LMFDB - Embedded newform 200.4.f.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 3x^{2} + 4 $ x^4 - 3*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$1.32288 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.4.f.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64575 - 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 + 5.29150i) q^{4} +(14.0000 + 5.29150i) q^{6} -8.00000i q^{7} +(-10.5830 - 20.0000i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-2.64575 - 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 + 5.29150i) q^{4} +(14.0000 + 5.29150i) q^{6} -8.00000i q^{7} +(-10.5830 - 20.0000i) q^{8} +1.00000 q^{9} +15.8745i q^{11} +(-31.7490 - 28.0000i) q^{12} -52.9150 q^{13} +(-8.00000 + 21.1660i) q^{14} +(8.00000 + 63.4980i) q^{16} -14.0000i q^{17} +(-2.64575 - 1.00000i) q^{18} -37.0405i q^{19} +42.3320i q^{21} +(15.8745 - 42.0000i) q^{22} +152.000i q^{23} +(56.0000 + 105.830i) q^{24} +(140.000 + 52.9150i) q^{26} +137.579 q^{27} +(42.3320 - 48.0000i) q^{28} -158.745i q^{29} +224.000 q^{31} +(42.3320 - 176.000i) q^{32} -84.0000i q^{33} +(-14.0000 + 37.0405i) q^{34} +(6.00000 + 5.29150i) q^{36} +243.409 q^{37} +(-37.0405 + 98.0000i) q^{38} +280.000 q^{39} -70.0000 q^{41} +(42.3320 - 112.000i) q^{42} +439.195 q^{43} +(-84.0000 + 95.2470i) q^{44} +(152.000 - 402.154i) q^{46} +336.000i q^{47} +(-42.3320 - 336.000i) q^{48} +279.000 q^{49} +74.0810i q^{51} +(-317.490 - 280.000i) q^{52} -31.7490 q^{53} +(-364.000 - 137.579i) q^{54} +(-160.000 + 84.6640i) q^{56} +196.000i q^{57} +(-158.745 + 420.000i) q^{58} +534.442i q^{59} -95.2470i q^{61} +(-592.648 - 224.000i) q^{62} -8.00000i q^{63} +(-288.000 + 423.320i) q^{64} +(-84.0000 + 222.243i) q^{66} +174.620 q^{67} +(74.0810 - 84.0000i) q^{68} -804.308i q^{69} -72.0000 q^{71} +(-10.5830 - 20.0000i) q^{72} +294.000i q^{73} +(-644.000 - 243.409i) q^{74} +(196.000 - 222.243i) q^{76} +126.996 q^{77} +(-740.810 - 280.000i) q^{78} +464.000 q^{79} -755.000 q^{81} +(185.203 + 70.0000i) q^{82} +545.025 q^{83} +(-224.000 + 253.992i) q^{84} +(-1162.00 - 439.195i) q^{86} +840.000i q^{87} +(317.490 - 168.000i) q^{88} -266.000 q^{89} +423.320i q^{91} +(-804.308 + 912.000i) q^{92} -1185.30 q^{93} +(336.000 - 888.972i) q^{94} +(-224.000 + 931.304i) q^{96} +994.000i q^{97} +(-738.165 - 279.000i) q^{98} +15.8745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 24 * q^4 + 56 * q^6 + 4 * q^9	$ 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9} - 32 q^{14} + 32 q^{16} + 224 q^{24} + 560 q^{26} + 896 q^{31} - 56 q^{34} + 24 q^{36} + 1120 q^{39} - 280 q^{41} - 336 q^{44} + 608 q^{46} + 1116 q^{49} - 1456 q^{54} - 640 q^{56} - 1152 q^{64} - 336 q^{66} - 288 q^{71} - 2576 q^{74} + 784 q^{76} + 1856 q^{79} - 3020 q^{81} - 896 q^{84} - 4648 q^{86} - 1064 q^{89} + 1344 q^{94} - 896 q^{96}+O(q^{100}) $ 4 * q + 24 * q^4 + 56 * q^6 + 4 * q^9 - 32 * q^14 + 32 * q^16 + 224 * q^24 + 560 * q^26 + 896 * q^31 - 56 * q^34 + 24 * q^36 + 1120 * q^39 - 280 * q^41 - 336 * q^44 + 608 * q^46 + 1116 * q^49 - 1456 * q^54 - 640 * q^56 - 1152 * q^64 - 336 * q^66 - 288 * q^71 - 2576 * q^74 + 784 * q^76 + 1856 * q^79 - 3020 * q^81 - 896 * q^84 - 4648 * q^86 - 1064 * q^89 + 1344 * q^94 - 896 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.64575	−	1.00000i	−0.935414	−	0.353553i
$2$	−2.64575	−	1.00000i	−0.935414	−	0.353553i
$3$	−5.29150			−1.01835			−0.509175	−	0.860663i	$-0.670049\pi$
$3$	−5.29150			−1.01835			−0.509175	+	0.860663i	$0.670049\pi$
$4$	6.00000	+	5.29150i	0.750000	+	0.661438i
$5$		0			0
$5$		0			0
$6$	14.0000	+	5.29150i	0.952579	+	0.360041i
$7$		−	8.00000i		−	0.431959i	−0.976398	−	0.215980i	$-0.930705\pi$
$7$		−	8.00000i		−	0.431959i	0.976398	−	0.215980i	$-0.0692945\pi$
$8$	−10.5830	−	20.0000i	−0.467707	−	0.883883i
$9$	1.00000			0.0370370
$10$		0			0
$11$			15.8745i			0.435122i	0.976047	+	0.217561i	$0.0698101\pi$
$11$			15.8745i			0.435122i	−0.976047	+	0.217561i	$0.930190\pi$
$12$	−31.7490	−	28.0000i	−0.763763	−	0.673575i
$13$	−52.9150			−1.12892			−0.564461	−	0.825460i	$-0.690916\pi$
$13$	−52.9150			−1.12892			−0.564461	+	0.825460i	$0.690916\pi$
$14$	−8.00000	+	21.1660i	−0.152721	+	0.404061i
$15$		0			0
$16$	8.00000	+	63.4980i	0.125000	+	0.992157i
$17$		−	14.0000i		−	0.199735i	−0.995001	−	0.0998676i	$-0.968158\pi$
$17$		−	14.0000i		−	0.199735i	0.995001	−	0.0998676i	$-0.0318419\pi$
$18$	−2.64575	−	1.00000i	−0.0346450	−	0.0130946i
$19$		−	37.0405i		−	0.447246i	−0.974676	−	0.223623i	$-0.928212\pi$
$19$		−	37.0405i		−	0.447246i	0.974676	−	0.223623i	$-0.0717885\pi$
$20$		0			0
$21$			42.3320i			0.439886i
$22$	15.8745	−	42.0000i	0.153839	−	0.407020i
$23$			152.000i			1.37801i	0.724757	+	0.689004i	$0.241952\pi$
$23$			152.000i			1.37801i	−0.724757	+	0.689004i	$0.758048\pi$
$24$	56.0000	+	105.830i	0.476290	+	0.900103i
$25$		0			0
$26$	140.000	+	52.9150i	1.05601	+	0.399134i
$27$	137.579			0.980633
$28$	42.3320	−	48.0000i	0.285714	−	0.323970i
$29$		−	158.745i		−	1.01649i	−0.861212	−	0.508245i	$-0.830294\pi$
$29$		−	158.745i		−	1.01649i	0.861212	−	0.508245i	$-0.169706\pi$
$30$		0			0
$31$	224.000			1.29779			0.648897	−	0.760877i	$-0.275231\pi$
$31$	224.000			1.29779			0.648897	+	0.760877i	$0.275231\pi$
$32$	42.3320	−	176.000i	0.233854	−	0.972272i
$33$		−	84.0000i		−	0.443107i
$34$	−14.0000	+	37.0405i	−0.0706171	+	0.186835i
$35$		0			0
$36$	6.00000	+	5.29150i	0.0277778	+	0.0244977i
$37$	243.409			1.08152			0.540760	−	0.841177i	$-0.318137\pi$
$37$	243.409			1.08152			0.540760	+	0.841177i	$0.318137\pi$
$38$	−37.0405	+	98.0000i	−0.158125	+	0.418361i
$39$	280.000			1.14964
$40$		0			0
$41$	−70.0000			−0.266638			−0.133319	−	0.991073i	$-0.542564\pi$
$41$	−70.0000			−0.266638			−0.133319	+	0.991073i	$0.542564\pi$
$42$	42.3320	−	112.000i	0.155523	−	0.411476i
$43$	439.195			1.55759			0.778797	−	0.627276i	$-0.215830\pi$
$43$	439.195			1.55759			0.778797	+	0.627276i	$0.215830\pi$
$44$	−84.0000	+	95.2470i	−0.287806	+	0.326342i
$45$		0			0
$46$	152.000	−	402.154i	0.487200	−	1.28901i
$47$			336.000i			1.04278i	0.853319	+	0.521390i	$0.174586\pi$
$47$			336.000i			1.04278i	−0.853319	+	0.521390i	$0.825414\pi$
$48$	−42.3320	−	336.000i	−0.127294	−	1.01036i
$49$	279.000			0.813411
$50$		0			0
$51$			74.0810i			0.203400i
$52$	−317.490	−	280.000i	−0.846692	−	0.746712i
$53$	−31.7490			−0.0822842			−0.0411421	−	0.999153i	$-0.513100\pi$
$53$	−31.7490			−0.0822842			−0.0411421	+	0.999153i	$0.513100\pi$
$54$	−364.000	−	137.579i	−0.917299	−	0.346706i
$55$		0			0
$56$	−160.000	+	84.6640i	−0.381802	+	0.202031i
$57$			196.000i			0.455453i
$58$	−158.745	+	420.000i	−0.359384	+	0.950840i
$59$			534.442i			1.17929i	0.807661	+	0.589647i	$0.200733\pi$
$59$			534.442i			1.17929i	−0.807661	+	0.589647i	$0.799267\pi$
$60$		0			0
$61$		−	95.2470i		−	0.199920i	−0.994991	−	0.0999601i	$-0.968128\pi$
$61$		−	95.2470i		−	0.199920i	0.994991	−	0.0999601i	$-0.0318715\pi$
$62$	−592.648	−	224.000i	−1.21397	−	0.458839i
$63$		−	8.00000i		−	0.0159985i
$64$	−288.000	+	423.320i	−0.562500	+	0.826797i
$65$		0			0
$66$	−84.0000	+	222.243i	−0.156662	+	0.414488i
$67$	174.620			0.318406			0.159203	−	0.987246i	$-0.449108\pi$
$67$	174.620			0.318406			0.159203	+	0.987246i	$0.449108\pi$
$68$	74.0810	−	84.0000i	0.132112	−	0.149801i
$69$		−	804.308i		−	1.40329i
$70$		0			0
