LMFDB - Embedded newform 882.4.g.bk.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.667
Dual form			882.4.g.bk.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.70711 - 6.42090i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.70711 - 6.42090i) q^{5} -8.00000 q^{8} +(-7.41421 - 12.8418i) q^{10} +(5.24264 + 9.08052i) q^{11} +2.78680 q^{13} +(-8.00000 + 13.8564i) q^{16} +(25.2218 + 43.6855i) q^{17} +(-62.5269 + 108.300i) q^{19} -29.6569 q^{20} +20.9706 q^{22} +(-91.1249 + 157.833i) q^{23} +(35.0147 + 60.6473i) q^{25} +(2.78680 - 4.82687i) q^{26} -156.132 q^{29} +(-69.8162 - 120.925i) q^{31} +(16.0000 + 27.7128i) q^{32} +100.887 q^{34} +(197.279 - 341.698i) q^{37} +(125.054 + 216.600i) q^{38} +(-29.6569 + 51.3672i) q^{40} -197.605 q^{41} +343.294 q^{43} +(20.9706 - 36.3221i) q^{44} +(182.250 + 315.666i) q^{46} +(-305.002 + 528.279i) q^{47} +140.059 q^{50} +(-5.57359 - 9.65375i) q^{52} +(-68.7645 - 119.104i) q^{53} +77.7401 q^{55} +(-156.132 + 270.429i) q^{58} +(294.718 + 510.466i) q^{59} +(-123.609 + 214.097i) q^{61} -279.265 q^{62} +64.0000 q^{64} +(10.3310 - 17.8937i) q^{65} +(197.823 + 342.640i) q^{67} +(100.887 - 174.742i) q^{68} -285.661 q^{71} +(498.729 + 863.823i) q^{73} +(-394.558 - 683.395i) q^{74} +500.215 q^{76} +(424.132 - 734.618i) q^{79} +(59.3137 + 102.734i) q^{80} +(-197.605 + 342.262i) q^{82} +210.863 q^{83} +374.000 q^{85} +(343.294 - 594.602i) q^{86} +(-41.9411 - 72.6442i) q^{88} +(-276.744 + 479.334i) q^{89} +728.999 q^{92} +(610.004 + 1056.56i) q^{94} +(463.588 + 802.958i) q^{95} -903.910 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8} - 24 q^{10} + 4 q^{11} + 96 q^{13} - 32 q^{16} + 132 q^{17} - 120 q^{19} - 96 q^{20} + 16 q^{22} - 76 q^{23} + 174 q^{25} + 96 q^{26} + 224 q^{29} - 432 q^{31} + 64 q^{32} + 528 q^{34} + 280 q^{37} + 240 q^{38} - 96 q^{40} - 72 q^{41} - 256 q^{43} + 16 q^{44} + 152 q^{46} - 264 q^{47} + 696 q^{50} - 192 q^{52} + 268 q^{53} + 96 q^{55} + 224 q^{58} + 336 q^{59} + 504 q^{61} - 1728 q^{62} + 256 q^{64} + 228 q^{65} + 384 q^{67} + 528 q^{68} + 792 q^{71} + 312 q^{73} - 560 q^{74} + 960 q^{76} + 848 q^{79} + 192 q^{80} - 72 q^{82} + 1296 q^{83} + 1496 q^{85} - 256 q^{86} - 32 q^{88} - 612 q^{89} + 608 q^{92} + 528 q^{94} + 904 q^{95} - 4368 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8 - 24 * q^10 + 4 * q^11 + 96 * q^13 - 32 * q^16 + 132 * q^17 - 120 * q^19 - 96 * q^20 + 16 * q^22 - 76 * q^23 + 174 * q^25 + 96 * q^26 + 224 * q^29 - 432 * q^31 + 64 * q^32 + 528 * q^34 + 280 * q^37 + 240 * q^38 - 96 * q^40 - 72 * q^41 - 256 * q^43 + 16 * q^44 + 152 * q^46 - 264 * q^47 + 696 * q^50 - 