LMFDB - Embedded newform 10.4.b.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,4,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, 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("10.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	10.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:	$0.590019100057$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.4.b.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +(-5.00000 + 10.0000i) q^{5} +4.00000 q^{6} -26.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +(-5.00000 + 10.0000i) q^{5} +4.00000 q^{6} -26.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +(20.0000 + 10.0000i) q^{10} -28.0000 q^{11} -8.00000i q^{12} +12.0000i q^{13} -52.0000 q^{14} +(-20.0000 - 10.0000i) q^{15} +16.0000 q^{16} +64.0000i q^{17} -46.0000i q^{18} +60.0000 q^{19} +(20.0000 - 40.0000i) q^{20} +52.0000 q^{21} +56.0000i q^{22} -58.0000i q^{23} -16.0000 q^{24} +(-75.0000 - 100.000i) q^{25} +24.0000 q^{26} +100.000i q^{27} +104.000i q^{28} -90.0000 q^{29} +(-20.0000 + 40.0000i) q^{30} -128.000 q^{31} -32.0000i q^{32} -56.0000i q^{33} +128.000 q^{34} +(260.000 + 130.000i) q^{35} -92.0000 q^{36} -236.000i q^{37} -120.000i q^{38} -24.0000 q^{39} +(-80.0000 - 40.0000i) q^{40} +242.000 q^{41} -104.000i q^{42} +362.000i q^{43} +112.000 q^{44} +(-115.000 + 230.000i) q^{45} -116.000 q^{46} -226.000i q^{47} +32.0000i q^{48} -333.000 q^{49} +(-200.000 + 150.000i) q^{50} -128.000 q^{51} -48.0000i q^{52} -108.000i q^{53} +200.000 q^{54} +(140.000 - 280.000i) q^{55} +208.000 q^{56} +120.000i q^{57} +180.000i q^{58} +20.0000 q^{59} +(80.0000 + 40.0000i) q^{60} +542.000 q^{61} +256.000i q^{62} -598.000i q^{63} -64.0000 q^{64} +(-120.000 - 60.0000i) q^{65} -112.000 q^{66} +434.000i q^{67} -256.000i q^{68} +116.000 q^{69} +(260.000 - 520.000i) q^{70} -1128.00 q^{71} +184.000i q^{72} +632.000i q^{73} -472.000 q^{74} +(200.000 - 150.000i) q^{75} -240.000 q^{76} +728.000i q^{77} +48.0000i q^{78} +720.000 q^{79} +(-80.0000 + 160.000i) q^{80} +421.000 q^{81} -484.000i q^{82} -478.000i q^{83} -208.000 q^{84} +(-640.000 - 320.000i) q^{85} +724.000 q^{86} -180.000i q^{87} -224.000i q^{88} +490.000 q^{89} +(460.000 + 230.000i) q^{90} +312.000 q^{91} +232.000i q^{92} -256.000i q^{93} -452.000 q^{94} +(-300.000 + 600.000i) q^{95} +64.0000 q^{96} -1456.00i q^{97} +666.000i q^{98} -644.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 - 10 * q^5 + 8 * q^6 + 46 * q^9	$ 2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9} + 40 q^{10} - 56 q^{11} - 104 q^{14} - 40 q^{15} + 32 q^{16} + 120 q^{19} + 40 q^{20} + 104 q^{21} - 32 q^{24} - 150 q^{25} + 48 q^{26} - 180 q^{29} - 40 q^{30} - 256 q^{31} + 256 q^{34} + 520 q^{35} - 184 q^{36} - 48 q^{39} - 160 q^{40} + 484 q^{41} + 224 q^{44} - 230 q^{45} - 232 q^{46} - 666 q^{49} - 400 q^{50} - 256 q^{51} + 400 q^{54} + 280 q^{55} + 416 q^{56} + 40 q^{59} + 160 q^{60} + 1084 q^{61} - 128 q^{64} - 240 q^{65} - 224 q^{66} + 232 q^{69} + 520 q^{70} - 2256 q^{71} - 944 q^{74} + 400 q^{75} - 480 q^{76} + 1440 q^{79} - 160 q^{80} + 842 q^{81} - 416 q^{84} - 1280 q^{85} + 1448 q^{86} + 980 q^{89} + 920 q^{90} + 624 q^{91} - 904 q^{94} - 600 q^{95} + 128 q^{96} - 1288 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 - 10 * q^5 + 8 * q^6 + 46 * q^9 + 40 * q^10 - 56 * q^11 - 104 * q^14 - 40 * q^15 + 32 * q^16 + 120 * q^19 + 40 * q^20 + 104 * q^21 - 32 * q^24 - 150 * q^25 + 48 * q^26 - 180 * q^29 - 40 * q^30 - 256 * q^31 + 256 * q^34 + 520 * q^35 - 184 * q^36 - 48 * q^39 - 160 * q^40 + 484 * q^41 + 224 * q^44 - 230 * q^45 - 232 * q^46 - 666 * q^49 - 400 * q^50 - 256 * q^51 + 400 * q^54 + 280 * q^55 + 416 * q^56 + 40 * q^59 + 160 * q^60 + 1084 * q^61 - 128 * q^64 - 240 * q^65 - 224 * q^66 + 232 * q^69 + 520 * q^70 - 2256 * q^71 - 944 * q^74 + 400 * q^75 - 480 * q^76 + 1440 * q^79 - 160 * q^80 + 842 * q^81 - 416 * q^84 - 1280 * q^85 + 1448 * q^86 + 980 * q^89 + 920 * q^90 + 624 * q^91 - 904 * q^94 - 600 * q^95 + 128 * q^96 - 1288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$			2.00000i			0.384900i	0.981307	+	0.192450i	$0.0616434\pi$
$3$			2.00000i			0.384900i	−0.981307	+	0.192450i	$0.938357\pi$
$4$	−4.00000			−0.500000
$5$	−5.00000	+	10.0000i	−0.447214	+	0.894427i
$5$	−5.00000	+	10.0000i	−0.447214	+	0.894427i
$6$	4.00000			0.272166
$7$		−	26.0000i		−	1.40387i	−0.712242	−	0.701934i	$-0.752320\pi$
$7$		−	26.0000i		−	1.40387i	0.712242	−	0.701934i	$-0.247680\pi$
$8$			8.00000i			0.353553i
$9$	23.0000			0.851852
$10$	20.0000	+	10.0000i	0.632456	+	0.316228i
$11$	−28.0000			−0.767483			−0.383742	−	0.923440i	$-0.625365\pi$
$11$	−28.0000			−0.767483			−0.383742	+	0.923440i	$0.625365\pi$
$12$		−	8.00000i		−	0.192450i
$13$			12.0000i			0.256015i	0.991773	+	0.128008i	$0.0408582\pi$
$13$			12.0000i			0.256015i	−0.991773	+	0.128008i	$0.959142\pi$
$14$	−52.0000			−0.992685
$15$	−20.0000	−	10.0000i	−0.344265	−	0.172133i
$16$	16.0000			0.250000
$17$			64.0000i			0.913075i	0.889704	+	0.456538i	$0.150911\pi$
$17$			64.0000i			0.913075i	−0.889704	+	0.456538i	$0.849089\pi$
$18$		−	46.0000i		−	0.602350i
$19$	60.0000			0.724471			0.362235	−	0.932087i	$-0.382014\pi$
$19$	60.0000			0.724471			0.362235	+	0.932087i	$0.382014\pi$
$20$	20.0000	−	40.0000i	0.223607	−	0.447214i
$21$	52.0000			0.540349
$22$			56.0000i			0.542693i
$23$		−	58.0000i		−	0.525819i	−0.964821	−	0.262909i	$-0.915318\pi$
$23$		−	58.0000i		−	0.525819i	0.964821	−	0.262909i	$-0.0846821\pi$
$24$	−16.0000			−0.136083
$25$	−75.0000	−	100.000i	−0.600000	−	0.800000i
$26$	24.0000			0.181030
$27$			100.000i			0.712778i
$28$			104.000i			0.701934i
$29$	−90.0000			−0.576296			−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000			−0.576296			−0.288148	+	0.957586i	$0.593039\pi$
$30$	−20.0000	+	40.0000i	−0.121716	+	0.243432i
$31$	−128.000			−0.741596			−0.370798	−	0.928714i	$-0.620916\pi$
$31$	−128.000			−0.741596			−0.370798	+	0.928714i	$0.620916\pi$
$32$		−	32.0000i		−	0.176777i
$33$		−	56.0000i		−	0.295405i
$34$	128.000			0.645642
$35$	260.000	+	130.000i	1.25566	+	0.627829i
$36$	−92.0000			−0.425926
$37$		−	236.000i		−	1.04860i	−0.851534	−	0.524299i	$-0.824327\pi$
$37$		−	236.000i		−	1.04860i	0.851534	−	0.524299i	$-0.175673\pi$
$38$		−	120.000i		−	0.512278i
$39$	−24.0000			−0.0985404
$40$	−80.0000	−	40.0000i	−0.316228	−	0.158114i
$41$	242.000			0.921806			0.460903	−	0.887450i	$-0.347526\pi$
$41$	242.000			0.921806			0.460903	+	0.887450i	$0.347526\pi$
$42$		−	104.000i		−	0.382084i
$43$			362.000i			1.28383i	0.766778	+	0.641913i	$0.221859\pi$
$43$			362.000i			1.28383i	−0.766778	+	0.641913i	$0.778141\pi$
$44$	112.000			0.383742
$45$	−115.000	+	230.000i	−0.380960	+	0.761919i
$46$	−116.000			−0.371810
$47$		−	226.000i		−	0.701393i	−0.936489	−	0.350697i	$-0.885945\pi$
$47$		−	226.000i		−	0.701393i	0.936489	−	0.350697i	$-0.114055\pi$
$48$			32.0000i			0.0962250i
$49$	−333.000			−0.970845
$50$	−200.000	+	150.000i	−0.565685	+	0.424264i
$51$	−128.000			−0.351443
$52$		−	48.0000i		−	0.128008i
$53$		−	108.000i		−	0.279905i	−0.990158	−	0.139952i	$-0.955305\pi$
$53$		−	108.000i		−	0.279905i	0.990158	−	0.139952i	$-0.0446949\pi$
$54$	200.000			0.504010
$55$	140.000	−	280.000i	0.343229	−	0.686458i
$56$	208.000			0.496342
$57$			120.000i			0.278849i
$58$			180.000i			0.407503i
$59$	20.0000			0.0441318			0.0220659	−	0.999757i	$-0.492976\pi$