$71$	−72.0000			−0.120350			−0.0601748	−	0.998188i	$-0.519166\pi$
$71$	−72.0000			−0.120350			−0.0601748	+	0.998188i	$0.519166\pi$
$72$	−10.5830	−	20.0000i	−0.0173225	−	0.0327364i
$73$			294.000i			0.471371i	0.971829	+	0.235686i	$0.0757336\pi$
$73$			294.000i			0.471371i	−0.971829	+	0.235686i	$0.924266\pi$
$74$	−644.000	−	243.409i	−1.01167	−	0.382375i
$75$		0			0
$76$	196.000	−	222.243i	0.295826	−	0.335435i
$77$	126.996			0.187955
$78$	−740.810	−	280.000i	−1.07539	−	0.406458i
$79$	464.000			0.660811			0.330406	−	0.943839i	$-0.392814\pi$
$79$	464.000			0.660811			0.330406	+	0.943839i	$0.392814\pi$
$80$		0			0
$81$	−755.000			−1.03567
$82$	185.203	+	70.0000i	0.249417	+	0.0942708i
$83$	545.025			0.720774			0.360387	−	0.932803i	$-0.382645\pi$
$83$	545.025			0.720774			0.360387	+	0.932803i	$0.382645\pi$
$84$	−224.000	+	253.992i	−0.290957	+	0.329914i
$85$		0			0
$86$	−1162.00	−	439.195i	−1.45700	−	0.550693i
$87$			840.000i			1.03514i
$88$	317.490	−	168.000i	0.384597	−	0.203510i
$89$	−266.000			−0.316808			−0.158404	−	0.987374i	$-0.550635\pi$
$89$	−266.000			−0.316808			−0.158404	+	0.987374i	$0.550635\pi$
$90$		0			0
$91$			423.320i			0.487649i
$92$	−804.308	+	912.000i	−0.911467	+	1.03351i
$93$	−1185.30			−1.32161
$94$	336.000	−	888.972i	0.368678	−	0.975431i
$95$		0			0
$96$	−224.000	+	931.304i	−0.238145	+	0.990113i
$97$			994.000i			1.04047i	0.854024	+	0.520234i	$0.174155\pi$
$97$			994.000i			1.04047i	−0.854024	+	0.520234i	$0.825845\pi$
$98$	−738.165	−	279.000i	−0.760876	−	0.287584i
$99$			15.8745i			0.0161156i
$100$		0			0
$101$		−	751.393i		−	0.740262i	−0.928980	−	0.370131i	$-0.879313\pi$
$101$		−	751.393i		−	0.740262i	0.928980	−	0.370131i	$-0.120687\pi$
$102$	74.0810	−	196.000i	0.0719129	−	0.190264i
$103$		−	1176.00i		−	1.12500i	−0.826798	−	0.562499i	$-0.809840\pi$
$103$		−	1176.00i		−	1.12500i	0.826798	−	0.562499i	$-0.190160\pi$
$104$	560.000	+	1058.30i	0.528005	+	0.997836i
$105$		0			0
$106$	84.0000	+	31.7490i	0.0769698	+	0.0290919i
$107$	−269.867			−0.243822			−0.121911	−	0.992541i	$-0.538902\pi$
$107$	−269.867			−0.243822			−0.121911	+	0.992541i	$0.538902\pi$
$108$	825.474	+	728.000i	0.735475	+	0.648628i
$109$		−	1894.36i		−	1.66465i	−0.554290	−	0.832324i	$-0.687010\pi$
$109$		−	1894.36i		−	1.66465i	0.554290	−	0.832324i	$-0.312990\pi$
$110$		0			0
$111$	−1288.00			−1.10137
$112$	507.984	−	64.0000i	0.428571	−	0.0539949i
$113$			1710.00i			1.42357i	0.702398	+	0.711784i	$0.252113\pi$
$113$			1710.00i			1.42357i	−0.702398	+	0.711784i	$0.747887\pi$
$114$	196.000	−	518.567i	0.161027	−	0.426037i
$115$		0			0
$116$	840.000	−	952.470i	0.672345	−	0.762368i
$117$	−52.9150			−0.0418119
$118$	534.442	−	1414.00i	0.416944	−	1.10313i
$119$	−112.000			−0.0862775
$120$		0			0
$121$	1079.00			0.810669
$122$	−95.2470	+	252.000i	−0.0706825	+	0.187008i
$123$	370.405			0.271531
$124$	1344.00	+	1185.30i	0.973345	+	0.858409i
$125$		0			0
$126$	−8.00000	+	21.1660i	−0.00565632	+	0.0149652i
$127$		−	1664.00i		−	1.16265i	−0.813673	−	0.581323i	$-0.802535\pi$
$127$		−	1664.00i		−	1.16265i	0.813673	−	0.581323i	$-0.197465\pi$
$128$	1185.30	−	832.000i	0.818488	−	0.574524i
$129$	−2324.00			−1.58618
$130$		0			0
$131$			672.021i			0.448204i	0.974566	+	0.224102i	$0.0719449\pi$
$131$			672.021i			0.448204i	−0.974566	+	0.224102i	$0.928055\pi$
$132$	444.486	−	504.000i	0.293088	−	0.332330i
$133$	−296.324			−0.193192
$134$	−462.000	−	174.620i	−0.297841	−	0.112573i
$135$		0			0
$136$	−280.000	+	148.162i	−0.176543	+	0.0934176i
$137$		−	1062.00i		−	0.662283i	−0.943581	−	0.331142i	$-0.892566\pi$
$137$		−	1062.00i		−	0.662283i	0.943581	−	0.331142i	$-0.107434\pi$
$138$	−804.308	+	2128.00i	−0.496140	+	1.31266i
$139$			2693.37i			1.64352i	0.569835	+	0.821759i	$0.307007\pi$
$139$			2693.37i			1.64352i	−0.569835	+	0.821759i	$0.692993\pi$
$140$		0			0
$141$		−	1777.94i		−	1.06191i
$142$	190.494	+	72.0000i	0.112577	+	0.0425500i
$143$		−	840.000i		−	0.491219i
$144$	8.00000	+	63.4980i	0.00462963	+	0.0367465i
$145$		0			0
$146$	294.000	−	777.851i	0.166655	−	0.440927i
$147$	−1476.33			−0.828337
$148$	1460.45	+	1288.00i	0.811139	+	0.715358i
$149$			793.725i			0.436406i	0.975903	+	0.218203i	$0.0700195\pi$
$149$			793.725i			0.436406i	−0.975903	+	0.218203i	$0.929980\pi$
$150$		0			0
$151$	744.000			0.400966			0.200483	−	0.979697i	$-0.435749\pi$
$151$	744.000			0.400966			0.200483	+	0.979697i	$0.435749\pi$
$152$	−740.810	+	392.000i	−0.395314	+	0.209180i
$153$		−	14.0000i		−	0.00739760i
$154$	−336.000	−	126.996i	−0.175816	−	0.0664522i
$155$		0			0
$156$	1680.00	+	1481.62i	0.862229	+	0.760414i
$157$	179.911			0.0914552			0.0457276	−	0.998954i	$-0.485439\pi$
$157$	179.911			0.0914552			0.0457276	+	0.998954i	$0.485439\pi$
$158$	−1227.63	−	464.000i	−0.618132	−	0.233632i
$159$	168.000			0.0837941
$160$		0			0
$161$	1216.00			0.595244
$162$	1997.54	+	755.000i	0.968776	+	0.366163i
$163$	1772.65			0.851809			0.425905	−	0.904768i	$-0.359956\pi$
$163$	1772.65			0.851809			0.425905	+	0.904768i	$0.359956\pi$
$164$	−420.000	−	370.405i	−0.199979	−	0.176365i
$165$		0			0
$166$	−1442.00	−	545.025i	−0.674222	−	0.254832i
$167$		−	1960.00i		−	0.908200i	−0.890951	−	0.454100i	$-0.849961\pi$
$167$		−	1960.00i		−	0.908200i	0.890951	−	0.454100i	$-0.150039\pi$
$168$	846.640	−	448.000i	0.388808	−	0.205738i
$169$	603.000			0.274465
$170$		0			0
$171$		−	37.0405i		−	0.0165647i
$172$	2635.17	+	2324.00i	1.16820	+	1.03025i
$173$	−2000.19			−0.879026			−0.439513	−	0.898236i	$-0.644849\pi$
$173$	−2000.19			−0.879026			−0.439513	+	0.898236i	$0.644849\pi$
$174$	840.000	−	2222.43i	0.365978	−	0.968288i
$175$		0			0
$176$	−1008.00	+	126.996i	−0.431709	+	0.0543903i
$177$		−	2828.00i		−	1.20094i
$178$	703.770	+	266.000i	0.296347	+	0.112009i
$179$			3264.86i			1.36328i	0.731688	+	0.681639i	$0.238733\pi$
$179$			3264.86i			1.36328i	−0.731688	+	0.681639i	$0.761267\pi$
$180$		0			0
$181$			2338.84i			0.960469i	0.877140	+	0.480235i	$0.159448\pi$
$181$			2338.84i			0.960469i	−0.877140	+	0.480235i	$0.840552\pi$
$182$	423.320	−	1120.00i	0.172410	−	0.456153i
$183$			504.000i			0.203589i
$184$	3040.00	−	1608.62i	1.21800	−	0.644504i
$185$		0			0
$186$	3136.00	+	1185.30i	1.23625	+	0.467259i
$187$	222.243			0.0869092
$188$	−1777.94	+	2016.00i	−0.689734	+	0.782085i
$189$		−	1100.63i		−	0.423594i
$190$		0			0
$191$	3904.00			1.47897			0.739486	−	0.673172i	$-0.235069\pi$
$191$	3904.00			1.47897			0.739486	+	0.673172i	$0.235069\pi$
$192$	1523.95	−	2240.00i	0.572822	−	0.841969i
$193$		−	3330.00i		−	1.24196i	−0.783826	−	0.620981i	$-0.786734\pi$
$193$		−	3330.00i		−	1.24196i	0.783826	−	0.620981i	$-0.213266\pi$
$194$	994.000	−	2629.88i	0.367861	−	0.973269i
$195$		0			0
$196$	1674.00	+	1476.33i	0.610058	+	0.538021i
$197$	−1195.88			−0.432502			−0.216251	−	0.976338i	$-0.569383\pi$
$197$	−1195.88			−0.432502			−0.216251	+	0.976338i	$0.569383\pi$
$198$	15.8745	−	42.0000i	0.00569774	−	0.0150748i
$199$	1736.00			0.618401			0.309200	−	0.950997i	$-0.399939\pi$
$199$	1736.00			0.618401			0.309200	+	0.950997i	$0.399939\pi$
$200$		0			0
$201$	−924.000			−0.324248
$202$	−751.393	+	1988.00i	−0.261722	+	0.692451i
$203$	−1269.96			−0.439083
$204$	−392.000	+	444.486i	−0.134537	+	0.152550i
$205$		0			0
$206$	−1176.00	+	3111.40i	−0.397747	+	1.05234i
$207$			152.000i			0.0510373i
