{19} + 72 q^{21} - 150 q^{25} - 148 q^{26} + 108 q^{30} - 128 q^{32} + 162 q^{33} - 60 q^{34}+ \cdots - 2456 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 16 * q^4 - 32 * q^8 - 36 * q^9 + 74 * q^13 - 54 * q^15 + 64 * q^16 + 30 * q^17 + 72 * q^18 - 154 * q^19 + 72 * q^21 - 150 * q^25 - 148 * q^26 + 108 * q^30 - 128 * q^32 + 162 * q^33 - 60 * q^34 + 108 * q^35 - 144 * q^36 + 308 * q^38 - 144 * q^42 - 70 * q^43 + 396 * q^47 + 1228 * q^49 + 300 * q^50 - 54 * q^51 + 296 * q^52 - 1680 * q^53 - 326 * q^55 - 480 * q^59 - 216 * q^60 + 256 * q^64 - 324 * q^66 + 248 * q^67 + 120 * q^68 + 630 * q^69 - 216 * q^70 + 288 * q^72 - 616 * q^76 - 324 * q^77 + 324 * q^81 + 3540 * q^83 + 288 * q^84 - 2926 * q^85 + 140 * q^86 - 144 * q^87 - 888 * q^89 + 360 * q^93 - 792 * q^94 - 2456 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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