$59$	20.0000			0.0441318			0.0220659	+	0.999757i	$0.492976\pi$
$60$	80.0000	+	40.0000i	0.172133	+	0.0860663i
$61$	542.000			1.13764			0.568820	−	0.822462i	$-0.307400\pi$
$61$	542.000			1.13764			0.568820	+	0.822462i	$0.307400\pi$
$62$			256.000i			0.524388i
$63$		−	598.000i		−	1.19589i
$64$	−64.0000			−0.125000
$65$	−120.000	−	60.0000i	−0.228987	−	0.114494i
$66$	−112.000			−0.208883
$67$			434.000i			0.791366i	0.918387	+	0.395683i	$0.129492\pi$
$67$			434.000i			0.791366i	−0.918387	+	0.395683i	$0.870508\pi$
$68$		−	256.000i		−	0.456538i
$69$	116.000			0.202388
$70$	260.000	−	520.000i	0.443942	−	0.887884i
$71$	−1128.00			−1.88548			−0.942739	−	0.333531i	$-0.891760\pi$
$71$	−1128.00			−1.88548			−0.942739	+	0.333531i	$0.891760\pi$
$72$			184.000i			0.301175i
$73$			632.000i			1.01329i	0.862155	+	0.506644i	$0.169114\pi$
$73$			632.000i			1.01329i	−0.862155	+	0.506644i	$0.830886\pi$
$74$	−472.000			−0.741471
$75$	200.000	−	150.000i	0.307920	−	0.230940i
$76$	−240.000			−0.362235
$77$			728.000i			1.07745i
$78$			48.0000i			0.0696786i
$79$	720.000			1.02540			0.512698	−	0.858569i	$-0.328646\pi$
$79$	720.000			1.02540			0.512698	+	0.858569i	$0.328646\pi$
$80$	−80.0000	+	160.000i	−0.111803	+	0.223607i
$81$	421.000			0.577503
$82$		−	484.000i		−	0.651815i
$83$		−	478.000i		−	0.632136i	−0.948736	−	0.316068i	$-0.897637\pi$
$83$		−	478.000i		−	0.632136i	0.948736	−	0.316068i	$-0.102363\pi$
$84$	−208.000			−0.270175
$85$	−640.000	−	320.000i	−0.816679	−	0.408340i
$86$	724.000			0.907801
$87$		−	180.000i		−	0.221816i
$88$		−	224.000i		−	0.271346i
$89$	490.000			0.583594			0.291797	−	0.956480i	$-0.405747\pi$
$89$	490.000			0.583594			0.291797	+	0.956480i	$0.405747\pi$
$90$	460.000	+	230.000i	0.538758	+	0.269379i
$91$	312.000			0.359412
$92$			232.000i			0.262909i
$93$		−	256.000i		−	0.285440i
$94$	−452.000			−0.495960
$95$	−300.000	+	600.000i	−0.323993	+	0.647986i
$96$	64.0000			0.0680414
$97$		−	1456.00i		−	1.52407i	−0.647538	−	0.762033i	$-0.724201\pi$
$97$		−	1456.00i		−	1.52407i	0.647538	−	0.762033i	$-0.275799\pi$
$98$			666.000i			0.686491i
$99$	−644.000			−0.653782
$100$	300.000	+	400.000i	0.300000	+	0.400000i
$101$	−578.000			−0.569437			−0.284719	−	0.958611i	$-0.591900\pi$
$101$	−578.000			−0.569437			−0.284719	+	0.958611i	$0.591900\pi$
$102$			256.000i			0.248508i
$103$			1462.00i			1.39859i	0.714831	+	0.699297i	$0.246503\pi$
$103$			1462.00i			1.39859i	−0.714831	+	0.699297i	$0.753497\pi$
$104$	−96.0000			−0.0905151
$105$	−260.000	+	520.000i	−0.241651	+	0.483303i
$106$	−216.000			−0.197922
$107$		−	966.000i		−	0.872773i	−0.899759	−	0.436387i	$-0.856258\pi$
$107$		−	966.000i		−	0.872773i	0.899759	−	0.436387i	$-0.143742\pi$
$108$		−	400.000i		−	0.356389i
$109$	−370.000			−0.325134			−0.162567	−	0.986698i	$-0.551977\pi$
$109$	−370.000			−0.325134			−0.162567	+	0.986698i	$0.551977\pi$
$110$	−560.000	−	280.000i	−0.485399	−	0.242700i
$111$	472.000			0.403606
$112$		−	416.000i		−	0.350967i
$113$		−	528.000i		−	0.439558i	−0.975550	−	0.219779i	$-0.929466\pi$
$113$		−	528.000i		−	0.439558i	0.975550	−	0.219779i	$-0.0705336\pi$
$114$	240.000			0.197176
$115$	580.000	+	290.000i	0.470307	+	0.235153i
$116$	360.000			0.288148
$117$			276.000i			0.218087i
$118$		−	40.0000i		−	0.0312059i
$119$	1664.00			1.28184
$120$	80.0000	−	160.000i	0.0608581	−	0.121716i
$121$	−547.000			−0.410969
$122$		−	1084.00i		−	0.804432i
$123$			484.000i			0.354803i
$124$	512.000			0.370798
$125$	1375.00	−	250.000i	0.983870	−	0.178885i
$126$	−1196.00			−0.845620
$127$			1534.00i			1.07181i	0.844277	+	0.535907i	$0.180030\pi$
$127$			1534.00i			1.07181i	−0.844277	+	0.535907i	$0.819970\pi$
$128$			128.000i			0.0883883i
$129$	−724.000			−0.494145
$130$	−120.000	+	240.000i	−0.0809592	+	0.161918i
$131$	12.0000			0.00800340			0.00400170	−	0.999992i	$-0.498726\pi$
$131$	12.0000			0.00800340			0.00400170	+	0.999992i	$0.498726\pi$
$132$			224.000i			0.147702i
$133$		−	1560.00i		−	1.01706i
$134$	868.000			0.559580
$135$	−1000.00	−	500.000i	−0.637528	−	0.318764i
$136$	−512.000			−0.322821
$137$			1224.00i			0.763309i	0.924305	+	0.381655i	$0.124646\pi$
$137$			1224.00i			0.763309i	−0.924305	+	0.381655i	$0.875354\pi$
$138$		−	232.000i		−	0.143110i
$139$	−3100.00			−1.89164			−0.945822	−	0.324685i	$-0.894742\pi$
$139$	−3100.00			−1.89164			−0.945822	+	0.324685i	$0.894742\pi$
$140$	−1040.00	−	520.000i	−0.627829	−	0.313914i
$141$	452.000			0.269966
$142$			2256.00i			1.33323i
$143$		−	336.000i		−	0.196488i
$144$	368.000			0.212963
$145$	450.000	−	900.000i	0.257727	−	0.515455i
$146$	1264.00			0.716503
$147$		−	666.000i		−	0.373679i
$148$			944.000i			0.524299i
$149$	−250.000			−0.137455			−0.0687275	−	0.997635i	$-0.521894\pi$
$149$	−250.000			−0.137455			−0.0687275	+	0.997635i	$0.521894\pi$
$150$	−300.000	−	400.000i	−0.163299	−	0.217732i
$151$	2152.00			1.15978			0.579892	−	0.814694i	$-0.303095\pi$
$151$	2152.00			1.15978			0.579892	+	0.814694i	$0.303095\pi$
$152$			480.000i			0.256139i
$153$			1472.00i			0.777805i
$154$	1456.00			0.761869
$155$	640.000	−	1280.00i	0.331652	−	0.663304i
$156$	96.0000			0.0492702
$157$			524.000i			0.266368i	0.991091	+	0.133184i	$0.0425201\pi$
$157$			524.000i			0.266368i	−0.991091	+	0.133184i	$0.957480\pi$
$158$		−	1440.00i		−	0.725065i
$159$	216.000			0.107735
$160$	320.000	+	160.000i	0.158114	+	0.0790569i
$161$	−1508.00			−0.738180
$162$		−	842.000i		−	0.408357i
$163$		−	3518.00i		−	1.69050i	−0.534373	−	0.845249i	$-0.679452\pi$
$163$		−	3518.00i		−	1.69050i	0.534373	−	0.845249i	$-0.320548\pi$
$164$	−968.000			−0.460903
$165$	560.000	+	280.000i	0.264218	+	0.132109i
$166$	−956.000			−0.446988
$167$			534.000i			0.247438i	0.992317	+	0.123719i	$0.0394822\pi$
$167$			534.000i			0.247438i	−0.992317	+	0.123719i	$0.960518\pi$
$168$			416.000i			0.191042i
$169$	2053.00			0.934456
$170$	−640.000	+	1280.00i	−0.288740	+	0.577480i
$171$	1380.00			0.617142
$172$		−	1448.00i		−	0.641913i
$173$			4252.00i			1.86863i	0.356444	+	0.934317i	$0.383989\pi$
$173$			4252.00i			1.86863i	−0.356444	+	0.934317i	$0.616011\pi$
$174$	−360.000			−0.156848
$175$	−2600.00	+	1950.00i	−1.12309	+	0.842321i
$176$	−448.000			−0.191871
$177$			40.0000i			0.0169864i
$178$		−	980.000i		−	0.412664i
$179$	−2500.00			−1.04390			−0.521952	−	0.852975i	$-0.674796\pi$
$179$	−2500.00			−1.04390			−0.521952	+	0.852975i	$0.674796\pi$
$180$	460.000	−	920.000i	0.190480	−	0.380960i
$181$	−2578.00			−1.05868			−0.529340	−	0.848410i	$-0.677561\pi$
$181$	−2578.00			−1.05868			−0.529340	+	0.848410i	$0.677561\pi$
$182$		−	624.000i		−	0.254143i
$183$			1084.00i			0.437878i
$184$	464.000			0.185905
$185$	2360.00	+	1180.00i	0.937895	+	0.468948i
$186$	−512.000			−0.201837
$187$		−	1792.00i		−	0.700770i
$188$			904.000i			0.350697i
$189$	2600.00			1.00065
$190$	1200.00	+	600.000i	0.458196	+	0.229098i
$191$	−768.000			−0.290945			−0.145473	−	0.989362i	$-0.546470\pi$
$191$	−768.000			−0.290945			−0.145473	+	0.989362i	$0.546470\pi$
$192$		−	128.000i		−	0.0481125i
$193$		−	2608.00i		−	0.972684i	−0.873769	−	0.486342i	$-0.838331\pi$
$193$		−	2608.00i		−	0.972684i	0.873769	−	0.486342i	$-0.161669\pi$
$194$	−2912.00			−1.07768
$195$	120.000	−	240.000i	0.0440686	−	0.0881372i
$196$	1332.00			0.485423
$197$		−	5116.00i		−	1.85025i	−0.379659	−	0.925127i	$-0.623959\pi$
$197$		−	5116.00i		−	1.85025i	0.379659	−	0.925127i	$-0.376041\pi$