$208$	−423.320	−	3360.00i	−0.141115	−	1.12007i
$209$	588.000			0.194607
$210$		0			0
$211$			2915.62i			0.951277i	0.879641	+	0.475638i	$0.157783\pi$
$211$			2915.62i			0.951277i	−0.879641	+	0.475638i	$0.842217\pi$
$212$	−190.494	−	168.000i	−0.0617132	−	0.0544259i
$213$	380.988			0.122558
$214$	714.000	+	269.867i	0.228075	+	0.0862042i
$215$		0			0
$216$	−1456.00	−	2751.58i	−0.458649	−	0.866766i
$217$		−	1792.00i		−	0.560594i
$218$	−1894.36	+	5012.00i	−0.588542	+	1.55714i
$219$		−	1555.70i		−	0.480021i
$220$		0			0
$221$			740.810i			0.225486i
$222$	3407.73	+	1288.00i	1.03023	+	0.389391i
$223$		−	1568.00i		−	0.470857i	−0.971892	−	0.235428i	$-0.924351\pi$
$223$		−	1568.00i		−	0.470857i	0.971892	−	0.235428i	$-0.0756493\pi$
$224$	−1408.00	−	338.656i	−0.419982	−	0.101015i
$225$		0			0
$226$	1710.00	−	4524.23i	0.503308	−	1.33163i
$227$	−1264.67			−0.369775			−0.184888	−	0.982760i	$-0.559192\pi$
$227$	−1264.67			−0.369775			−0.184888	+	0.982760i	$0.559192\pi$
$228$	−1037.13	+	1176.00i	−0.301254	+	0.341590i
$229$			5153.92i			1.48725i	0.668595	+	0.743626i	$0.266896\pi$
$229$			5153.92i			1.48725i	−0.668595	+	0.743626i	$0.733104\pi$
$230$		0			0
$231$	−672.000			−0.191404
$232$	−3174.90	+	1680.00i	−0.898459	+	0.475420i
$233$			838.000i			0.235619i	0.993036	+	0.117809i	$0.0375872\pi$
$233$			838.000i			0.235619i	−0.993036	+	0.117809i	$0.962413\pi$
$234$	140.000	+	52.9150i	0.0391115	+	0.0147827i
$235$		0			0
$236$	−2828.00	+	3206.65i	−0.780030	+	0.884471i
$237$	−2455.26			−0.672937
$238$	296.324	+	112.000i	0.0807052	+	0.0305037i
$239$	−6288.00			−1.70183			−0.850914	−	0.525305i	$-0.823951\pi$
$239$	−6288.00			−1.70183			−0.850914	+	0.525305i	$0.823951\pi$
$240$		0			0
$241$	−2926.00			−0.782076			−0.391038	−	0.920375i	$-0.627884\pi$
$241$	−2926.00			−0.782076			−0.391038	+	0.920375i	$0.627884\pi$
$242$	−2854.77	−	1079.00i	−0.758311	−	0.286615i
$243$	280.450			0.0740364
$244$	504.000	−	571.482i	0.132235	−	0.149940i
$245$		0			0
$246$	−980.000	−	370.405i	−0.253994	−	0.0960007i
$247$			1960.00i			0.504906i
$248$	−2370.59	−	4480.00i	−0.606987	−	1.14710i
$249$	−2884.00			−0.734000
$250$		0			0
$251$		−	5444.96i		−	1.36925i	−0.728894	−	0.684627i	$-0.759965\pi$
$251$		−	5444.96i		−	1.36925i	0.728894	−	0.684627i	$-0.240035\pi$
$252$	42.3320	−	48.0000i	0.0105820	−	0.0119989i
$253$	−2412.93			−0.599602
$254$	−1664.00	+	4402.53i	−0.411058	+	1.08756i
$255$		0			0
$256$	−3968.00	+	1015.97i	−0.968750	+	0.248039i
$257$			2562.00i			0.621841i	0.950436	+	0.310921i	$0.100637\pi$
$257$			2562.00i			0.621841i	−0.950436	+	0.310921i	$0.899363\pi$
$258$	6148.73	+	2324.00i	1.48373	+	0.560798i
$259$		−	1947.27i		−	0.467172i
$260$		0			0
$261$		−	158.745i		−	0.0376478i
$262$	672.021	−	1778.00i	0.158464	−	0.419257i
$263$			5896.00i			1.38237i	0.722679	+	0.691184i	$0.242911\pi$
$263$			5896.00i			1.38237i	−0.722679	+	0.691184i	$0.757089\pi$
$264$	−1680.00	+	888.972i	−0.391655	+	0.207244i
$265$		0			0
$266$	784.000	+	296.324i	0.180715	+	0.0683038i
$267$	1407.54			0.322622
$268$	1047.72	+	924.000i	0.238804	+	0.210606i
$269$		−	5365.58i		−	1.21615i	−0.793878	−	0.608077i	$-0.791941\pi$
$269$		−	5365.58i		−	1.21615i	0.793878	−	0.608077i	$-0.208059\pi$
$270$		0			0
$271$	−1680.00			−0.376578			−0.188289	−	0.982114i	$-0.560294\pi$
$271$	−1680.00			−0.376578			−0.188289	+	0.982114i	$0.560294\pi$
$272$	888.972	−	112.000i	0.198169	−	0.0249669i
$273$		−	2240.00i		−	0.496597i
$274$	−1062.00	+	2809.79i	−0.234152	+	0.619509i
$275$		0			0
$276$	4256.00	−	4825.85i	0.928192	−	1.05247i
$277$	−1576.87			−0.342039			−0.171019	−	0.985268i	$-0.554706\pi$
$277$	−1576.87			−0.342039			−0.171019	+	0.985268i	$0.554706\pi$
$278$	2693.37	−	7126.00i	0.581072	−	1.53737i
$279$	224.000			0.0480664
$280$		0			0
$281$	−2742.00			−0.582114			−0.291057	−	0.956706i	$-0.594007\pi$
$281$	−2742.00			−0.582114			−0.291057	+	0.956706i	$0.594007\pi$
$282$	−1777.94	+	4704.00i	−0.375444	+	0.993330i
$283$	−2989.70			−0.627983			−0.313991	−	0.949426i	$-0.601666\pi$
$283$	−2989.70			−0.627983			−0.313991	+	0.949426i	$0.601666\pi$
$284$	−432.000	−	380.988i	−0.0902623	−	0.0796038i
$285$		0			0
$286$	−840.000	+	2222.43i	−0.173672	+	0.459493i
$287$			560.000i			0.115177i
$288$	42.3320	−	176.000i	0.00866124	−	0.0360101i
$289$	4717.00			0.960106
$290$		0			0
$291$		−	5259.75i		−	1.05956i
$292$	−1555.70	+	1764.00i	−0.311783	+	0.353528i
$293$	9238.96			1.84214			0.921068	−	0.389401i	$-0.127318\pi$
$293$	9238.96			1.84214			0.921068	+	0.389401i	$0.127318\pi$
$294$	3906.00	+	1476.33i	0.774839	+	0.292861i
$295$		0			0
$296$	−2576.00	−	4868.18i	−0.505834	−	0.955937i
$297$			2184.00i			0.426695i
$298$	793.725	−	2100.00i	0.154293	−	0.408221i
$299$		−	8043.08i		−	1.55566i
$300$		0			0
$301$		−	3513.56i		−	0.672818i
$302$	−1968.44	−	744.000i	−0.375069	−	0.141763i
$303$			3976.00i			0.753846i
$304$	2352.00	−	296.324i	0.443738	−	0.0559058i
$305$		0			0
$306$	−14.0000	+	37.0405i	−0.00261545	+	0.00691982i
$307$	2587.54			0.481039			0.240520	−	0.970644i	$-0.422682\pi$
$307$	2587.54			0.481039			0.240520	+	0.970644i	$0.422682\pi$
$308$	761.976	+	672.000i	0.140966	+	0.124321i
$309$			6222.81i			1.14564i
$310$		0			0
$311$	−2744.00			−0.500315			−0.250157	−	0.968205i	$-0.580482\pi$
$311$	−2744.00			−0.500315			−0.250157	+	0.968205i	$0.580482\pi$
$312$	−2963.24	−	5600.00i	−0.537694	−	1.01615i
$313$		−	2282.00i		−	0.412097i	−0.978542	−	0.206048i	$-0.933940\pi$
$313$		−	2282.00i		−	0.412097i	0.978542	−	0.206048i	$-0.0660604\pi$
$314$	−476.000	−	179.911i	−0.0855485	−	0.0323343i
$315$		0			0
$316$	2784.00	+	2455.26i	0.495608	+	0.437085i
$317$	9577.62			1.69695			0.848474	−	0.529237i	$-0.177522\pi$
$317$	9577.62			1.69695			0.848474	+	0.529237i	$0.177522\pi$
$318$	−444.486	−	168.000i	−0.0783822	−	0.0296257i
$319$	2520.00			0.442298
$320$		0			0
$321$	1428.00			0.248297
$322$	−3217.23	−	1216.00i	−0.556799	−	0.210450i
$323$	−518.567			−0.0893308
$324$	−4530.00	−	3995.08i	−0.776749	−	0.685028i
$325$		0			0
$326$	−4690.00	−	1772.65i	−0.796795	−	0.301160i
$327$			10024.0i			1.69519i
$328$	740.810	+	1400.00i	0.124709	+	0.235677i
$329$	2688.00			0.450438
$330$		0			0
$331$			4249.08i			0.705590i	0.935701	+	0.352795i	$0.114769\pi$
$331$			4249.08i			0.705590i	−0.935701	+	0.352795i	$0.885231\pi$
$332$	3270.15	+	2884.00i	0.540580	+	0.476747i
$333$	243.409			0.0400563
$334$	−1960.00	+	5185.67i	−0.321097	+	0.849543i
$335$		0			0
$336$	−2688.00	+	338.656i	−0.436436	+	0.0549857i
$337$			6130.00i			0.990868i	0.868646	+	0.495434i	$0.164991\pi$
$337$			6130.00i			0.990868i	−0.868646	+	0.495434i	$0.835009\pi$
$338$	−1595.39	−	603.000i	−0.256739	−	0.0970381i
$339$		−	9048.47i		−	1.44969i
$340$		0			0
$341$			3555.89i			0.564699i
$342$	−37.0405	+	98.0000i	−0.00585650	+	0.0154948i
$343$		−	4976.00i		−	0.783320i
$344$	−4648.00	−	8783.89i	−0.728498	−	1.37673i
$345$		0			0
$346$	5292.00	+	2000.19i	0.822253	+	0.310783i
$347$	2481.71			0.383935			0.191967	−	0.981401i	$-0.438513\pi$
$347$	2481.71			0.383935			0.191967	+	0.981401i	$0.438513\pi$
$348$	−4444.86	+	5040.00i	−0.684683	+	0.776357i
$349$		−	328.073i		−	0.0503191i	−0.999683	−	0.0251595i	$-0.991991\pi$
$349$		−	328.073i		−	0.0503191i	0.999683	−	0.0251595i	$-0.00800937\pi$
$350$		0			0
$351$	−7280.00			−1.10706
$352$	2793.91	+	672.000i	0.423057	+	0.101755i