$198$			1288.00i			0.462294i
$199$	3480.00			1.23965			0.619826	−	0.784739i	$-0.287203\pi$
$199$	3480.00			1.23965			0.619826	+	0.784739i	$0.287203\pi$
$200$	800.000	−	600.000i	0.282843	−	0.212132i
$201$	−868.000			−0.304597
$202$			1156.00i			0.402653i
$203$			2340.00i			0.809043i
$204$	512.000			0.175721
$205$	−1210.00	+	2420.00i	−0.412244	+	0.824488i
$206$	2924.00			0.988955
$207$		−	1334.00i		−	0.447920i
$208$			192.000i			0.0640039i
$209$	−1680.00			−0.556019
$210$	1040.00	+	520.000i	0.341747	+	0.170873i
$211$	3132.00			1.02188			0.510938	−	0.859618i	$-0.329298\pi$
$211$	3132.00			1.02188			0.510938	+	0.859618i	$0.329298\pi$
$212$			432.000i			0.139952i
$213$		−	2256.00i		−	0.725721i
$214$	−1932.00			−0.617144
$215$	−3620.00	−	1810.00i	−1.14829	−	0.574144i
$216$	−800.000			−0.252005
$217$			3328.00i			1.04110i
$218$			740.000i			0.229904i
$219$	−1264.00			−0.390015
$220$	−560.000	+	1120.00i	−0.171615	+	0.343229i
$221$	−768.000			−0.233761
$222$		−	944.000i		−	0.285392i
$223$			62.0000i			0.0186181i	0.999957	+	0.00930903i	$0.00296320\pi$
$223$			62.0000i			0.0186181i	−0.999957	+	0.00930903i	$0.997037\pi$
$224$	−832.000			−0.248171
$225$	−1725.00	−	2300.00i	−0.511111	−	0.681481i
$226$	−1056.00			−0.310814
$227$			5314.00i			1.55376i	0.629651	+	0.776878i	$0.283198\pi$
$227$			5314.00i			1.55376i	−0.629651	+	0.776878i	$0.716802\pi$
$228$		−	480.000i		−	0.139424i
$229$	190.000			0.0548277			0.0274139	−	0.999624i	$-0.491273\pi$
$229$	190.000			0.0548277			0.0274139	+	0.999624i	$0.491273\pi$
$230$	580.000	−	1160.00i	0.166279	−	0.332557i
$231$	−1456.00			−0.414709
$232$		−	720.000i		−	0.203751i
$233$		−	2408.00i		−	0.677053i	−0.940957	−	0.338526i	$-0.890072\pi$
$233$		−	2408.00i		−	0.677053i	0.940957	−	0.338526i	$-0.109928\pi$
$234$	552.000			0.154211
$235$	2260.00	+	1130.00i	0.627345	+	0.313673i
$236$	−80.0000			−0.0220659
$237$			1440.00i			0.394675i
$238$		−	3328.00i		−	0.906396i
$239$	5680.00			1.53727			0.768637	−	0.639685i	$-0.220935\pi$
$239$	5680.00			1.53727			0.768637	+	0.639685i	$0.220935\pi$
$240$	−320.000	−	160.000i	−0.0860663	−	0.0430331i
$241$	−278.000			−0.0743052			−0.0371526	−	0.999310i	$-0.511829\pi$
$241$	−278.000			−0.0743052			−0.0371526	+	0.999310i	$0.511829\pi$
$242$			1094.00i			0.290599i
$243$			3542.00i			0.935059i
$244$	−2168.00			−0.568820
$245$	1665.00	−	3330.00i	0.434175	−	0.868351i
$246$	968.000			0.250884
$247$			720.000i			0.185476i
$248$		−	1024.00i		−	0.262194i
$249$	956.000			0.243309
$250$	−500.000	−	2750.00i	−0.126491	−	0.695701i
$251$	3252.00			0.817787			0.408893	−	0.912582i	$-0.365915\pi$
$251$	3252.00			0.817787			0.408893	+	0.912582i	$0.365915\pi$
$252$			2392.00i			0.597944i
$253$			1624.00i			0.403557i
$254$	3068.00			0.757888
$255$	640.000	−	1280.00i	0.157170	−	0.314340i
$256$	256.000			0.0625000
$257$		−	1536.00i		−	0.372813i	−0.982473	−	0.186407i	$-0.940316\pi$
$257$		−	1536.00i		−	0.372813i	0.982473	−	0.186407i	$-0.0596842\pi$
$258$			1448.00i			0.349413i
$259$	−6136.00			−1.47209
$260$	480.000	+	240.000i	0.114494	+	0.0572468i
$261$	−2070.00			−0.490919
$262$		−	24.0000i		−	0.00565926i
$263$		−	4858.00i		−	1.13900i	−0.821991	−	0.569500i	$-0.807137\pi$
$263$		−	4858.00i		−	1.13900i	0.821991	−	0.569500i	$-0.192863\pi$
$264$	448.000			0.104441
$265$	1080.00	+	540.000i	0.250354	+	0.125177i
$266$	−3120.00			−0.719171
$267$			980.000i			0.224626i
$268$		−	1736.00i		−	0.395683i
$269$	−2610.00			−0.591578			−0.295789	−	0.955253i	$-0.595583\pi$
$269$	−2610.00			−0.591578			−0.295789	+	0.955253i	$0.595583\pi$
$270$	−1000.00	+	2000.00i	−0.225400	+	0.450800i
$271$	−5168.00			−1.15843			−0.579213	−	0.815176i	$-0.696640\pi$
$271$	−5168.00			−1.15843			−0.579213	+	0.815176i	$0.696640\pi$
$272$			1024.00i			0.228269i
$273$			624.000i			0.138338i
$274$	2448.00			0.539741
$275$	2100.00	+	2800.00i	0.460490	+	0.613987i
$276$	−464.000			−0.101194
$277$			1924.00i			0.417336i	0.977987	+	0.208668i	$0.0669127\pi$
$277$			1924.00i			0.417336i	−0.977987	+	0.208668i	$0.933087\pi$
$278$			6200.00i			1.33759i
$279$	−2944.00			−0.631730
$280$	−1040.00	+	2080.00i	−0.221971	+	0.443942i
$281$	3042.00			0.645803			0.322901	−	0.946433i	$-0.395342\pi$
$281$	3042.00			0.645803			0.322901	+	0.946433i	$0.395342\pi$
$282$		−	904.000i		−	0.190895i
$283$		−	1718.00i		−	0.360864i	−0.983587	−	0.180432i	$-0.942250\pi$
$283$		−	1718.00i		−	0.360864i	0.983587	−	0.180432i	$-0.0577496\pi$
$284$	4512.00			0.942739
$285$	−1200.00	−	600.000i	−0.249410	−	0.124705i
$286$	−672.000			−0.138938
$287$		−	6292.00i		−	1.29409i
$288$		−	736.000i		−	0.150588i
$289$	817.000			0.166294
$290$	−1800.00	−	900.000i	−0.364482	−	0.182241i
$291$	2912.00			0.586613
$292$		−	2528.00i		−	0.506644i
$293$			2292.00i			0.456997i	0.973544	+	0.228498i	$0.0733816\pi$
$293$			2292.00i			0.456997i	−0.973544	+	0.228498i	$0.926618\pi$
$294$	−1332.00			−0.264231
$295$	−100.000	+	200.000i	−0.0197364	+	0.0394727i
$296$	1888.00			0.370736
$297$		−	2800.00i		−	0.547045i
$298$			500.000i			0.0971954i
$299$	696.000			0.134618
$300$	−800.000	+	600.000i	−0.153960	+	0.115470i
$301$	9412.00			1.80232
$302$		−	4304.00i		−	0.820091i
$303$		−	1156.00i		−	0.219176i
$304$	960.000			0.181118
$305$	−2710.00	+	5420.00i	−0.508768	+	1.01754i
$306$	2944.00			0.549991
$307$		−	5406.00i		−	1.00501i	−0.864576	−	0.502503i	$-0.832413\pi$
$307$		−	5406.00i		−	1.00501i	0.864576	−	0.502503i	$-0.167587\pi$
$308$		−	2912.00i		−	0.538723i
$309$	−2924.00			−0.538319
$310$	−2560.00	−	1280.00i	−0.469027	−	0.234513i
$311$	−5688.00			−1.03710			−0.518548	−	0.855048i	$-0.673527\pi$
$311$	−5688.00			−1.03710			−0.518548	+	0.855048i	$0.673527\pi$
$312$		−	192.000i		−	0.0348393i
$313$			7352.00i			1.32767i	0.747881	+	0.663833i	$0.231072\pi$
$313$			7352.00i			1.32767i	−0.747881	+	0.663833i	$0.768928\pi$
$314$	1048.00			0.188351
$315$	5980.00	+	2990.00i	1.06963	+	0.534817i
$316$	−2880.00			−0.512698
$317$			3484.00i			0.617290i	0.951177	+	0.308645i	$0.0998755\pi$
$317$			3484.00i			0.617290i	−0.951177	+	0.308645i	$0.900124\pi$
$318$		−	432.000i		−	0.0761804i
$319$	2520.00			0.442298
$320$	320.000	−	640.000i	0.0559017	−	0.111803i
$321$	1932.00			0.335931
$322$			3016.00i			0.521972i
$323$			3840.00i			0.661496i
$324$	−1684.00			−0.288752
$325$	1200.00	−	900.000i	0.204812	−	0.153609i
$326$	−7036.00			−1.19536
$327$		−	740.000i		−	0.125144i
$328$			1936.00i			0.325908i
$329$	−5876.00			−0.984664
$330$	560.000	−	1120.00i	0.0934151	−	0.186830i
$331$	−7868.00			−1.30654			−0.653269	−	0.757125i	$-0.726603\pi$
$331$	−7868.00			−1.30654			−0.653269	+	0.757125i	$0.726603\pi$
$332$			1912.00i			0.316068i
$333$		−	5428.00i		−	0.893251i
$334$	1068.00			0.174965
$335$	−4340.00	−	2170.00i	−0.707819	−	0.353910i
$336$	832.000			0.135087
$337$		−	656.000i		−	0.106037i	−0.998594	−	0.0530187i	$-0.983116\pi$
$337$		−	656.000i		−	0.106037i	0.998594	−	0.0530187i	$-0.0168843\pi$
$338$		−	4106.00i		−	0.660760i
$339$	1056.00			0.169186
$340$	2560.00	+	1280.00i	0.408340	+	0.204170i
$341$	3584.00			0.569163
$342$		−	2760.00i		−	0.436385i
$343$		−	260.000i		−	0.0409291i
$344$	−2896.00			−0.453901
$345$	−580.000	+	1160.00i	−0.0905106	+	0.181021i
$346$	8504.00			1.32132
$347$			5754.00i			0.890176i	0.895487	+	0.445088i	$0.146828\pi$
$347$			5754.00i			0.890176i	−0.895487	+	0.445088i	$0.853172\pi$
$348$			720.000i			0.110908i
$349$	3110.00			0.477004			0.238502	−	0.971142i	$-0.423344\pi$
$349$	3110.00			0.477004			0.238502	+	0.971142i	$0.423344\pi$
$350$	3900.00	+	5200.00i	0.595611	+	0.794148i
$351$	−1200.00			−0.182482
$352$			896.000i			0.135673i
$353$		−	7808.00i		−	1.17727i	−0.808397	−	0.588637i	$-0.799665\pi$
$353$		−	7808.00i		−	1.17727i	0.808397	−	0.588637i	$-0.200335\pi$
$354$	80.0000			0.0120112
$355$	5640.00	−	11280.0i	0.843212	−	1.68642i
$356$	−1960.00			−0.291797
$357$			3328.00i			0.493379i
$358$			5000.00i			0.738151i
$359$	9240.00			1.35841			0.679204	−	0.733949i	$-0.262325\pi$
$359$	9240.00			1.35841			0.679204	+	0.733949i	$0.262325\pi$
$360$	−1840.00	−	920.000i	−0.269379	−	0.134690i
$361$	−3259.00			−0.475142
$362$			5156.00i			0.748600i
$363$		−	1094.00i		−	0.158182i
$364$	−1248.00			−0.179706
$365$	−6320.00	−	3160.00i	−0.906312	−	0.453156i
$366$	2168.00			0.309626
$367$			3214.00i			0.457137i	0.973528	+	0.228569i	$0.0734046\pi$
$367$			3214.00i			0.457137i	−0.973528	+	0.228569i	$0.926595\pi$
$368$		−	928.000i		−	0.131455i
$369$	5566.00			0.785242
$370$	2360.00	−	4720.00i	0.331596	−	0.663192i
$371$	−2808.00			−0.392949
$372$			1024.00i			0.142720i
$373$		−	348.000i		−	0.0483077i	−0.999708	−	0.0241538i	$-0.992311\pi$
$373$		−	348.000i		−	0.0483077i	0.999708	−	0.0241538i	$-0.00768915\pi$
$374$	−3584.00			−0.495519
$375$	500.000	+	2750.00i	0.0688530	+	0.378692i
$376$	1808.00			0.247980
$377$		−	1080.00i		−	0.147541i
$378$		−	5200.00i		−	0.707564i
$379$	−4940.00			−0.669527			−0.334764	−	0.942302i	$-0.608656\pi$
$379$	−4940.00			−0.669527			−0.334764	+	0.942302i	$0.608656\pi$
$380$	1200.00	−	2400.00i	0.161997	−	0.323993i
$381$	−3068.00			−0.412542
$382$			1536.00i			0.205729i
$383$			6142.00i			0.819430i	0.912214	+	0.409715i	$0.134372\pi$
$383$			6142.00i			0.819430i	−0.912214	+	0.409715i	$0.865628\pi$
$384$	−256.000			−0.0340207
$385$	−7280.00	−	3640.00i	−0.963697	−	0.481848i
$386$	−5216.00			−0.687791
$387$			8326.00i			1.09363i
$388$			5824.00i			0.762033i
$389$	−3050.00			−0.397535			−0.198768	−	0.980047i	$-0.563694\pi$
$389$	−3050.00			−0.397535			−0.198768	+	0.980047i	$0.563694\pi$
$390$	−480.000	−	240.000i	−0.0623224	−	0.0311612i
$391$	3712.00			0.480112
$392$		−	2664.00i		−	0.343246i
$393$			24.0000i			0.00308051i
$394$	−10232.0			−1.30833
$395$	−3600.00	+	7200.00i	−0.458571	+	0.917143i
$396$	2576.00			0.326891
$397$		−	5396.00i		−	0.682160i	−0.940034	−	0.341080i	$-0.889207\pi$
$397$		−	5396.00i		−	0.682160i	0.940034	−	0.341080i	$-0.110793\pi$
$398$		−	6960.00i		−	0.876566i
$399$	3120.00			0.391467
$400$	−1200.00	−	1600.00i	−0.150000	−	0.200000i
$401$	14482.0			1.80348			0.901741	−	0.432276i	$-0.142289\pi$
$401$	14482.0			1.80348			0.901741	+	0.432276i	$0.142289\pi$
$402$			1736.00i			0.215383i
$403$		−	1536.00i		−	0.189860i
$404$	2312.00			0.284719
$405$	−2105.00	+	4210.00i	−0.258267	+	0.516535i
$406$	4680.00			0.572080
$407$			6608.00i			0.804782i
$408$		−	1024.00i		−	0.124254i
$409$	1090.00			0.131778			0.0658888	−	0.997827i	$-0.479012\pi$
$409$	1090.00			0.131778			0.0658888	+	0.997827i	$0.479012\pi$
$410$	4840.00	+	2420.00i	0.583001	+	0.291501i
$411$	−2448.00			−0.293798
$412$		−	5848.00i		−	0.699297i
$413$		−	520.000i		−	0.0619553i
$414$	−2668.00			−0.316727
$415$	4780.00	+	2390.00i	0.565400	+	0.282700i
$416$	384.000			0.0452576
$417$		−	6200.00i		−	0.728094i
$418$			3360.00i			0.393165i
$419$	7180.00			0.837150			0.418575	−	0.908182i	$-0.362530\pi$
$419$	7180.00			0.837150			0.418575	+	0.908182i	$0.362530\pi$
$420$	1040.00	−	2080.00i	0.120826	−	0.241651i
$421$	−8138.00			−0.942095			−0.471047	−	0.882108i	$-0.656124\pi$
$421$	−8138.00			−0.942095			−0.471047	+	0.882108i	$0.656124\pi$
$422$		−	6264.00i		−	0.722575i
$423$		−	5198.00i		−	0.597483i
$424$	864.000			0.0989612
$425$	6400.00	−	4800.00i	0.730460	−	0.547845i
$426$	−4512.00			−0.513162
$427$		−	14092.0i		−	1.59710i
$428$			3864.00i			0.436387i
$429$	672.000			0.0756281
$430$	−3620.00	+	7240.00i	−0.405981	+	0.811962i
$431$	−208.000			−0.0232460			−0.0116230	−	0.999932i	$-0.503700\pi$
$431$	−208.000			−0.0232460			−0.0116230	+	0.999932i	$0.503700\pi$
$432$			1600.00i			0.178195i
$433$			12992.0i			1.44193i	0.692971	+	0.720965i	$0.256301\pi$
$433$			12992.0i			1.44193i	−0.692971	+	0.720965i	$0.743699\pi$
$434$	6656.00			0.736171
$435$	1800.00	+	900.000i	0.198399	+	0.0991993i
$436$	1480.00			0.162567
$437$		−	3480.00i		−	0.380940i
$438$			2528.00i			0.275782i
$439$	−1080.00			−0.117416			−0.0587080	−	0.998275i	$-0.518698\pi$
$439$	−1080.00			−0.117416			−0.0587080	+	0.998275i	$0.518698\pi$
$440$	2240.00	+	1120.00i	0.242700	+	0.121350i
$441$	−7659.00			−0.827017
$442$			1536.00i			0.165294i
$443$		−	9078.00i		−	0.973609i	−0.873511	−	0.486805i	$-0.838162\pi$
$443$		−	9078.00i		−	0.973609i	0.873511	−	0.486805i	$-0.161838\pi$
$444$	−1888.00			−0.201803
$445$	−2450.00	+	4900.00i	−0.260991	+	0.521983i
$446$	124.000			0.0131650
$447$		−	500.000i		−	0.0529065i
$448$			1664.00i			0.175484i
$449$	−14310.0			−1.50408			−0.752039	−	0.659119i	$-0.770929\pi$
$449$	−14310.0			−1.50408			−0.752039	+	0.659119i	$0.770929\pi$
$450$	−4600.00	+	3450.00i	−0.481880	+	0.361410i
$451$	−6776.00			−0.707471
$452$			2112.00i			0.219779i
$453$			4304.00i			0.446401i
$454$	10628.0			1.09867
$455$	−1560.00	+	3120.00i	−0.160734	+	0.321468i
$456$	−960.000			−0.0985880
$457$			2344.00i			0.239929i	0.992778	+	0.119965i	$0.0382781\pi$
$457$			2344.00i			0.239929i	−0.992778	+	0.119965i	$0.961722\pi$
$458$		−	380.000i		−	0.0387691i
$459$	−6400.00			−0.650820
$460$	−2320.00	−	1160.00i	−0.235153	−	0.117577i
$461$	11382.0			1.14992			0.574959	−	0.818182i	$-0.305018\pi$
$461$	11382.0			1.14992			0.574959	+	0.818182i	$0.305018\pi$
$462$			2912.00i			0.293244i
$463$			16062.0i			1.61223i	0.591756	+	0.806117i	$0.298435\pi$
$463$			16062.0i			1.61223i	−0.591756	+	0.806117i	$0.701565\pi$
$464$	−1440.00			−0.144074
$465$	2560.00	+	1280.00i	0.255306	+	0.127653i
$466$	−4816.00			−0.478749
$467$		−	17166.0i		−	1.70096i	−0.526008	−	0.850479i	$-0.676312\pi$
$467$		−	17166.0i		−	1.70096i	0.526008	−	0.850479i	$-0.323688\pi$
$468$		−	1104.00i		−	0.109044i
$469$	11284.0			1.11097
$470$	2260.00	−	4520.00i	0.221800	−	0.443600i
$471$	−1048.00			−0.102525
$472$			160.000i			0.0156030i
$473$		−	10136.0i		−	0.985315i
$474$	2880.00			0.279078
$475$	−4500.00	−	6000.00i	−0.434682	−	0.579577i
$476$	−6656.00			−0.640919
$477$		−	2484.00i		−	0.238437i
$478$		−	11360.0i		−	1.08702i
$479$	−7520.00			−0.717323			−0.358661	−	0.933468i	$-0.616767\pi$
$479$	−7520.00			−0.717323			−0.358661	+	0.933468i	$0.616767\pi$
$480$	−320.000	+	640.000i	−0.0304290	+	0.0608581i
$481$	2832.00			0.268458
$482$			556.000i			0.0525417i
$483$		−	3016.00i		−	0.284126i
$484$	2188.00			0.205485
$485$	14560.0	+	7280.00i	1.36317	+	0.681583i
$486$	7084.00			0.661187
$487$			11814.0i			1.09927i	0.835406	+	0.549634i	$0.185233\pi$
$487$			11814.0i			1.09927i	−0.835406	+	0.549634i	$0.814767\pi$
$488$			4336.00i			0.402216i
$489$	7036.00			0.650673
$490$	−6660.00	−	3330.00i	−0.614017	−	0.307008i
$491$	14052.0			1.29156			0.645782	−	0.763522i	$-0.276532\pi$
$491$	14052.0			1.29156			0.645782	+	0.763522i	$0.276532\pi$
$492$		−	1936.00i		−	0.177402i
$493$		−	5760.00i		−	0.526202i
$494$	1440.00			0.131151
$495$	3220.00	−	6440.00i	0.292380	−	0.584761i