$353$			10206.0i			1.53884i	0.638743	+	0.769420i	$0.279455\pi$
$353$			10206.0i			1.53884i	−0.638743	+	0.769420i	$0.720545\pi$
$354$	−2828.00	+	7482.18i	−0.424595	+	1.12337i
$355$		0			0
$356$	−1596.00	−	1407.54i	−0.237606	−	0.209549i
$357$	592.648			0.0878607
$358$	3264.86	−	8638.00i	0.481992	−	1.27523i
$359$	3176.00			0.466916			0.233458	−	0.972367i	$-0.424996\pi$
$359$	3176.00			0.466916			0.233458	+	0.972367i	$0.424996\pi$
$360$		0			0
$361$	5487.00			0.799971
$362$	2338.84	−	6188.00i	0.339577	−	0.898437i
$363$	−5709.53			−0.825545
$364$	−2240.00	+	2539.92i	−0.322549	+	0.365736i
$365$		0			0
$366$	504.000	−	1333.46i	0.0719795	−	0.190440i
$367$		−	11760.0i		−	1.67266i	−0.548225	−	0.836331i	$-0.684696\pi$
$367$		−	11760.0i		−	1.67266i	0.548225	−	0.836331i	$-0.315304\pi$
$368$	−9651.70	+	1216.00i	−1.36720	+	0.172251i
$369$	−70.0000			−0.00987549
$370$		0			0
$371$			253.992i			0.0355434i
$372$	−7111.78	−	6272.00i	−0.991206	−	0.874161i
$373$	10974.6			1.52344			0.761719	−	0.647908i	$-0.224356\pi$
$373$	10974.6			1.52344			0.761719	+	0.647908i	$0.224356\pi$
$374$	−588.000	−	222.243i	−0.0812961	−	0.0307271i
$375$		0			0
$376$	6720.00	−	3555.89i	0.921696	−	0.487715i
$377$			8400.00i			1.14754i
$378$	−1100.63	+	2912.00i	−0.149763	+	0.396236i
$379$			3074.36i			0.416674i	0.978057	+	0.208337i	$0.0668051\pi$
$379$			3074.36i			0.416674i	−0.978057	+	0.208337i	$0.933195\pi$
$380$		0			0
$381$			8805.06i			1.18398i
$382$	−10329.0	−	3904.00i	−1.38345	−	0.522895i
$383$		−	2688.00i		−	0.358617i	−0.983793	−	0.179309i	$-0.942614\pi$
$383$		−	2688.00i		−	0.358617i	0.983793	−	0.179309i	$-0.0573861\pi$
$384$	−6272.00	+	4402.53i	−0.833507	+	0.585067i
$385$		0			0
$386$	−3330.00	+	8810.35i	−0.439100	+	1.16175i
$387$	439.195			0.0576887
$388$	−5259.75	+	5964.00i	−0.688205	+	0.780351i
$389$			10487.8i			1.36697i	0.729966	+	0.683484i	$0.239536\pi$
$389$			10487.8i			1.36697i	−0.729966	+	0.683484i	$0.760464\pi$
$390$		0			0
$391$	2128.00			0.275237
$392$	−2952.66	−	5580.00i	−0.380438	−	0.718961i
$393$		−	3556.00i		−	0.456429i
$394$	3164.00	+	1195.88i	0.404569	+	0.152913i
$395$		0			0
$396$	−84.0000	+	95.2470i	−0.0106595	+	0.0120867i
$397$	−5704.24			−0.721127			−0.360564	−	0.932735i	$-0.617416\pi$
$397$	−5704.24			−0.721127			−0.360564	+	0.932735i	$0.617416\pi$
$398$	−4593.02	−	1736.00i	−0.578461	−	0.218638i
$399$	1568.00			0.196737
$400$		0			0
$401$	12402.0			1.54445			0.772227	−	0.635346i	$-0.219143\pi$
$401$	12402.0			1.54445			0.772227	+	0.635346i	$0.219143\pi$
$402$	2444.67	+	924.000i	0.303307	+	0.114639i
$403$	−11853.0			−1.46511
$404$	3976.00	−	4508.36i	0.489637	−	0.555196i
$405$		0			0
$406$	3360.00	+	1269.96i	0.410724	+	0.155239i
$407$			3864.00i			0.470593i
$408$	1481.62	−	784.000i	0.179782	−	0.0951318i
$409$	12278.0			1.48437			0.742186	−	0.670194i	$-0.233789\pi$
$409$	12278.0			1.48437			0.742186	+	0.670194i	$0.233789\pi$
$410$		0			0
$411$			5619.58i			0.674436i
$412$	6222.81	−	7056.00i	0.744116	−	0.843748i
$413$	4275.53			0.509407
$414$	152.000	−	402.154i	0.0180444	−	0.0477411i
$415$		0			0
$416$	−2240.00	+	9313.04i	−0.264002	+	1.09762i
$417$		−	14252.0i		−	1.67368i
$418$	−1555.70	−	588.000i	−0.182038	−	0.0688039i
$419$		−	8207.12i		−	0.956907i	−0.878113	−	0.478454i	$-0.841198\pi$
$419$		−	8207.12i		−	0.956907i	0.878113	−	0.478454i	$-0.158802\pi$
$420$		0			0
$421$			1449.87i			0.167844i	0.996472	+	0.0839221i	$0.0267447\pi$
$421$			1449.87i			0.167844i	−0.996472	+	0.0839221i	$0.973255\pi$
$422$	2915.62	−	7714.00i	0.336327	−	0.889838i
$423$			336.000i			0.0386215i
$424$	336.000	+	634.980i	0.0384849	+	0.0727296i
$425$		0			0
$426$	−1008.00	−	380.988i	−0.114643	−	0.0433308i
$427$	−761.976			−0.0863574
$428$	−1619.20	−	1428.00i	−0.182867	−	0.161273i
$429$			4444.86i			0.500233i
$430$		0			0
$431$	7632.00			0.852948			0.426474	−	0.904500i	$-0.359756\pi$
$431$	7632.00			0.852948			0.426474	+	0.904500i	$0.359756\pi$
$432$	1100.63	+	8736.00i	0.122579	+	0.972942i
$433$		−	3794.00i		−	0.421081i	−0.977585	−	0.210540i	$-0.932478\pi$
$433$		−	3794.00i		−	0.421081i	0.977585	−	0.210540i	$-0.0675224\pi$
$434$	−1792.00	+	4741.19i	−0.198200	+	0.524388i
$435$		0			0
$436$	10024.0	−	11366.1i	1.10106	−	1.24849i
$437$	5630.16			0.616309
$438$	−1555.70	+	4116.00i	−0.169713	+	0.449018i
$439$	1848.00			0.200912			0.100456	−	0.994942i	$-0.467970\pi$
$439$	1848.00			0.200912			0.100456	+	0.994942i	$0.467970\pi$
$440$		0			0
$441$	279.000			0.0301263
$442$	740.810	−	1960.00i	0.0797212	−	0.210922i
$443$	12334.5			1.32287			0.661433	−	0.750004i	$-0.269949\pi$
$443$	12334.5			1.32287			0.661433	+	0.750004i	$0.269949\pi$
$444$	−7728.00	−	6815.46i	−0.826024	−	0.728485i
$445$		0			0
$446$	−1568.00	+	4148.54i	−0.166473	+	0.440446i
$447$		−	4200.00i		−	0.444414i
$448$	3386.56	+	2304.00i	0.357143	+	0.242977i
$449$	3582.00			0.376492			0.188246	−	0.982122i	$-0.439720\pi$
$449$	3582.00			0.376492			0.188246	+	0.982122i	$0.439720\pi$
$450$		0			0
$451$		−	1111.22i		−	0.116020i
$452$	−9048.47	+	10260.0i	−0.941602	+	1.06768i
$453$	−3936.88			−0.408324
$454$	3346.00	+	1264.67i	0.345893	+	0.130735i
$455$		0			0
$456$	3920.00	−	2074.27i	0.402568	−	0.213019i
$457$			2714.00i			0.277802i	0.990306	+	0.138901i	$0.0443570\pi$
$457$			2714.00i			0.277802i	−0.990306	+	0.138901i	$0.955643\pi$
$458$	5153.92	−	13636.0i	0.525823	−	1.39120i
$459$		−	1926.11i		−	0.195867i
$460$		0			0
$461$		−	8349.99i		−	0.843596i	−0.906690	−	0.421798i	$-0.861399\pi$
$461$		−	8349.99i		−	0.843596i	0.906690	−	0.421798i	$-0.138601\pi$
$462$	1777.94	+	672.000i	0.179042	+	0.0676716i
$463$		−	2224.00i		−	0.223236i	−0.993751	−	0.111618i	$-0.964397\pi$
$463$		−	2224.00i		−	0.223236i	0.993751	−	0.111618i	$-0.0356032\pi$
$464$	10080.0	−	1269.96i	1.00852	−	0.127061i
$465$		0			0
$466$	838.000	−	2217.14i	0.0833039	−	0.220401i
$467$	10292.0			1.01982			0.509910	−	0.860228i	$-0.329679\pi$
$467$	10292.0			1.01982			0.509910	+	0.860228i	$0.329679\pi$
$468$	−317.490	−	280.000i	−0.0313589	−	0.0276560i
$469$		−	1396.96i		−	0.137538i
$470$		0			0
$471$	−952.000			−0.0931334
$472$	10688.8	−	5656.00i	1.04236	−	0.551565i
$473$			6972.00i			0.677744i
$474$	6496.00	+	2455.26i	0.629475	+	0.237919i
$475$		0			0
$476$	−672.000	−	592.648i	−0.0647081	−	0.0570672i
$477$	−31.7490			−0.00304756
$478$	16636.5	+	6288.00i	1.59191	+	0.601687i
$479$	−17696.0			−1.68800			−0.843999	−	0.536345i	$-0.819805\pi$
$479$	−17696.0			−1.68800			−0.843999	+	0.536345i	$0.819805\pi$
$480$		0			0
$481$	−12880.0			−1.22095
$482$	7741.47	+	2926.00i	0.731565	+	0.276505i
$483$	−6434.47			−0.606166
$484$	6474.00	+	5709.53i	0.608002	+	0.536207i
$485$		0			0
$486$	−742.000	−	280.450i	−0.0692547	−	0.0261758i
$487$			1304.00i			0.121334i	0.998158	+	0.0606672i	$0.0193228\pi$
$487$			1304.00i			0.121334i	−0.998158	+	0.0606672i	$0.980677\pi$
$488$	−1904.94	+	1008.00i	−0.176706	+	0.0935041i
$489$	−9380.00			−0.867440
$490$		0			0
$491$		−	16662.9i		−	1.53154i	−0.643112	−	0.765772i	$-0.722357\pi$
$491$		−	16662.9i		−	1.53154i	0.643112	−	0.765772i	$-0.277643\pi$
$492$	2222.43	+	1960.00i	0.203648	+	0.179601i
$493$	−2222.43			−0.203029
$494$	1960.00	−	5185.67i	0.178511	−	0.472296i
$495$		0			0
$496$	1792.00	+	14223.6i	0.162224	+	1.28761i
$497$			576.000i			0.0519862i
$498$	7630.35	+	2884.00i	0.686594	+	0.259508i