$496$	−2048.00			−0.185399
$497$			29328.0i			2.64696i
$498$		−	1912.00i		−	0.172046i
$499$	−7620.00			−0.683603			−0.341802	−	0.939772i	$-0.611037\pi$
$499$	−7620.00			−0.683603			−0.341802	+	0.939772i	$0.611037\pi$
$500$	−5500.00	+	1000.00i	−0.491935	+	0.0894427i
$501$	−1068.00			−0.0952390
$502$		−	6504.00i		−	0.578262i
$503$		−	1818.00i		−	0.161154i	−0.996748	−	0.0805772i	$-0.974324\pi$
$503$		−	1818.00i		−	0.161154i	0.996748	−	0.0805772i	$-0.0256763\pi$
$504$	4784.00			0.422810
$505$	2890.00	−	5780.00i	0.254660	−	0.509320i
$506$	3248.00			0.285358
$507$			4106.00i			0.359672i
$508$		−	6136.00i		−	0.535907i
$509$	−17850.0			−1.55440			−0.777198	−	0.629256i	$-0.783360\pi$
$509$	−17850.0			−1.55440			−0.777198	+	0.629256i	$0.783360\pi$
$510$	−2560.00	−	1280.00i	−0.222272	−	0.111136i
$511$	16432.0			1.42252
$512$		−	512.000i		−	0.0441942i
$513$			6000.00i			0.516387i
$514$	−3072.00			−0.263619
$515$	−14620.0	−	7310.00i	−1.25094	−	0.625470i
$516$	2896.00			0.247072
$517$			6328.00i			0.538308i
$518$			12272.0i			1.04093i
$519$	−8504.00			−0.719237
$520$	480.000	−	960.000i	0.0404796	−	0.0809592i
$521$	−19238.0			−1.61772			−0.808860	−	0.588001i	$-0.799915\pi$
$521$	−19238.0			−1.61772			−0.808860	+	0.588001i	$0.799915\pi$
$522$			4140.00i			0.347132i
$523$		−	6278.00i		−	0.524891i	−0.964947	−	0.262445i	$-0.915471\pi$
$523$		−	6278.00i		−	0.524891i	0.964947	−	0.262445i	$-0.0845289\pi$
$524$	−48.0000			−0.00400170
$525$	−3900.00	−	5200.00i	−0.324209	−	0.432279i
$526$	−9716.00			−0.805395
$527$		−	8192.00i		−	0.677133i
$528$		−	896.000i		−	0.0738511i
$529$	8803.00			0.723514
$530$	1080.00	−	2160.00i	0.0885136	−	0.177027i
$531$	460.000			0.0375938
$532$			6240.00i			0.508531i
$533$			2904.00i			0.235997i
$534$	1960.00			0.158834
$535$	9660.00	+	4830.00i	0.780632	+	0.390316i
$536$	−3472.00			−0.279790
$537$		−	5000.00i		−	0.401799i
$538$			5220.00i			0.418309i
$539$	9324.00			0.745108
$540$	4000.00	+	2000.00i	0.318764	+	0.159382i
$541$	−9818.00			−0.780238			−0.390119	−	0.920764i	$-0.627566\pi$
$541$	−9818.00			−0.780238			−0.390119	+	0.920764i	$0.627566\pi$
$542$			10336.0i			0.819131i
$543$		−	5156.00i		−	0.407486i
$544$	2048.00			0.161410
$545$	1850.00	−	3700.00i	0.145404	−	0.290808i
$546$	1248.00			0.0978195
$547$			12514.0i			0.978172i	0.872236	+	0.489086i	$0.162670\pi$
$547$			12514.0i			0.978172i	−0.872236	+	0.489086i	$0.837330\pi$
$548$		−	4896.00i		−	0.381655i
$549$	12466.0			0.969100
$550$	5600.00	−	4200.00i	0.434154	−	0.325616i
$551$	−5400.00			−0.417509
$552$			928.000i			0.0715549i
$553$		−	18720.0i		−	1.43952i
$554$	3848.00			0.295101
$555$	−2360.00	+	4720.00i	−0.180498	+	0.360996i
$556$	12400.0			0.945822
$557$		−	10596.0i		−	0.806045i	−0.915190	−	0.403022i	$-0.867960\pi$
$557$		−	10596.0i		−	0.806045i	0.915190	−	0.403022i	$-0.132040\pi$
$558$			5888.00i			0.446701i
$559$	−4344.00			−0.328679
$560$	4160.00	+	2080.00i	0.313914	+	0.156957i
$561$	3584.00			0.269727
$562$		−	6084.00i		−	0.456651i
$563$			14002.0i			1.04816i	0.851669	+	0.524080i	$0.175591\pi$
$563$			14002.0i			1.04816i	−0.851669	+	0.524080i	$0.824409\pi$
$564$	−1808.00			−0.134983
$565$	5280.00	+	2640.00i	0.393153	+	0.196576i
$566$	−3436.00			−0.255169
$567$		−	10946.0i		−	0.810739i
$568$		−	9024.00i		−	0.666617i
$569$	7330.00			0.540052			0.270026	−	0.962853i	$-0.412968\pi$
$569$	7330.00			0.540052			0.270026	+	0.962853i	$0.412968\pi$
$570$	−1200.00	+	2400.00i	−0.0881798	+	0.176360i
$571$	5812.00			0.425963			0.212981	−	0.977056i	$-0.431683\pi$
$571$	5812.00			0.425963			0.212981	+	0.977056i	$0.431683\pi$
$572$			1344.00i			0.0982438i
$573$		−	1536.00i		−	0.111985i
$574$	−12584.0			−0.915063
$575$	−5800.00	+	4350.00i	−0.420655	+	0.315491i
$576$	−1472.00			−0.106481
$577$		−	16736.0i		−	1.20750i	−0.797173	−	0.603751i	$-0.793672\pi$
$577$		−	16736.0i		−	1.20750i	0.797173	−	0.603751i	$-0.206328\pi$
$578$		−	1634.00i		−	0.117587i
$579$	5216.00			0.374386
$580$	−1800.00	+	3600.00i	−0.128864	+	0.257727i
$581$	−12428.0			−0.887436
$582$		−	5824.00i		−	0.414798i
$583$			3024.00i			0.214822i
$584$	−5056.00			−0.358251
$585$	−2760.00	−	1380.00i	−0.195063	−	0.0975316i
$586$	4584.00			0.323146
$587$			7434.00i			0.522716i	0.965242	+	0.261358i	$0.0841702\pi$
$587$			7434.00i			0.522716i	−0.965242	+	0.261358i	$0.915830\pi$
$588$			2664.00i			0.186839i
$589$	−7680.00			−0.537265
$590$	400.000	+	200.000i	0.0279114	+	0.0139557i
$591$	10232.0			0.712163
$592$		−	3776.00i		−	0.262150i
$593$			25872.0i			1.79163i	0.444429	+	0.895814i	$0.353407\pi$
$593$			25872.0i			1.79163i	−0.444429	+	0.895814i	$0.646593\pi$
$594$	−5600.00			−0.386820
$595$	−8320.00	+	16640.0i	−0.573255	+	1.14651i
$596$	1000.00			0.0687275
$597$			6960.00i			0.477142i
$598$		−	1392.00i		−	0.0951892i
$599$	3720.00			0.253748			0.126874	−	0.991919i	$-0.459506\pi$
$599$	3720.00			0.253748			0.126874	+	0.991919i	$0.459506\pi$
$600$	1200.00	+	1600.00i	0.0816497	+	0.108866i
$601$	−12958.0			−0.879481			−0.439740	−	0.898125i	$-0.644930\pi$
$601$	−12958.0			−0.879481			−0.439740	+	0.898125i	$0.644930\pi$
$602$		−	18824.0i		−	1.27443i
$603$			9982.00i			0.674127i
$604$	−8608.00			−0.579892
$605$	2735.00	−	5470.00i	0.183791	−	0.367582i
$606$	−2312.00			−0.154981
$607$			7214.00i			0.482384i	0.970477	+	0.241192i	$0.0775384\pi$
$607$			7214.00i			0.482384i	−0.970477	+	0.241192i	$0.922462\pi$
$608$		−	1920.00i		−	0.128070i
$609$	−4680.00			−0.311401
$610$	10840.0	+	5420.00i	0.719506	+	0.359753i
$611$	2712.00			0.179568
$612$		−	5888.00i		−	0.388902i
$613$		−	4828.00i		−	0.318109i	−0.987270	−	0.159055i	$-0.949155\pi$
$613$		−	4828.00i		−	0.318109i	0.987270	−	0.159055i	$-0.0508446\pi$
$614$	−10812.0			−0.710646
$615$	−4840.00	−	2420.00i	−0.317346	−	0.158673i
$616$	−5824.00			−0.380934
$617$		−	27656.0i		−	1.80452i	−0.431193	−	0.902260i	$-0.641907\pi$
$617$		−	27656.0i		−	1.80452i	0.431193	−	0.902260i	$-0.358093\pi$
$618$			5848.00i			0.380649i
$619$	21220.0			1.37787			0.688937	−	0.724821i	$-0.258078\pi$
$619$	21220.0			1.37787			0.688937	+	0.724821i	$0.258078\pi$
$620$	−2560.00	+	5120.00i	−0.165826	+	0.331652i
$621$	5800.00			0.374792
$622$			11376.0i			0.733338i
$623$		−	12740.0i		−	0.819289i
$624$	−384.000			−0.0246351
$625$	−4375.00	+	15000.0i	−0.280000	+	0.960000i
$626$	14704.0			0.938802
$627$		−	3360.00i		−	0.214012i
$628$		−	2096.00i		−	0.133184i
$629$	15104.0			0.957450
$630$	5980.00	−	11960.0i	0.378173	−	0.756346i
$631$	17672.0			1.11491			0.557457	−	0.830206i	$-0.311777\pi$
$631$	17672.0			1.11491			0.557457	+	0.830206i	$0.311777\pi$
$632$			5760.00i			0.362532i
$633$			6264.00i			0.393320i
$634$	6968.00			0.436490
$635$	−15340.0	−	7670.00i	−0.958660	−	0.479330i
$636$	−864.000			−0.0538677
$637$		−	3996.00i		−	0.248551i
$638$		−	5040.00i		−	0.312752i
$639$	−25944.0			−1.60615
$640$	−1280.00	−	640.000i	−0.0790569	−	0.0395285i
$641$	7322.00			0.451173			0.225586	−	0.974223i	$-0.427570\pi$
$641$	7322.00			0.451173			0.225586	+	0.974223i	$0.427570\pi$
$642$		−	3864.00i		−	0.237539i
$643$		−	8238.00i		−	0.505249i	−0.967564	−	0.252624i	$-0.918706\pi$
$643$		−	8238.00i		−	0.505249i	0.967564	−	0.252624i	$-0.0812937\pi$
$644$	6032.00			0.369090
$645$	3620.00	−	7240.00i	0.220988	−	0.441976i
$646$	7680.00			0.467749
$647$		−	6426.00i		−	0.390467i	−0.980757	−	0.195233i	$-0.937454\pi$
$647$		−	6426.00i		−	0.390467i	0.980757	−	0.195233i	$-0.0625465\pi$
$648$			3368.00i			0.204178i
$649$	−560.000			−0.0338705
$650$	−1800.00	−	2400.00i	−0.108618	−	0.144824i
$651$	−6656.00			−0.400721
$652$			14072.0i			0.845249i
$653$		−	5908.00i		−	0.354055i	−0.984206	−	0.177027i	$-0.943352\pi$
$653$		−	5908.00i		−	0.354055i	0.984206	−	0.177027i	$-0.0566482\pi$
$654$	−1480.00			−0.0884902
$655$	−60.0000	+	120.000i	−0.00357923	+	0.00715845i
$656$	3872.00			0.230452
$657$			14536.0i			0.863171i
$658$			11752.0i			0.696262i
$659$	26780.0			1.58301			0.791503	−	0.611166i	$-0.209299\pi$
$659$	26780.0			1.58301			0.791503	+	0.611166i	$0.209299\pi$
$660$	−2240.00	−	1120.00i	−0.132109	−	0.0660545i
$661$	−24538.0			−1.44390			−0.721950	−	0.691945i	$-0.756754\pi$
$661$	−24538.0			−1.44390			−0.721950	+	0.691945i	$0.756754\pi$
$662$			15736.0i			0.923863i
$663$		−	1536.00i		−	0.0899748i
$664$	3824.00			0.223494
$665$	15600.0	+	7800.00i	0.909687	+	0.454844i
$666$	−10856.0			−0.631624
$667$			5220.00i			0.303027i
$668$		−	2136.00i		−	0.123719i
$669$	−124.000			−0.00716609
$670$	−4340.00	+	8680.00i	−0.250252	+	0.500504i
$671$	−15176.0			−0.873119
$672$		−	1664.00i		−	0.0955211i
$673$		−	28848.0i		−	1.65232i	−0.563439	−	0.826158i	$-0.690522\pi$
$673$		−	28848.0i		−	1.65232i	0.563439	−	0.826158i	$-0.309478\pi$
$674$	−1312.00			−0.0749798
$675$	10000.0	−	7500.00i	0.570222	−	0.427667i
$676$	−8212.00			−0.467228
$677$			26884.0i			1.52620i	0.646282	+	0.763099i	$0.276323\pi$
$677$			26884.0i			1.52620i	−0.646282	+	0.763099i	$0.723677\pi$
$678$		−	2112.00i		−	0.119633i
$679$	−37856.0			−2.13959
$680$	2560.00	−	5120.00i	0.144370	−	0.288740i
$681$	−10628.0			−0.598041
$682$		−	7168.00i		−	0.402459i
$683$			14282.0i			0.800125i	0.916488	+	0.400063i	$0.131012\pi$
$683$			14282.0i			0.800125i	−0.916488	+	0.400063i	$0.868988\pi$
$684$	−5520.00			−0.308571
$685$	−12240.0	−	6120.00i	−0.682725	−	0.341362i
$686$	−520.000			−0.0289412
$687$			380.000i			0.0211032i
$688$			5792.00i			0.320956i
$689$	1296.00			0.0716599
$690$	2320.00	+	1160.00i	0.128001	+	0.0640006i
$691$	−3428.00			−0.188723			−0.0943613	−	0.995538i	$-0.530081\pi$
$691$	−3428.00			−0.188723			−0.0943613	+	0.995538i	$0.530081\pi$
$692$		−	17008.0i		−	0.934317i
$693$			16744.0i			0.917824i
$694$	11508.0			0.629449
$695$	15500.0	−	31000.0i	0.845969	−	1.69194i
$696$	1440.00			0.0784239
$697$			15488.0i			0.841678i
$698$		−	6220.00i		−	0.337293i
$699$	4816.00			0.260598
$700$	10400.0	−	7800.00i	0.561547	−	0.421160i
$701$	26942.0			1.45162			0.725810	−	0.687895i	$-0.241465\pi$
$701$	26942.0			1.45162			0.725810	+	0.687895i	$0.241465\pi$
$702$			2400.00i			0.129034i
$703$		−	14160.0i		−	0.759679i
$704$	1792.00			0.0959354
$705$	−2260.00	+	4520.00i	−0.120733	+	0.241465i
$706$	−15616.0			−0.832459
$707$			15028.0i			0.799415i
$708$		−	160.000i		−	0.00849318i
$709$	1950.00			0.103292			0.0516458	−	0.998665i	$-0.483553\pi$
$709$	1950.00			0.103292			0.0516458	+	0.998665i	$0.483553\pi$
$710$	−22560.0	−	11280.0i	−1.19248	−	0.596241i
$711$	16560.0			0.873486
$712$			3920.00i			0.206332i
$713$			7424.00i			0.389945i
$714$	6656.00			0.348872
$715$	3360.00	+	1680.00i	0.175744	+	0.0878719i
$716$	10000.0			0.521952
$717$			11360.0i			0.591697i
$718$		−	18480.0i		−	0.960540i
$719$	−12080.0			−0.626576			−0.313288	−	0.949658i	$-0.601430\pi$
$719$	−12080.0			−0.626576			−0.313288	+	0.949658i	$0.601430\pi$
$720$	−1840.00	+	3680.00i	−0.0952399	+	0.190480i
$721$	38012.0			1.96344
$722$			6518.00i			0.335976i
$723$		−	556.000i		−	0.0286001i
$724$	10312.0			0.529340
$725$	6750.00	+	9000.00i	0.345778	+	0.461037i
$726$	−2188.00			−0.111852
$727$		−	17226.0i		−	0.878785i	−0.898295	−	0.439393i	$-0.855194\pi$
$727$		−	17226.0i		−	0.878785i	0.898295	−	0.439393i	$-0.144806\pi$
$728$			2496.00i			0.127071i
$729$	4283.00			0.217599
$730$	−6320.00	+	12640.0i	−0.320430	+	0.640859i
$731$	−23168.0			−1.17223
$732$		−	4336.00i		−	0.218939i
$733$		−	788.000i		−	0.0397073i	−0.999803	−	0.0198536i	$-0.993680\pi$
$733$		−	788.000i		−	0.0397073i	0.999803	−	0.0198536i	$-0.00632003\pi$
$734$	6428.00			0.323245
$735$	6660.00	+	3330.00i	0.334228	+	0.167114i
$736$	−1856.00			−0.0929525
$737$		−	12152.0i		−	0.607360i
$738$		−	11132.0i		−	0.555250i
$739$	2060.00			0.102542			0.0512709	−	0.998685i	$-0.483673\pi$
$739$	2060.00			0.102542			0.0512709	+	0.998685i	$0.483673\pi$
$740$	−9440.00	−	4720.00i	−0.468948	−	0.234474i
$741$	−1440.00			−0.0713896
$742$			5616.00i			0.277857i
$743$		−	3258.00i		−	0.160867i	−0.996760	−	0.0804337i	$-0.974369\pi$
$743$		−	3258.00i		−	0.160867i	0.996760	−	0.0804337i	$-0.0256305\pi$
$744$	2048.00			0.100918
$745$	1250.00	−	2500.00i	0.0614718	−	0.122944i
$746$	−696.000			−0.0341587
$747$		−	10994.0i		−	0.538487i
$748$			7168.00i			0.350385i
$749$	−25116.0			−1.22526
$750$	5500.00	−	1000.00i	0.267775	−	0.0486864i
$751$	−4528.00			−0.220012			−0.110006	−	0.993931i	$-0.535087\pi$
$751$	−4528.00			−0.220012			−0.110006	+	0.993931i	$0.535087\pi$
$752$		−	3616.00i		−	0.175348i
$753$			6504.00i			0.314766i
$754$	−2160.00			−0.104327
$755$	−10760.0	+	21520.0i	−0.518671	+	1.03734i
$756$	−10400.0			−0.500323
$757$		−	18236.0i		−	0.875560i	−0.899082	−	0.437780i	$-0.855765\pi$
$757$		−	18236.0i		−	0.875560i	0.899082	−	0.437780i	$-0.144235\pi$
$758$			9880.00i			0.473427i
$759$	−3248.00			−0.155329
$760$	−4800.00	−	2400.00i	−0.229098	−	0.114549i
$761$	−18678.0			−0.889720			−0.444860	−	0.895600i	$-0.646747\pi$
$761$	−18678.0			−0.889720			−0.444860	+	0.895600i	$0.646747\pi$
$762$			6136.00i			0.291711i
$763$			9620.00i			0.456445i
$764$	3072.00			0.145473
$765$	−14720.0	−	7360.00i	−0.695690	−	0.347845i
$766$	12284.0			0.579424
$767$			240.000i			0.0112984i
$768$			512.000i			0.0240563i
$769$	−27390.0			−1.28441			−0.642203	−	0.766534i	$-0.721980\pi$
$769$	−27390.0			−1.28441			−0.642203	+	0.766534i	$0.721980\pi$
$770$	−7280.00	+	14560.0i	−0.340718	+	0.681436i
$771$	3072.00			0.143496
$772$			10432.0i			0.486342i
$773$			9252.00i			0.430493i	0.976560	+	0.215247i	$0.0690555\pi$
$773$			9252.00i			0.430493i	−0.976560	+	0.215247i	$0.930944\pi$
$774$	16652.0			0.773312
$775$	9600.00	+	12800.0i	0.444958	+	0.593277i
$776$	11648.0			0.538839
$777$		−	12272.0i		−	0.566609i
$778$			6100.00i			0.281100i
$779$	14520.0			0.667822
$780$	−480.000	+	960.000i	−0.0220343	+	0.0440686i
$781$	31584.0			1.44707
$782$		−	7424.00i		−	0.339491i
$783$		−	9000.00i		−	0.410771i
$784$	−5328.00			−0.242711
$785$	−5240.00	−	2620.00i	−0.238247	−	0.119123i
$786$	48.0000			0.00217825
$787$		−	5726.00i		−	0.259352i	−0.991556	−	0.129676i	$-0.958606\pi$
$787$		−	5726.00i		−	0.259352i	0.991556	−	0.129676i	$-0.0413937\pi$
$788$			20464.0i			0.925127i
$789$	9716.00			0.438401
$790$	14400.0	+	7200.00i	0.648518	+	0.324259i
$791$	−13728.0			−0.617082
$792$		−	5152.00i		−	0.231147i
$793$			6504.00i			0.291253i
$794$	−10792.0			−0.482360
$795$	−1080.00	+	2160.00i	−0.0481807	+	0.0963614i
$796$	−13920.0			−0.619826
$797$		−	27236.0i		−	1.21048i	−0.796045	−	0.605238i	$-0.793078\pi$
$797$		−	27236.0i		−	1.21048i	0.796045	−	0.605238i	$-0.206922\pi$
$798$		−	6240.00i		−	0.276809i
$799$	14464.0			0.640425
$800$	−3200.00	+	2400.00i	−0.141421	+	0.106066i
$801$	11270.0			0.497136
$802$		−	28964.0i		−	1.27525i
$803$		−	17696.0i		−	0.777682i
$804$	3472.00			0.152299