$499$			3095.53i			0.277705i	0.990313	+	0.138853i	$0.0443414\pi$
$499$			3095.53i			0.277705i	−0.990313	+	0.138853i	$0.955659\pi$
$500$		0			0
$501$			10371.3i			0.924865i
$502$	−5444.96	+	14406.0i	−0.484104	+	1.28082i
$503$			19320.0i			1.71260i	0.516481	+	0.856298i	$0.327242\pi$
$503$			19320.0i			1.71260i	−0.516481	+	0.856298i	$0.672758\pi$
$504$	−160.000	+	84.6640i	−0.0141408	+	0.00748261i
$505$		0			0
$506$	6384.00	+	2412.93i	0.560876	+	0.211991i
$507$	−3190.78			−0.279502
$508$	8805.06	−	9984.00i	0.769018	−	0.871985i
$509$		−	4476.61i		−	0.389828i	−0.980820	−	0.194914i	$-0.937557\pi$
$509$		−	4476.61i		−	0.389828i	0.980820	−	0.194914i	$-0.0624427\pi$
$510$		0			0
$511$	2352.00			0.203613
$512$	11514.3	+	1280.00i	0.993878	+	0.110485i
$513$		−	5096.00i		−	0.438585i
$514$	2562.00	−	6778.41i	0.219854	−	0.581679i
$515$		0			0
$516$	−13944.0	−	12297.5i	−1.18963	−	1.04916i
$517$	−5333.83			−0.453737
$518$	−1947.27	+	5152.00i	−0.165170	+	0.437000i
$519$	10584.0			0.895156
$520$		0			0
$521$	−2982.00			−0.250756			−0.125378	−	0.992109i	$-0.540014\pi$
$521$	−2982.00			−0.250756			−0.125378	+	0.992109i	$0.540014\pi$
$522$	−158.745	+	420.000i	−0.0133105	+	0.0352163i
$523$	−2016.06			−0.168559			−0.0842794	−	0.996442i	$-0.526859\pi$
$523$	−2016.06			−0.168559			−0.0842794	+	0.996442i	$0.526859\pi$
$524$	−3556.00	+	4032.12i	−0.296459	+	0.336153i
$525$		0			0
$526$	5896.00	−	15599.3i	0.488741	−	1.29309i
$527$		−	3136.00i		−	0.259215i
$528$	5333.83	−	672.000i	0.439631	−	0.0553883i
$529$	−10937.0			−0.898907
$530$		0			0
$531$			534.442i			0.0436776i
$532$	−1777.94	−	1568.00i	−0.144894	−	0.127785i
$533$	3704.05			0.301014
$534$	−3724.00	−	1407.54i	−0.301785	−	0.114064i
$535$		0			0
$536$	−1848.00	−	3492.39i	−0.148921	−	0.281433i
$537$		−	17276.0i		−	1.38830i
$538$	−5365.58	+	14196.0i	−0.429975	+	1.13761i
$539$			4428.99i			0.353933i
$540$		0			0
$541$		−	15419.4i		−	1.22539i	−0.790321	−	0.612693i	$-0.790086\pi$
$541$		−	15419.4i		−	1.22539i	0.790321	−	0.612693i	$-0.209914\pi$
$542$	4444.86	+	1680.00i	0.352257	+	0.133141i
$543$		−	12376.0i		−	0.978094i
$544$	−2464.00	−	592.648i	−0.194197	−	0.0467088i
$545$		0			0
$546$	−2240.00	+	5926.48i	−0.175574	+	0.464524i
$547$	−12609.7			−0.985649			−0.492824	−	0.870129i	$-0.664035\pi$
$547$	−12609.7			−0.985649			−0.492824	+	0.870129i	$0.664035\pi$
$548$	5619.58	−	6372.00i	0.438059	−	0.496712i
$549$		−	95.2470i		−	0.00740445i
$550$		0			0
$551$	−5880.00			−0.454621
$552$	−16086.2	+	8512.00i	−1.24035	+	0.656331i
$553$		−	3712.00i		−	0.285444i
$554$	4172.00	+	1576.87i	0.319948	+	0.120929i
$555$		0			0
$556$	−14252.0	+	16160.2i	−1.08709	+	1.23264i
$557$	−7143.53			−0.543413			−0.271706	−	0.962380i	$-0.587588\pi$
$557$	−7143.53			−0.543413			−0.271706	+	0.962380i	$0.587588\pi$
$558$	−592.648	−	224.000i	−0.0449620	−	0.0169940i
$559$	−23240.0			−1.75840
$560$		0			0
$561$	−1176.00			−0.0885040
$562$	7254.65	+	2742.00i	0.544518	+	0.205808i
$563$	7572.14			0.566834			0.283417	−	0.958997i	$-0.408532\pi$
$563$	7572.14			0.566834			0.283417	+	0.958997i	$0.408532\pi$
$564$	9408.00	−	10667.7i	0.702391	−	0.796436i
$565$		0			0
$566$	7910.00	+	2989.70i	0.587424	+	0.222025i
$567$			6040.00i			0.447365i
$568$	761.976	+	1440.00i	0.0562884	+	0.106375i
$569$	−15594.0			−1.14892			−0.574459	−	0.818533i	$-0.694788\pi$
$569$	−15594.0			−1.14892			−0.574459	+	0.818533i	$0.694788\pi$
$570$		0			0
$571$			16737.0i			1.22666i	0.789827	+	0.613330i	$0.210170\pi$
$571$			16737.0i			1.22666i	−0.789827	+	0.613330i	$0.789830\pi$
$572$	4444.86	−	5040.00i	0.324911	−	0.368414i
$573$	−20658.0			−1.50611
$574$	560.000	−	1481.62i	0.0407212	−	0.107738i
$575$		0			0
$576$	−288.000	+	423.320i	−0.0208333	+	0.0306221i
$577$			6594.00i			0.475757i	0.971295	+	0.237879i	$0.0764520\pi$
$577$			6594.00i			0.475757i	−0.971295	+	0.237879i	$0.923548\pi$
$578$	−12480.0	−	4717.00i	−0.898097	−	0.339449i
$579$			17620.7i			1.26475i
$580$		0			0
$581$		−	4360.20i		−	0.311345i
$582$	−5259.75	+	13916.0i	−0.374611	+	0.991128i
$583$		−	504.000i		−	0.0358037i
$584$	5880.00	−	3111.40i	0.416637	−	0.220464i
$585$		0			0
$586$	−24444.0	−	9238.96i	−1.72316	−	0.651294i
$587$	−23213.8			−1.63226			−0.816130	−	0.577868i	$-0.803885\pi$
$587$	−23213.8			−1.63226			−0.816130	+	0.577868i	$0.803885\pi$
$588$	−8857.98	−	7812.00i	−0.621253	−	0.547894i
$589$		−	8297.08i		−	0.580433i
$590$		0			0
$591$	6328.00			0.440438
$592$	1947.27	+	15456.0i	0.135190	+	1.07304i
$593$		−	14322.0i		−	0.991794i	−0.868381	−	0.495897i	$-0.834839\pi$
$593$		−	14322.0i		−	0.991794i	0.868381	−	0.495897i	$-0.165161\pi$
$594$	2184.00	−	5778.32i	0.150860	−	0.399137i
$595$		0			0
$596$	−4200.00	+	4762.35i	−0.288656	+	0.327305i
$597$	−9186.05			−0.629749
$598$	−8043.08	+	21280.0i	−0.550010	+	1.45519i
$599$	16088.0			1.09739			0.548696	−	0.836022i	$-0.315124\pi$
$599$	16088.0			1.09739			0.548696	+	0.836022i	$0.315124\pi$
$600$		0			0
$601$	−21238.0			−1.44146			−0.720729	−	0.693217i	$-0.756193\pi$
$601$	−21238.0			−1.44146			−0.720729	+	0.693217i	$0.756193\pi$
$602$	−3513.56	+	9296.00i	−0.237877	+	0.629363i
$603$	174.620			0.0117928
$604$	4464.00	+	3936.88i	0.300724	+	0.265214i
$605$		0			0
$606$	3976.00	−	10519.5i	0.266525	−	0.705158i
$607$		−	13664.0i		−	0.913681i	−0.889549	−	0.456841i	$-0.848981\pi$
$607$		−	13664.0i		−	0.913681i	0.889549	−	0.456841i	$-0.151019\pi$
$608$	−6519.13	−	1568.00i	−0.434845	−	0.104590i
$609$	6720.00			0.447140
$610$		0			0
$611$		−	17779.4i		−	1.17722i
$612$	74.0810	−	84.0000i	0.00489305	−	0.00554820i
$613$	−20393.5			−1.34369			−0.671846	−	0.740690i	$-0.734499\pi$
$613$	−20393.5			−1.34369			−0.671846	+	0.740690i	$0.734499\pi$
$614$	−6846.00	−	2587.54i	−0.449971	−	0.170073i
$615$		0			0
$616$	−1344.00	−	2539.92i	−0.0879080	−	0.166130i
$617$		−	3782.00i		−	0.246771i	−0.992359	−	0.123385i	$-0.960625\pi$
$617$		−	3782.00i		−	0.246771i	0.992359	−	0.123385i	$-0.0393751\pi$
$618$	6222.81	−	16464.0i	0.405045	−	1.07165i
$619$			5825.94i			0.378295i	0.981949	+	0.189147i	$0.0605724\pi$
$619$			5825.94i			0.378295i	−0.981949	+	0.189147i	$0.939428\pi$
$620$		0			0
$621$			20912.0i			1.35132i
$622$	7259.94	+	2744.00i	0.468002	+	0.176888i
$623$			2128.00i			0.136848i
$624$	2240.00	+	17779.4i	0.143705	+	1.14062i
$625$		0			0
$626$	−2282.00	+	6037.60i	−0.145698	+	0.385481i
$627$	−3111.40			−0.198178
$628$	1079.47	+	952.000i	0.0685914	+	0.0604919i
$629$		−	3407.73i		−	0.216017i
$630$		0			0
$631$	2056.00			0.129712			0.0648558	−	0.997895i	$-0.479341\pi$
$631$	2056.00			0.129712			0.0648558	+	0.997895i	$0.479341\pi$
$632$	−4910.51	−	9280.00i	−0.309066	−	0.584080i
$633$		−	15428.0i		−	0.968733i
$634$	−25340.0	−	9577.62i	−1.58735	−	0.599962i
$635$		0			0
$636$	1008.00	+	888.972i	0.0628456	+	0.0554246i
$637$	−14763.3			−0.918278
$638$	−6667.29	−	2520.00i	−0.413731	−	0.156376i
$639$	−72.0000			−0.00445740
$640$		0			0
$641$	11842.0			0.729689			0.364845	−	0.931068i	$-0.381122\pi$
$641$	11842.0			0.729689			0.364845	+	0.931068i	$0.381122\pi$
$642$	−3778.13	−	1428.00i	−0.232260	−	0.0877861i
$643$	16250.2			0.996649			0.498325	−	0.866991i	$-0.333949\pi$
$643$	16250.2			0.996649			0.498325	+	0.866991i	$0.333949\pi$
$644$	7296.00	+	6434.47i	0.446433	+	0.393717i
$645$		0			0
$646$	1372.00	+	518.567i	0.0835613	+	0.0315832i