$805$	7540.00	−	15080.0i	0.330124	−	0.660249i
$806$	−3072.00			−0.134251
$807$		−	5220.00i		−	0.227699i
$808$		−	4624.00i		−	0.201326i
$809$	−10950.0			−0.475873			−0.237937	−	0.971281i	$-0.576471\pi$
$809$	−10950.0			−0.475873			−0.237937	+	0.971281i	$0.576471\pi$
$810$	8420.00	+	4210.00i	0.365245	+	0.182623i
$811$	−8828.00			−0.382236			−0.191118	−	0.981567i	$-0.561211\pi$
$811$	−8828.00			−0.382236			−0.191118	+	0.981567i	$0.561211\pi$
$812$		−	9360.00i		−	0.404522i
$813$		−	10336.0i		−	0.445879i
$814$	13216.0			0.569067
$815$	35180.0	+	17590.0i	1.51203	+	0.756013i
$816$	−2048.00			−0.0878607
$817$			21720.0i			0.930094i
$818$		−	2180.00i		−	0.0931808i
$819$	7176.00			0.306166
$820$	4840.00	−	9680.00i	0.206122	−	0.412244i
$821$	−16058.0			−0.682616			−0.341308	−	0.939951i	$-0.610870\pi$
$821$	−16058.0			−0.682616			−0.341308	+	0.939951i	$0.610870\pi$
$822$			4896.00i			0.207746i
$823$			41862.0i			1.77305i	0.462684	+	0.886523i	$0.346887\pi$
$823$			41862.0i			1.77305i	−0.462684	+	0.886523i	$0.653113\pi$
$824$	−11696.0			−0.494478
$825$	−5600.00	+	4200.00i	−0.236324	+	0.177243i
$826$	−1040.00			−0.0438090
$827$			12154.0i			0.511047i	0.966803	+	0.255524i	$0.0822478\pi$
$827$			12154.0i			0.511047i	−0.966803	+	0.255524i	$0.917752\pi$
$828$			5336.00i			0.223960i
$829$	15390.0			0.644773			0.322386	−	0.946608i	$-0.395515\pi$
$829$	15390.0			0.644773			0.322386	+	0.946608i	$0.395515\pi$
$830$	4780.00	−	9560.00i	0.199899	−	0.399798i
$831$	−3848.00			−0.160633
$832$		−	768.000i		−	0.0320019i
$833$		−	21312.0i		−	0.886455i
$834$	−12400.0			−0.514840
$835$	−5340.00	−	2670.00i	−0.221315	−	0.110658i
$836$	6720.00			0.278010
$837$		−	12800.0i		−	0.528593i
$838$		−	14360.0i		−	0.591955i
$839$	4280.00			0.176117			0.0880584	−	0.996115i	$-0.471934\pi$
$839$	4280.00			0.176117			0.0880584	+	0.996115i	$0.471934\pi$
$840$	−4160.00	−	2080.00i	−0.170873	−	0.0854367i
$841$	−16289.0			−0.667883
$842$			16276.0i			0.666162i
$843$			6084.00i			0.248570i
$844$	−12528.0			−0.510938
$845$	−10265.0	+	20530.0i	−0.417901	+	0.835803i
$846$	−10396.0			−0.422484
$847$			14222.0i			0.576947i
$848$		−	1728.00i		−	0.0699761i
$849$	3436.00			0.138897
$850$	−9600.00	−	12800.0i	−0.387385	−	0.516513i
$851$	−13688.0			−0.551373
$852$			9024.00i			0.362860i
$853$			14452.0i			0.580102i	0.957011	+	0.290051i	$0.0936723\pi$
$853$			14452.0i			0.580102i	−0.957011	+	0.290051i	$0.906328\pi$
$854$	−28184.0			−1.12932
$855$	−6900.00	+	13800.0i	−0.275994	+	0.551988i
$856$	7728.00			0.308572
$857$			22584.0i			0.900181i	0.892983	+	0.450090i	$0.148608\pi$
$857$			22584.0i			0.900181i	−0.892983	+	0.450090i	$0.851392\pi$
$858$		−	1344.00i		−	0.0534772i
$859$	26740.0			1.06212			0.531058	−	0.847336i	$-0.321795\pi$
$859$	26740.0			1.06212			0.531058	+	0.847336i	$0.321795\pi$
$860$	14480.0	+	7240.00i	0.574144	+	0.287072i
$861$	12584.0			0.498097
$862$			416.000i			0.0164374i
$863$		−	498.000i		−	0.0196432i	−0.999952	−	0.00982162i	$-0.996874\pi$
$863$		−	498.000i		−	0.0196432i	0.999952	−	0.00982162i	$-0.00312637\pi$
$864$	3200.00			0.126003
$865$	−42520.0	−	21260.0i	−1.67136	−	0.835678i
$866$	25984.0			1.01960
$867$			1634.00i			0.0640064i
$868$		−	13312.0i		−	0.520552i
$869$	−20160.0			−0.786975
$870$	1800.00	−	3600.00i	0.0701445	−	0.140289i
$871$	−5208.00			−0.202602
$872$		−	2960.00i		−	0.114952i
$873$		−	33488.0i		−	1.29828i
$874$	−6960.00			−0.269366
$875$	−6500.00	−	35750.0i	−0.251132	−	1.38122i
$876$	5056.00			0.195007
$877$			13244.0i			0.509941i	0.966949	+	0.254970i	$0.0820657\pi$
$877$			13244.0i			0.509941i	−0.966949	+	0.254970i	$0.917934\pi$
$878$			2160.00i			0.0830256i
$879$	−4584.00			−0.175898
$880$	2240.00	−	4480.00i	0.0858073	−	0.171615i
$881$	40842.0			1.56186			0.780932	−	0.624616i	$-0.214745\pi$
$881$	40842.0			1.56186			0.780932	+	0.624616i	$0.214745\pi$
$882$			15318.0i			0.584789i
$883$		−	12078.0i		−	0.460314i	−0.973154	−	0.230157i	$-0.926076\pi$
$883$		−	12078.0i		−	0.460314i	0.973154	−	0.230157i	$-0.0739239\pi$
$884$	3072.00			0.116881
$885$	−400.000	−	200.000i	−0.0151931	−	0.00759653i
$886$	−18156.0			−0.688446
$887$			18294.0i			0.692506i	0.938141	+	0.346253i	$0.112546\pi$
$887$			18294.0i			0.692506i	−0.938141	+	0.346253i	$0.887454\pi$
$888$			3776.00i			0.142696i
$889$	39884.0			1.50469
$890$	9800.00	+	4900.00i	0.369097	+	0.184549i
$891$	−11788.0			−0.443224
$892$		−	248.000i		−	0.00930903i
$893$		−	13560.0i		−	0.508139i
$894$	−1000.00			−0.0374105
$895$	12500.0	−	25000.0i	0.466848	−	0.933696i
$896$	3328.00			0.124086
$897$			1392.00i			0.0518144i
$898$			28620.0i			1.06354i
$899$	11520.0			0.427379
$900$	6900.00	+	9200.00i	0.255556	+	0.340741i
$901$	6912.00			0.255574
$902$			13552.0i			0.500257i
$903$			18824.0i			0.693714i
$904$	4224.00			0.155407
$905$	12890.0	−	25780.0i	0.473456	−	0.946913i
$906$	8608.00			0.315653
$907$		−	22566.0i		−	0.826121i	−0.910704	−	0.413060i	$-0.864460\pi$
$907$		−	22566.0i		−	0.826121i	0.910704	−	0.413060i	$-0.135540\pi$
$908$		−	21256.0i		−	0.776878i
$909$	−13294.0			−0.485076
$910$	6240.00	+	3120.00i	0.227312	+	0.113656i
$911$	−6768.00			−0.246140			−0.123070	−	0.992398i	$-0.539274\pi$
$911$	−6768.00			−0.246140			−0.123070	+	0.992398i	$0.539274\pi$
$912$			1920.00i			0.0697122i
$913$			13384.0i			0.485154i
$914$	4688.00			0.169656
$915$	−10840.0	−	5420.00i	−0.391650	−	0.195825i
$916$	−760.000			−0.0274139
$917$		−	312.000i		−	0.0112357i
$918$			12800.0i			0.460199i
$919$	−22200.0			−0.796856			−0.398428	−	0.917200i	$-0.630444\pi$
$919$	−22200.0			−0.796856			−0.398428	+	0.917200i	$0.630444\pi$
$920$	−2320.00	+	4640.00i	−0.0831393	+	0.166279i
$921$	10812.0			0.386827
$922$		−	22764.0i		−	0.813115i
$923$		−	13536.0i		−	0.482712i
$924$	5824.00			0.207354
$925$	−23600.0	+	17700.0i	−0.838879	+	0.629159i
$926$	32124.0			1.14002
$927$			33626.0i			1.19139i
$928$			2880.00i			0.101876i
$929$	6330.00			0.223553			0.111776	−	0.993733i	$-0.464346\pi$
$929$	6330.00			0.223553			0.111776	+	0.993733i	$0.464346\pi$
$930$	2560.00	−	5120.00i	0.0902642	−	0.180528i
$931$	−19980.0			−0.703349
$932$			9632.00i			0.338526i
$933$		−	11376.0i		−	0.399178i
$934$	−34332.0			−1.20276
$935$	17920.0	+	8960.00i	0.626788	+	0.313394i
$936$	−2208.00			−0.0771055
$937$			19544.0i			0.681403i	0.940172	+	0.340702i	$0.110665\pi$
$937$			19544.0i			0.681403i	−0.940172	+	0.340702i	$0.889335\pi$
$938$		−	22568.0i		−	0.785577i
$939$	−14704.0			−0.511019
$940$	−9040.00	−	4520.00i	−0.313673	−	0.156836i
$941$	−9898.00			−0.342896			−0.171448	−	0.985193i	$-0.554845\pi$
$941$	−9898.00			−0.342896			−0.171448	+	0.985193i	$0.554845\pi$
$942$			2096.00i			0.0724961i
$943$		−	14036.0i		−	0.484703i
$944$	320.000			0.0110330
$945$	−13000.0	+	26000.0i	−0.447503	+	0.895005i
$946$	−20272.0			−0.696723
$947$		−	41406.0i		−	1.42082i	−0.703789	−	0.710409i	$-0.748510\pi$
$947$		−	41406.0i		−	1.42082i	0.703789	−	0.710409i	$-0.251490\pi$
$948$		−	5760.00i		−	0.197338i
$949$	−7584.00			−0.259417
$950$	−12000.0	+	9000.00i	−0.409823	+	0.307367i
$951$	−6968.00			−0.237595
$952$			13312.0i			0.453198i
$953$			25432.0i			0.864453i	0.901765	+	0.432226i	$0.142272\pi$
$953$			25432.0i			0.864453i	−0.901765	+	0.432226i	$0.857728\pi$
$954$	−4968.00			−0.168601
$955$	3840.00	−	7680.00i	0.130115	−	0.260229i
$956$	−22720.0			−0.768637
$957$			5040.00i			0.170240i
$958$			15040.0i			0.507224i