$647$			19320.0i			1.17395i	0.809604	+	0.586976i	$0.199682\pi$
$647$			19320.0i			1.17395i	−0.809604	+	0.586976i	$0.800318\pi$
$648$	7990.17	+	15100.0i	0.484388	+	0.915407i
$649$	−8484.00			−0.513137
$650$		0			0
$651$			9482.37i			0.570881i
$652$	10635.9	+	9380.00i	0.638857	+	0.563419i
$653$	2317.68			0.138894			0.0694470	−	0.997586i	$-0.477877\pi$
$653$	2317.68			0.138894			0.0694470	+	0.997586i	$0.477877\pi$
$654$	10024.0	−	26521.0i	0.599342	−	1.58571i
$655$		0			0
$656$	−560.000	−	4444.86i	−0.0333298	−	0.264547i
$657$			294.000i			0.0174582i
$658$	−7111.78	−	2688.00i	−0.421347	−	0.159254i
$659$			27732.8i			1.63932i	0.572847	+	0.819662i	$0.305839\pi$
$659$			27732.8i			1.63932i	−0.572847	+	0.819662i	$0.694161\pi$
$660$		0			0
$661$		−	22467.7i		−	1.32208i	−0.750352	−	0.661039i	$-0.770116\pi$
$661$		−	22467.7i		−	1.32208i	0.750352	−	0.661039i	$-0.229884\pi$
$662$	4249.08	−	11242.0i	0.249464	−	0.660019i
$663$		−	3920.00i		−	0.229623i
$664$	−5768.00	−	10900.5i	−0.337111	−	0.637080i
$665$		0			0
$666$	−644.000	−	243.409i	−0.0374692	−	0.0141620i
$667$	24129.3			1.40073
$668$	10371.3	−	11760.0i	0.600718	−	0.681150i
$669$			8297.08i			0.479497i
$670$		0			0
$671$	1512.00			0.0869897
$672$	7450.44	+	1792.00i	0.427689	+	0.102869i
$673$			10078.0i			0.577234i	0.957445	+	0.288617i	$0.0931954\pi$
$673$			10078.0i			0.577234i	−0.957445	+	0.288617i	$0.906805\pi$
$674$	6130.00	−	16218.5i	0.350325	−	0.926872i
$675$		0			0
$676$	3618.00	+	3190.78i	0.205849	+	0.181542i
$677$	16160.2			0.917413			0.458707	−	0.888588i	$-0.348313\pi$
$677$	16160.2			0.917413			0.458707	+	0.888588i	$0.348313\pi$
$678$	−9048.47	+	23940.0i	−0.512543	+	1.35606i
$679$	7952.00			0.449440
$680$		0			0
$681$	6692.00			0.376561
$682$	3555.89	−	9408.00i	0.199651	−	0.528227i
$683$	16356.0			0.916320			0.458160	−	0.888870i	$-0.348509\pi$
$683$	16356.0			0.916320			0.458160	+	0.888870i	$0.348509\pi$
$684$	196.000	−	222.243i	0.0109565	−	0.0124235i
$685$		0			0
$686$	−4976.00	+	13165.3i	−0.276945	+	0.732729i
$687$		−	27272.0i		−	1.51454i
$688$	3513.56	+	27888.0i	0.194699	+	1.54538i
$689$	1680.00			0.0928925
$690$		0			0
$691$			29246.1i			1.61009i	0.593211	+	0.805047i	$0.297860\pi$
$691$			29246.1i			1.61009i	−0.593211	+	0.805047i	$0.702140\pi$
$692$	−12001.1	−	10584.0i	−0.659269	−	0.581421i
$693$	126.996			0.00696130
$694$	−6566.00	−	2481.71i	−0.359138	−	0.135742i
$695$		0			0
$696$	16800.0	−	8889.72i	0.914946	−	0.484144i
$697$			980.000i			0.0532570i
$698$	−328.073	+	868.000i	−0.0177905	+	0.0470692i
$699$		−	4434.28i		−	0.239943i
$700$		0			0
$701$		−	2465.84i		−	0.132858i	−0.997791	−	0.0664290i	$-0.978839\pi$
$701$		−	2465.84i		−	0.132858i	0.997791	−	0.0664290i	$-0.0211606\pi$
$702$	19261.1	+	7280.00i	1.03556	+	0.391404i
$703$		−	9016.00i		−	0.483705i
$704$	−6720.00	−	4571.86i	−0.359758	−	0.244756i
$705$		0			0
$706$	10206.0	−	27002.5i	0.544062	−	1.43945i
$707$	−6011.15			−0.319763
$708$	14964.4	−	16968.0i	0.794344	−	0.900701i
$709$		−	31674.9i		−	1.67782i	−0.544267	−	0.838912i	$-0.683192\pi$
$709$		−	31674.9i		−	1.67782i	0.544267	−	0.838912i	$-0.316808\pi$
$710$		0			0
$711$	464.000			0.0244745
$712$	2815.08	+	5320.00i	0.148174	+	0.280022i
$713$			34048.0i			1.78837i
$714$	−1568.00	−	592.648i	−0.0821862	−	0.0310635i
$715$		0			0
$716$	−17276.0	+	19589.1i	−0.901724	+	1.02246i
$717$	33273.0			1.73306
$718$	−8402.91	−	3176.00i	−0.436760	−	0.165080i
$719$	9296.00			0.482173			0.241086	−	0.970504i	$-0.422496\pi$
$719$	9296.00			0.482173			0.241086	+	0.970504i	$0.422496\pi$
$720$		0			0
$721$	−9408.00			−0.485953
$722$	−14517.2	−	5487.00i	−0.748304	−	0.282832i
$723$	15482.9			0.796427
$724$	−12376.0	+	14033.1i	−0.635291	+	0.720352i
$725$		0			0
$726$	15106.0	+	5709.53i	0.772226	+	0.291874i
$727$			21672.0i			1.10560i	0.833315	+	0.552799i	$0.186440\pi$
$727$			21672.0i			1.10560i	−0.833315	+	0.552799i	$0.813560\pi$
$728$	8466.40	−	4480.00i	0.431024	−	0.228077i
$729$	18901.0			0.960270
$730$		0			0
$731$		−	6148.73i		−	0.311106i
$732$	−2666.92	+	3024.00i	−0.134661	+	0.152692i
$733$	9471.79			0.477283			0.238642	−	0.971108i	$-0.423298\pi$
$733$	9471.79			0.477283			0.238642	+	0.971108i	$0.423298\pi$
$734$	−11760.0	+	31114.0i	−0.591375	+	1.56463i
$735$		0			0
$736$	26752.0	+	6434.47i	1.33980	+	0.322252i
$737$			2772.00i			0.138545i
$738$	185.203	+	70.0000i	0.00923767	+	0.00349151i
$739$			6863.08i			0.341627i	0.985303	+	0.170814i	$0.0546396\pi$
$739$			6863.08i			0.341627i	−0.985303	+	0.170814i	$0.945360\pi$
$740$		0			0
$741$		−	10371.3i		−	0.514171i
$742$	253.992	−	672.000i	0.0125665	−	0.0332478i
$743$		−	17432.0i		−	0.860724i	−0.902656	−	0.430362i	$-0.858386\pi$
$743$		−	17432.0i		−	0.860724i	0.902656	−	0.430362i	$-0.141614\pi$
$744$	12544.0	+	23705.9i	0.618125	+	1.16815i
$745$		0			0
$746$	−29036.0	−	10974.6i	−1.42504	−	0.538616i
$747$	545.025			0.0266953
$748$	1333.46	+	1176.00i	0.0651819	+	0.0574851i
$749$			2158.93i			0.105321i
$750$		0			0
$751$	−11632.0			−0.565190			−0.282595	−	0.959239i	$-0.591195\pi$
$751$	−11632.0			−0.565190			−0.282595	+	0.959239i	$0.591195\pi$
$752$	−21335.3	+	2688.00i	−1.03460	+	0.130347i
$753$			28812.0i			1.39438i
$754$	8400.00	−	22224.3i	0.405716	−	1.07342i
$755$		0			0
$756$	5824.00	−	6603.80i	0.280181	−	0.317695i
$757$	−16731.7			−0.803336			−0.401668	−	0.915785i	$-0.631569\pi$
$757$	−16731.7			−0.803336			−0.401668	+	0.915785i	$0.631569\pi$
$758$	3074.36	−	8134.00i	0.147316	−	0.389763i
$759$	12768.0			0.610605
$760$		0			0
$761$	39466.0			1.87995			0.939975	−	0.341244i	$-0.110848\pi$
$761$	39466.0			1.87995			0.939975	+	0.341244i	$0.110848\pi$
$762$	8805.06	−	23296.0i	0.418601	−	1.10751i
$763$	−15154.9			−0.719060
$764$	23424.0	+	20658.0i	1.10923	+	0.978248i
$765$		0			0
$766$	−2688.00	+	7111.78i	−0.126790	+	0.335456i
$767$		−	28280.0i		−	1.33133i
$768$	20996.7	−	5376.00i	0.986527	−	0.252591i
$769$	−35266.0			−1.65374			−0.826869	−	0.562395i	$-0.809880\pi$
$769$	−35266.0			−1.65374			−0.826869	+	0.562395i	$0.809880\pi$
$770$		0			0
$771$		−	13556.8i		−	0.633252i
$772$	17620.7	−	19980.0i	0.821481	−	0.931471i
$773$	−16244.9			−0.755872			−0.377936	−	0.925832i	$-0.623366\pi$
$773$	−16244.9			−0.755872			−0.377936	+	0.925832i	$0.623366\pi$
$774$	−1162.00	−	439.195i	−0.0539628	−	0.0203960i
$775$		0			0
$776$	19880.0	−	10519.5i	0.919653	−	0.486634i
$777$			10304.0i			0.475745i
$778$	10487.8	−	27748.0i	0.483296	−	1.27868i
$779$			2592.84i			0.119253i
$780$		0			0
$781$		−	1142.96i		−	0.0523668i
$782$	−5630.16	−	2128.00i	−0.257460	−	0.0973109i
$783$		−	21840.0i		−	0.996805i
$784$	2232.00	+	17716.0i	0.101676	+	0.807031i
$785$		0			0
$786$	−3556.00	+	9408.29i	−0.161372	+	0.426950i
$787$	34844.5			1.57824			0.789119	−	0.614240i	$-0.210537\pi$
$787$	34844.5			1.57824			0.789119	+	0.614240i	$0.210537\pi$
$788$	−7175.28	−	6328.00i	−0.324376	−	0.286073i
$789$		−	31198.7i		−	1.40774i
$790$		0			0
$791$	13680.0			0.614924
$792$	317.490	−	168.000i	0.0142443	−	0.00753740i
$793$			5040.00i			0.225694i
$794$	15092.0	+	5704.24i	0.674553	+	0.254957i
$795$		0			0
$796$	10416.0	+	9186.05i	0.463801	+	0.409034i
$797$	2550.50			0.113354			0.0566772	−	0.998393i	$-0.481949\pi$
$797$	2550.50			0.113354			0.0566772	+	0.998393i	$0.481949\pi$
$798$	−4148.54	−	1568.00i	−0.184031	−	0.0695571i
$799$	4704.00			0.208280
$800$		0			0
$801$	−266.000			−0.0117336
$802$	−32812.6	−	12402.0i	−1.44471	−	0.546047i
$803$	−4667.11			−0.205104
$804$	−5544.00	−	4889.35i	−0.243186	−	0.214470i
$805$		0			0
$806$	31360.0	+	11853.0i	1.37048	+	0.517994i
$807$			28392.0i			1.23847i
$808$	−15027.9	+	7952.00i	−0.654305	+	0.346226i
$809$	24390.0			1.05996			0.529979	−	0.848010i	$-0.322200\pi$
$809$	24390.0			1.05996			0.529979	+	0.848010i	$0.322200\pi$
$810$		0			0
$811$			9582.91i			0.414922i	0.978243	+	0.207461i	$0.0665200\pi$
$811$			9582.91i			0.414922i	−0.978243	+	0.207461i	$0.933480\pi$
$812$	−7619.76	−	6720.00i	−0.329312	−	0.290426i
$813$	8889.72			0.383489
$814$	3864.00	−	10223.2i	0.166380	−	0.440199i
$815$		0			0
$816$	−4704.00	+	592.648i	−0.201805	+	0.0254250i
$817$		−	16268.0i		−	0.696628i
$818$	−32484.5	−	12278.0i	−1.38850	−	0.524805i
$819$			423.320i			0.0180611i
$820$		0			0
$821$			8773.31i			0.372948i	0.982460	+	0.186474i	$0.0597061\pi$
$821$			8773.31i			0.372948i	−0.982460	+	0.186474i	$0.940294\pi$
$822$	5619.58	−	14868.0i	0.238449	−	0.630877i
$823$			21688.0i			0.918586i	0.888285	+	0.459293i	$0.151897\pi$
$823$			21688.0i			0.918586i	−0.888285	+	0.459293i	$0.848103\pi$
$824$	−23520.0	+	12445.6i	−0.994367	+	0.526169i
$825$		0			0
$826$	−11312.0	−	4275.53i	−0.476507	−	0.180103i
$827$	−19446.3			−0.817670			−0.408835	−	0.912608i	$-0.634065\pi$
$827$	−19446.3			−0.817670			−0.408835	+	0.912608i	$0.634065\pi$
$828$	−804.308	+	912.000i	−0.0337580	+	0.0382780i
$829$		−	19546.8i		−	0.818925i	−0.912327	−	0.409462i	$-0.865716\pi$
$829$		−	19546.8i		−	0.818925i	0.912327	−	0.409462i	$-0.134284\pi$
$830$		0			0
$831$	8344.00			0.348315
$832$	15239.5	−	22400.0i	0.635019	−	0.933390i
$833$		−	3906.00i		−	0.162467i
$834$	−14252.0	+	37707.2i	−0.591734	+	1.56558i
$835$		0			0
$836$	3528.00	+	3111.40i	0.145955	+	0.128720i
$837$	30817.7			1.27266
$838$	−8207.12	+	21714.0i	−0.338318	+	0.895105i
$839$	18760.0			0.771951			0.385976	−	0.922509i	$-0.373865\pi$
$839$	18760.0			0.771951			0.385976	+	0.922509i	$0.373865\pi$
$840$		0			0
$841$	−811.000			−0.0332527
$842$	1449.87	−	3836.00i	0.0593419	−	0.157004i
$843$	14509.3			0.592796
$844$	−15428.0	+	17493.7i	−0.629210	+	0.713458i
$845$		0			0
$846$	336.000	−	888.972i	0.0136547	−	0.0361271i
$847$		−	8632.00i		−	0.350176i
$848$	−253.992	−	2016.00i	−0.0102855	−	0.0816388i
$849$	15820.0			0.639506
$850$		0			0
$851$			36998.2i			1.49034i
$852$	2285.93	+	2016.00i	0.0919186	+	0.0810646i
$853$	−28732.9			−1.15333			−0.576667	−	0.816979i	$-0.695647\pi$
$853$	−28732.9			−1.15333			−0.576667	+	0.816979i	$0.695647\pi$
$854$	2016.00	+	761.976i	0.0807800	+	0.0305320i
$855$		0			0
$856$	2856.00	+	5397.33i	0.114037	+	0.215511i
$857$			8778.00i			0.349884i	0.984579	+	0.174942i	$0.0559738\pi$
$857$			8778.00i			0.349884i	−0.984579	+	0.174942i	$0.944026\pi$
$858$	4444.86	−	11760.0i	0.176859	−	0.467925i
$859$		−	5646.03i		−	0.224261i	−0.993693	−	0.112130i	$-0.964233\pi$
$859$		−	5646.03i		−	0.224261i	0.993693	−	0.112130i	$-0.0357675\pi$
$860$		0			0
$861$		−	2963.24i		−	0.117290i
$862$	−20192.4	−	7632.00i	−0.797860	−	0.301563i
$863$			9312.00i			0.367305i	0.982991	+	0.183652i	$0.0587921\pi$
$863$			9312.00i			0.367305i	−0.982991	+	0.183652i	$0.941208\pi$
$864$	5824.00	−	24213.9i	0.229325	−	0.953442i
$865$		0			0
$866$	−3794.00	+	10038.0i	−0.148875	+	0.393885i
$867$	−24960.0			−0.977724
$868$	9482.37	−	10752.0i	0.370798	−	0.420445i
$869$			7365.77i			0.287534i
$870$		0			0
$871$	−9240.00			−0.359455
$872$	−37887.2	+	20048.0i	−1.47135	+	0.778568i
$873$			994.000i			0.0385359i
$874$	−14896.0	−	5630.16i	−0.576504	−	0.217898i
$875$		0			0
$876$	8232.00	−	9334.21i	0.317504	−	0.360016i
$877$	137.579			0.00529728			0.00264864	−	0.999996i	$-0.499157\pi$
$877$	137.579			0.00529728			0.00264864	+	0.999996i	$0.499157\pi$
$878$	−4889.35	−	1848.00i	−0.187936	−	0.0710330i
$879$	−48888.0			−1.87594
$880$		0			0
$881$	−31150.0			−1.19123			−0.595613	−	0.803272i	$-0.703091\pi$
$881$	−31150.0			−1.19123			−0.595613	+	0.803272i	$0.703091\pi$
$882$	−738.165	−	279.000i	−0.0281806	−	0.0106513i
$883$	−12577.9			−0.479366			−0.239683	−	0.970851i	$-0.577043\pi$
$883$	−12577.9			−0.479366			−0.239683	+	0.970851i	$0.577043\pi$
$884$	−3920.00	+	4444.86i	−0.149145	+	0.169114i
$885$		0			0
$886$	−32634.0	−	12334.5i	−1.23743	−	0.467704i
$887$			37128.0i			1.40545i	0.711460	+	0.702726i	$0.248034\pi$
$887$			37128.0i			1.40545i	−0.711460	+	0.702726i	$0.751966\pi$
$888$	13630.9	+	25760.0i	0.515116	+	0.973479i
$889$	−13312.0			−0.502216
$890$		0			0
$891$		−	11985.3i		−	0.450641i
$892$	8297.08	−	9408.00i	0.311442	−	0.353143i
$893$	12445.6			0.466379
$894$	−4200.00	+	11112.2i	−0.157124	+	0.415711i
$895$		0			0
$896$	−6656.00	−	9482.37i	−0.248171	−	0.353553i
$897$			42560.0i			1.58421i
$898$	−9477.08	−	3582.00i	−0.352176	−	0.133110i
$899$		−	35558.9i		−	1.31919i
$900$		0			0
$901$			444.486i			0.0164351i
$902$	−1111.22	+	2940.00i	−0.0410193	+	0.108527i
$903$			18592.0i			0.685164i
$904$	34200.0	−	18096.9i	1.25827	−	0.665813i
$905$		0			0
$906$	10416.0	+	3936.88i	0.381952	+	0.144364i
$907$	35204.4			1.28880			0.644400	−	0.764688i	$-0.277107\pi$
$907$	35204.4			1.28880			0.644400	+	0.764688i	$0.277107\pi$
$908$	−7588.01	−	6692.00i	−0.277332	−	0.244584i
$909$		−	751.393i		−	0.0274171i
$910$		0			0
$911$	−10512.0			−0.382303			−0.191152	−	0.981561i	$-0.561222\pi$
$911$	−10512.0			−0.382303			−0.191152	+	0.981561i	$0.561222\pi$
$912$	−12445.6	+	1568.00i	−0.451881	+	0.0569317i
$913$			8652.00i			0.313625i
$914$	2714.00	−	7180.57i	0.0982179	−	0.259860i
$915$		0			0
$916$	−27272.0	+	30923.5i	−0.983725	+	1.11544i
$917$	5376.17			0.193606
$918$	−1926.11	+	5096.00i	−0.0692495	+	0.183217i
$919$	46104.0			1.65488			0.827438	−	0.561557i	$-0.189798\pi$
$919$	46104.0			1.65488			0.827438	+	0.561557i	$0.189798\pi$
$920$		0			0
$921$	−13692.0			−0.489866
$922$	−8349.99	+	22092.0i	−0.298256	+	0.789112i
$923$	3809.88			0.135865
$924$	−4032.00	−	3555.89i	−0.143553	−	0.126602i
$925$		0			0
$926$	−2224.00	+	5884.15i	−0.0789257	+	0.208818i
$927$		−	1176.00i		−	0.0416666i
$928$	−27939.1	−	6720.00i	−0.988305	−	0.237710i
$929$	5726.00			0.202222			0.101111	−	0.994875i	$-0.467760\pi$
$929$	5726.00			0.202222			0.101111	+	0.994875i	$0.467760\pi$
$930$		0			0
$931$		−	10334.3i		−	0.363795i
$932$	−4434.28	+	5028.00i	−0.155847	+	0.176714i
$933$	14519.9			0.509496
$934$	−27230.0	−	10292.0i	−0.953954	−	0.360561i
$935$		0			0
$936$	560.000	+	1058.30i	0.0195557	+	0.0369569i
$937$			1274.00i			0.0444181i	0.999753	+	0.0222091i	$0.00706994\pi$
$937$			1274.00i			0.0444181i	−0.999753	+	0.0222091i	$0.992930\pi$
$938$	−1396.96	+	3696.00i	−0.0486271	+	0.128655i
$939$			12075.2i			0.419659i
$940$		0			0
$941$			26446.9i			0.916201i	0.888900	+	0.458101i	$0.151470\pi$
$941$			26446.9i			0.916201i	−0.888900	+	0.458101i	$0.848530\pi$
$942$	2518.76	+	952.000i	0.0871183	+	0.0329276i
$943$		−	10640.0i		−	0.367430i
$944$	−33936.0	+	4275.53i	−1.17005	+	0.147412i
$945$		0			0
$946$	6972.00	−	18446.2i	0.239619	−	0.633971i
$947$	23922.9			0.820897			0.410448	−	0.911884i	$-0.365372\pi$
$947$	23922.9			0.820897			0.410448	+	0.911884i	$0.365372\pi$
$948$	−14731.5	−	12992.0i	−0.504703	−	0.445106i
$949$		−	15557.0i		−	0.532141i
$950$		0			0