$959$	31824.0			1.07159
$960$	1280.00	+	640.000i	0.0430331	+	0.0215166i
$961$	−13407.0			−0.450035
$962$		−	5664.00i		−	0.189828i
$963$		−	22218.0i		−	0.743474i
$964$	1112.00			0.0371526
$965$	26080.0	+	13040.0i	0.869995	+	0.434997i
$966$	−6032.00			−0.200907
$967$		−	12106.0i		−	0.402588i	−0.979531	−	0.201294i	$-0.935485\pi$
$967$		−	12106.0i		−	0.402588i	0.979531	−	0.201294i	$-0.0645147\pi$
$968$		−	4376.00i		−	0.145300i
$969$	−7680.00			−0.254610
$970$	14560.0	−	29120.0i	0.481952	−	0.963904i
$971$	7812.00			0.258186			0.129093	−	0.991632i	$-0.458793\pi$
$971$	7812.00			0.258186			0.129093	+	0.991632i	$0.458793\pi$
$972$		−	14168.0i		−	0.467530i
$973$			80600.0i			2.65562i
$974$	23628.0			0.777300
$975$	1800.00	+	2400.00i	0.0591242	+	0.0788323i
$976$	8672.00			0.284410
$977$		−	12576.0i		−	0.411814i	−0.978572	−	0.205907i	$-0.933986\pi$
$977$		−	12576.0i		−	0.411814i	0.978572	−	0.205907i	$-0.0660144\pi$
$978$		−	14072.0i		−	0.460095i
$979$	−13720.0			−0.447899
$980$	−6660.00	+	13320.0i	−0.217088	+	0.434175i
$981$	−8510.00			−0.276966
$982$		−	28104.0i		−	0.913274i
$983$			4342.00i			0.140883i	0.997516	+	0.0704417i	$0.0224409\pi$
$983$			4342.00i			0.140883i	−0.997516	+	0.0704417i	$0.977559\pi$
$984$	−3872.00			−0.125442
$985$	51160.0	+	25580.0i	1.65492	+	0.827458i
$986$	−11520.0			−0.372081
$987$		−	11752.0i		−	0.378997i
$988$		−	2880.00i		−	0.0927379i
$989$	20996.0			0.675060
$990$	−12880.0	−	6440.00i	−0.413488	−	0.206744i
$991$	26272.0			0.842137			0.421068	−	0.907029i	$-0.361655\pi$
$991$	26272.0			0.842137			0.421068	+	0.907029i	$0.361655\pi$
$992$			4096.00i			0.131097i
$993$		−	15736.0i		−	0.502887i
$994$	58656.0			1.87169
$995$	−17400.0	+	34800.0i	−0.554389	+	1.10878i
$996$	−3824.00			−0.121655
$997$		−	44796.0i		−	1.42297i	−0.702700	−	0.711486i	$-0.748022\pi$
$997$		−	44796.0i		−	1.42297i	0.702700	−	0.711486i	$-0.251978\pi$
$998$			15240.0i			0.483381i
$999$	23600.0			0.747418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.4.b.a.9.1	✓	2
3.2	odd	2		90.4.c.b.19.2		2
4.3	odd	2		80.4.c.a.49.1		2
5.2	odd	4		50.4.a.d.1.1		1
5.3	odd	4		50.4.a.b.1.1		1
5.4	even	2	inner	10.4.b.a.9.2	yes	2
7.6	odd	2		490.4.c.b.99.1		2
8.3	odd	2		320.4.c.c.129.2		2
8.5	even	2		320.4.c.d.129.1		2
12.11	even	2		720.4.f.f.289.1		2
15.2	even	4		450.4.a.j.1.1		1
15.8	even	4		450.4.a.k.1.1		1
15.14	odd	2		90.4.c.b.19.1		2
20.3	even	4		400.4.a.n.1.1		1
20.7	even	4		400.4.a.h.1.1		1
20.19	odd	2		80.4.c.a.49.2		2
35.13	even	4		2450.4.a.o.1.1		1
35.27	even	4		2450.4.a.bb.1.1		1
35.34	odd	2		490.4.c.b.99.2		2
40.3	even	4		1600.4.a.t.1.1		1
40.13	odd	4		1600.4.a.bh.1.1		1
40.19	odd	2		320.4.c.c.129.1		2
40.27	even	4		1600.4.a.bg.1.1		1
40.29	even	2		320.4.c.d.129.2		2
40.37	odd	4		1600.4.a.u.1.1		1
60.59	even	2		720.4.f.f.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.4.b.a.9.1	✓	2	1.1	even	1	trivial
10.4.b.a.9.2	yes	2	5.4	even	2	inner
50.4.a.b.1.1		1	5.3	odd	4
50.4.a.d.1.1		1	5.2	odd	4
80.4.c.a.49.1		2	4.3	odd	2
80.4.c.a.49.2		2	20.19	odd	2
90.4.c.b.19.1		2	15.14	odd	2
90.4.c.b.19.2		2	3.2	odd	2
320.4.c.c.129.1		2	40.19	odd	2
320.4.c.c.129.2		2	8.3	odd	2
320.4.c.d.129.1		2	8.5	even	2
320.4.c.d.129.2		2	40.29	even	2
400.4.a.h.1.1		1	20.7	even	4
400.4.a.n.1.1		1	20.3	even	4
450.4.a.j.1.1		1	15.2	even	4
450.4.a.k.1.1		1	15.8	even	4
490.4.c.b.99.1		2	7.6	odd	2
490.4.c.b.99.2		2	35.34	odd	2
720.4.f.f.289.1		2	12.11	even	2
720.4.f.f.289.2		2	60.59	even	2
1600.4.a.t.1.1		1	40.3	even	4
1600.4.a.u.1.1		1	40.37	odd	4
1600.4.a.bg.1.1		1	40.27	even	4
1600.4.a.bh.1.1		1	40.13	odd	4
2450.4.a.o.1.1		1	35.13	even	4
2450.4.a.bb.1.1		1	35.27	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +(-5.00000 + 10.0000i) q^{5} +4.00000 q^{6} -26.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +2.00000i q^{3} -4.00000 q^{4} +(-5.00000 + 10.0000i) q^{5} +4.00000 q^{6} -26.0000i q^{7} +8.00000i q^{8} +23.0000 q^{9} +(20.0000 + 10.0000i) q^{10} -28.0000 q^{11} -8.00000i q^{12} +12.0000i q^{13} -52.0000 q^{14} +(-20.0000 - 10.0000i) q^{15} +16.0000 q^{16} +64.0000i q^{17} -46.0000i q^{18} +60.0000 q^{19} +(20.0000 - 40.0000i) q^{20} +52.0000 q^{21} +56.0000i q^{22} -58.0000i q^{23} -16.0000 q^{24} +(-75.0000 - 100.000i) q^{25} +24.0000 q^{26} +100.000i q^{27} +104.000i q^{28} -90.0000 q^{29} +(-20.0000 + 40.0000i) q^{30} -128.000 q^{31} -32.0000i q^{32} -56.0000i q^{33} +128.000 q^{34} +(260.000 + 130.000i) q^{35} -92.0000 q^{36} -236.000i q^{37} -120.000i q^{38} -24.0000 q^{39} +(-80.0000 - 40.0000i) q^{40} +242.000 q^{41} -104.000i q^{42} +362.000i q^{43} +112.000 q^{44} +(-115.000 + 230.000i) q^{45} -116.000 q^{46} -226.000i q^{47} +32.0000i q^{48} -333.000 q^{49} +(-200.000 + 150.000i) q^{50} -128.000 q^{51} -48.0000i q^{52} -108.000i q^{53} +200.000 q^{54} +(140.000 - 280.000i) q^{55} +208.000 q^{56} +120.000i q^{57} +180.000i q^{58} +20.0000 q^{59} +(80.0000 + 40.0000i) q^{60} +542.000 q^{61} +256.000i q^{62} -598.000i q^{63} -64.0000 q^{64} +(-120.000 - 60.0000i) q^{65} -112.000 q^{66} +434.000i q^{67} -256.000i q^{68} +116.000 q^{69} +(260.000 - 520.000i) q^{70} -1128.00 q^{71} +184.000i q^{72} +632.000i q^{73} -472.000 q^{74} +(200.000 - 150.000i) q^{75} -240.000 q^{76} +728.000i q^{77} +48.0000i q^{78} +720.000 q^{79} +(-80.0000 + 160.000i) q^{80} +421.000 q^{81} -484.000i q^{82} -478.000i q^{83} -208.000 q^{84} +(-640.000 - 320.000i) q^{85} +724.000 q^{86} -180.000i q^{87} -224.000i q^{88} +490.000 q^{89} +(460.000 + 230.000i) q^{90} +312.000 q^{91} +232.000i q^{92} -256.000i q^{93} -452.000 q^{94} +(-300.000 + 600.000i) q^{95} +64.0000 q^{96} -1456.00i q^{97} +666.000i q^{98} -644.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 - 10 * q^5 + 8 * q^6 + 46 * q^9	\( 2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9} + 40 q^{10} - 56 q^{11} - 104 q^{14} - 40 q^{15} + 32 q^{16} + 120 q^{19} + 40 q^{20} + 104 q^{21} - 32 q^{24} - 150 q^{25} + 48 q^{26} - 180 q^{29} - 40 q^{30} - 256 q^{31} + 256 q^{34} + 520 q^{35} - 184 q^{36} - 48 q^{39} - 160 q^{40} + 484 q^{41} + 224 q^{44} - 230 q^{45} - 232 q^{46} - 666 q^{49} - 400 q^{50} - 256 q^{51} + 400 q^{54} + 280 q^{55} + 416 q^{56} + 40 q^{59} + 160 q^{60} + 1084 q^{61} - 128 q^{64} - 240 q^{65} - 224 q^{66} + 232 q^{69} + 520 q^{70} - 2256 q^{71} - 944 q^{74} + 400 q^{75} - 480 q^{76} + 1440 q^{79} - 160 q^{80} + 842 q^{81} - 416 q^{84} - 1280 q^{85} + 1448 q^{86} + 980 q^{89} + 920 q^{90} + 624 q^{91} - 904 q^{94} - 600 q^{95} + 128 q^{96} - 1288 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 - 10 * q^5 + 8 * q^6 + 46 * q^9 + 40 * q^10 - 56 * q^11 - 104 * q^14 - 40 * q^15 + 32 * q^16 + 120 * q^19 + 40 * q^20 + 104 * q^21 - 32 * q^24 - 150 * q^25 + 48 * q^26 - 180 * q^29 - 40 * q^30 - 256 * q^31 + 256 * q^34 + 520 * q^35 - 184 * q^36 - 48 * q^39 - 160 * q^40 + 484 * q^41 + 224 * q^44 - 230 * q^45 - 232 * q^46 - 666 * q^49 - 400 * q^50 - 256 * q^51 + 400 * q^54 + 280 * q^55 + 416 * q^56 + 40 * q^59 + 160 * q^60 + 1084 * q^61 - 128 * q^64 - 240 * q^65 - 224 * q^66 + 232 * q^69 + 520 * q^70 - 2256 * q^71 - 944 * q^74 + 400 * q^75 - 480 * q^76 + 1440 * q^79 - 160 * q^80 + 842 * q^81 - 416 * q^84 - 1280 * q^85 + 1448 * q^86 + 980 * q^89 + 920 * q^90 + 624 * q^91 - 904 * q^94 - 600 * q^95 + 128 * q^96 - 1288 * q^99

Introduction

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