$951$	−50680.0			−1.72809
$952$	1185.30	+	2240.00i	0.0403526	+	0.0762593i
$953$		−	38250.0i		−	1.30015i	−0.759872	−	0.650073i	$-0.774738\pi$
$953$		−	38250.0i		−	1.30015i	0.759872	−	0.650073i	$-0.225262\pi$
$954$	84.0000	+	31.7490i	0.00285073	+	0.00107748i
$955$		0			0
$956$	−37728.0	−	33273.0i	−1.27637	−	1.12565i
$957$	−13334.6			−0.450414
$958$	46819.2	+	17696.0i	1.57898	+	0.596797i
$959$	−8496.00			−0.286079
$960$		0			0
$961$	20385.0			0.684267
$962$	34077.3	+	12880.0i	1.14210	+	0.431671i
$963$	−269.867			−0.00903046
$964$	−17556.0	−	15482.9i	−0.586557	−	0.517294i
$965$		0			0
$966$	17024.0	+	6434.47i	0.567017	+	0.214312i
$967$			4664.00i			0.155103i	0.996988	+	0.0775513i	$0.0247101\pi$
$967$			4664.00i			0.155103i	−0.996988	+	0.0775513i	$0.975290\pi$
$968$	−11419.1	−	21580.0i	−0.379156	−	0.716537i
$969$	2744.00			0.0909701
$970$		0			0
$971$		−	30971.2i		−	1.02360i	−0.859106	−	0.511798i	$-0.828980\pi$
$971$		−	30971.2i		−	1.02360i	0.859106	−	0.511798i	$-0.171020\pi$
$972$	1682.70	+	1484.00i	0.0555273	+	0.0489705i
$973$	21547.0			0.709933
$974$	1304.00	−	3450.06i	0.0428982	−	0.113498i
$975$		0			0
$976$	6048.00	−	761.976i	0.198352	−	0.0249900i
$977$		−	4814.00i		−	0.157639i	−0.996889	−	0.0788196i	$-0.974885\pi$
$977$		−	4814.00i		−	0.157639i	0.996889	−	0.0788196i	$-0.0251151\pi$
$978$	24817.1	+	9380.00i	0.811416	+	0.306686i
$979$		−	4222.62i		−	0.137850i
$980$		0			0
$981$		−	1894.36i		−	0.0616536i
$982$	−16662.9	+	44086.0i	−0.541483	+	1.43263i
$983$			12376.0i			0.401560i	0.979636	+	0.200780i	$0.0643476\pi$
$983$			12376.0i			0.401560i	−0.979636	+	0.200780i	$0.935652\pi$
$984$	−3920.00	−	7408.10i	−0.126997	−	0.240002i
$985$		0			0
$986$	5880.00	+	2222.43i	0.189916	+	0.0717816i
$987$	−14223.6			−0.458704
$988$	−10371.3	+	11760.0i	−0.333964	+	0.378680i
$989$			66757.6i			2.14638i
$990$		0			0
$991$	45344.0			1.45348			0.726740	−	0.686912i	$-0.241034\pi$
$991$	45344.0			1.45348			0.726740	+	0.686912i	$0.241034\pi$
$992$	9482.37	−	39424.0i	0.303494	−	1.26181i
$993$		−	22484.0i		−	0.718538i
$994$	576.000	−	1523.95i	0.0183799	−	0.0486286i
$995$		0			0
$996$	−17304.0	−	15260.7i	−0.550500	−	0.485496i
$997$	−26002.4			−0.825984			−0.412992	−	0.910735i	$-0.635516\pi$
$997$	−26002.4			−0.825984			−0.412992	+	0.910735i	$0.635516\pi$
$998$	3095.53	−	8190.00i	0.0981836	−	0.259769i
$999$	33488.0			1.06057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.a.149.1		4
4.3	odd	2		800.4.f.a.49.4		4
5.2	odd	4		200.4.d.a.101.1		2
5.3	odd	4		8.4.b.a.5.2	yes	2
5.4	even	2	inner	200.4.f.a.149.4		4
8.3	odd	2		800.4.f.a.49.2		4
8.5	even	2	inner	200.4.f.a.149.3		4
15.8	even	4		72.4.d.b.37.1		2
20.3	even	4		32.4.b.a.17.2		2
20.7	even	4		800.4.d.a.401.1		2
20.19	odd	2		800.4.f.a.49.1		4
40.3	even	4		32.4.b.a.17.1		2
40.13	odd	4		8.4.b.a.5.1	✓	2
40.19	odd	2		800.4.f.a.49.3		4
40.27	even	4		800.4.d.a.401.2		2
40.29	even	2	inner	200.4.f.a.149.2		4
40.37	odd	4		200.4.d.a.101.2		2
60.23	odd	4		288.4.d.a.145.1		2
80.3	even	4		256.4.a.j.1.1		2
80.13	odd	4		256.4.a.l.1.2		2
80.43	even	4		256.4.a.j.1.2		2
80.53	odd	4		256.4.a.l.1.1		2
120.53	even	4		72.4.d.b.37.2		2
120.83	odd	4		288.4.d.a.145.2		2
240.53	even	4		2304.4.a.bn.1.2		2
240.83	odd	4		2304.4.a.v.1.1		2
240.173	even	4		2304.4.a.bn.1.1		2
240.203	odd	4		2304.4.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.4.b.a.5.1	✓	2	40.13	odd	4
8.4.b.a.5.2	yes	2	5.3	odd	4
32.4.b.a.17.1		2	40.3	even	4
32.4.b.a.17.2		2	20.3	even	4
72.4.d.b.37.1		2	15.8	even	4
72.4.d.b.37.2		2	120.53	even	4
200.4.d.a.101.1		2	5.2	odd	4
200.4.d.a.101.2		2	40.37	odd	4
200.4.f.a.149.1		4	1.1	even	1	trivial
200.4.f.a.149.2		4	40.29	even	2	inner
200.4.f.a.149.3		4	8.5	even	2	inner
200.4.f.a.149.4		4	5.4	even	2	inner
256.4.a.j.1.1		2	80.3	even	4
256.4.a.j.1.2		2	80.43	even	4
256.4.a.l.1.1		2	80.53	odd	4
256.4.a.l.1.2		2	80.13	odd	4
288.4.d.a.145.1		2	60.23	odd	4
288.4.d.a.145.2		2	120.83	odd	4
800.4.d.a.401.1		2	20.7	even	4
800.4.d.a.401.2		2	40.27	even	4
800.4.f.a.49.1		4	20.19	odd	2
800.4.f.a.49.2		4	8.3	odd	2
800.4.f.a.49.3		4	40.19	odd	2
800.4.f.a.49.4		4	4.3	odd	2
2304.4.a.v.1.1		2	240.83	odd	4
2304.4.a.v.1.2		2	240.203	odd	4
2304.4.a.bn.1.1		2	240.173	even	4
2304.4.a.bn.1.2		2	240.53	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.64575 - 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 + 5.29150i) q^{4} +(14.0000 + 5.29150i) q^{6} -8.00000i q^{7} +(-10.5830 - 20.0000i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-2.64575 - 1.00000i) q^{2} -5.29150 q^{3} +(6.00000 + 5.29150i) q^{4} +(14.0000 + 5.29150i) q^{6} -8.00000i q^{7} +(-10.5830 - 20.0000i) q^{8} +1.00000 q^{9} +15.8745i q^{11} +(-31.7490 - 28.0000i) q^{12} -52.9150 q^{13} +(-8.00000 + 21.1660i) q^{14} +(8.00000 + 63.4980i) q^{16} -14.0000i q^{17} +(-2.64575 - 1.00000i) q^{18} -37.0405i q^{19} +42.3320i q^{21} +(15.8745 - 42.0000i) q^{22} +152.000i q^{23} +(56.0000 + 105.830i) q^{24} +(140.000 + 52.9150i) q^{26} +137.579 q^{27} +(42.3320 - 48.0000i) q^{28} -158.745i q^{29} +224.000 q^{31} +(42.3320 - 176.000i) q^{32} -84.0000i q^{33} +(-14.0000 + 37.0405i) q^{34} +(6.00000 + 5.29150i) q^{36} +243.409 q^{37} +(-37.0405 + 98.0000i) q^{38} +280.000 q^{39} -70.0000 q^{41} +(42.3320 - 112.000i) q^{42} +439.195 q^{43} +(-84.0000 + 95.2470i) q^{44} +(152.000 - 402.154i) q^{46} +336.000i q^{47} +(-42.3320 - 336.000i) q^{48} +279.000 q^{49} +74.0810i q^{51} +(-317.490 - 280.000i) q^{52} -31.7490 q^{53} +(-364.000 - 137.579i) q^{54} +(-160.000 + 84.6640i) q^{56} +196.000i q^{57} +(-158.745 + 420.000i) q^{58} +534.442i q^{59} -95.2470i q^{61} +(-592.648 - 224.000i) q^{62} -8.00000i q^{63} +(-288.000 + 423.320i) q^{64} +(-84.0000 + 222.243i) q^{66} +174.620 q^{67} +(74.0810 - 84.0000i) q^{68} -804.308i q^{69} -72.0000 q^{71} +(-10.5830 - 20.0000i) q^{72} +294.000i q^{73} +(-644.000 - 243.409i) q^{74} +(196.000 - 222.243i) q^{76} +126.996 q^{77} +(-740.810 - 280.000i) q^{78} +464.000 q^{79} -755.000 q^{81} +(185.203 + 70.0000i) q^{82} +545.025 q^{83} +(-224.000 + 253.992i) q^{84} +(-1162.00 - 439.195i) q^{86} +840.000i q^{87} +(317.490 - 168.000i) q^{88} -266.000 q^{89} +423.320i q^{91} +(-804.308 + 912.000i) q^{92} -1185.30 q^{93} +(336.000 - 888.972i) q^{94} +(-224.000 + 931.304i) q^{96} +994.000i q^{97} +(-738.165 - 279.000i) q^{98} +15.8745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 24 * q^4 + 56 * q^6 + 4 * q^9	\( 4 q + 24 q^{4} + 56 q^{6} + 4 q^{9} - 32 q^{14} + 32 q^{16} + 224 q^{24} + 560 q^{26} + 896 q^{31} - 56 q^{34} + 24 q^{36} + 1120 q^{39} - 280 q^{41} - 336 q^{44} + 608 q^{46} + 1116 q^{49} - 1456 q^{54} - 640 q^{56} - 1152 q^{64} - 336 q^{66} - 288 q^{71} - 2576 q^{74} + 784 q^{76} + 1856 q^{79} - 3020 q^{81} - 896 q^{84} - 4648 q^{86} - 1064 q^{89} + 1344 q^{94} - 896 q^{96}+O(q^{100}) \) 4 * q + 24 * q^4 + 56 * q^6 + 4 * q^9 - 32 * q^14 + 32 * q^16 + 224 * q^24 + 560 * q^26 + 896 * q^31 - 56 * q^34 + 24 * q^36 + 1120 * q^39 - 280 * q^41 - 336 * q^44 + 608 * q^46 + 1116 * q^49 - 1456 * q^54 - 640 * q^56 - 1152 * q^64 - 336 * q^66 - 288 * q^71 - 2576 * q^74 + 784 * q^76 + 1856 * q^79 - 3020 * q^81 - 896 * q^84 - 4648 * q^86 - 1064 * q^89 + 1344 * q^94 - 896 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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