192 * q^52 + 268 * q^53 + 96 * q^55 + 224 * q^58 + 336 * q^59 + 504 * q^61 - 1728 * q^62 + 256 * q^64 + 228 * q^65 + 384 * q^67 + 528 * q^68 + 792 * q^71 + 312 * q^73 - 560 * q^74 + 960 * q^76 + 848 * q^79 + 192 * q^80 - 72 * q^82 + 1296 * q^83 + 1496 * q^85 - 256 * q^86 - 32 * q^88 - 612 * q^89 + 608 * q^92 + 528 * q^94 + 904 * q^95 - 4368 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	3.70711	−	6.42090i	0.331574	−	0.574303i	−0.651247	−	0.758866i	$-0.725754\pi$
$5$	3.70711	−	6.42090i	0.331574	−	0.574303i	0.982821	+	0.184563i	$0.0590871\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−7.41421	−	12.8418i	−0.234458	−	0.406093i
$11$	5.24264	+	9.08052i	0.143701	+	0.248898i	0.928888	−	0.370361i	$-0.120766\pi$
$11$	5.24264	+	9.08052i	0.143701	+	0.248898i	−0.785186	+	0.619260i	$0.787433\pi$
$12$		0			0
$13$	2.78680			0.0594553			0.0297276	−	0.999558i	$-0.490536\pi$
$13$	2.78680			0.0594553			0.0297276	+	0.999558i	$0.490536\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	25.2218	+	43.6855i	0.359835	+	0.623252i	0.987933	−	0.154882i	$-0.0494997\pi$
$17$	25.2218	+	43.6855i	0.359835	+	0.623252i	−0.628098	+	0.778134i	$0.716166\pi$
$18$		0			0
$19$	−62.5269	+	108.300i	−0.754982	+	1.30767i	0.190401	+	0.981706i	$0.439021\pi$
$19$	−62.5269	+	108.300i	−0.754982	+	1.30767i	−0.945383	+	0.325961i	$0.894312\pi$
$20$	−29.6569			−0.331574
$21$		0			0
$22$	20.9706			0.203225
$23$	−91.1249	+	157.833i	−0.826124	+	1.43089i	0.0749331	+	0.997189i	$0.476126\pi$
$23$	−91.1249	+	157.833i	−0.826124	+	1.43089i	−0.901057	+	0.433700i	$0.857208\pi$
$24$		0			0
$25$	35.0147	+	60.6473i	0.280118	+	0.485178i
$26$	2.78680	−	4.82687i	0.0210206	−	0.0364088i
$27$		0			0
$28$		0			0
$29$	−156.132			−0.999758			−0.499879	−	0.866095i	$-0.666622\pi$
$29$	−156.132			−0.999758			−0.499879	+	0.866095i	$0.666622\pi$
$30$		0			0
$31$	−69.8162	−	120.925i	−0.404496	−	0.700607i	0.589767	−	0.807573i	$-0.299220\pi$
$31$	−69.8162	−	120.925i	−0.404496	−	0.700607i	−0.994263	+	0.106966i	$0.965886\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	100.887			0.508883
$35$		0			0
$36$		0			0
$37$	197.279	−	341.698i	0.876554	−	1.51824i	0.0214563	−	0.999770i	$-0.493170\pi$
$37$	197.279	−	341.698i	0.876554	−	1.51824i	0.855098	−	0.518467i	$-0.173497\pi$
$38$	125.054	+	216.600i	0.533853	+	0.924660i
$39$		0			0
$40$	−29.6569	+	51.3672i	−0.117229	+	0.203047i
$41$	−197.605			−0.752701			−0.376350	−	0.926477i	$-0.622821\pi$
$41$	−197.605			−0.752701			−0.376350	+	0.926477i	$0.622821\pi$
$42$		0			0
$43$	343.294			1.21748			0.608741	−	0.793369i	$-0.291675\pi$
$43$	343.294			1.21748			0.608741	+	0.793369i	$0.291675\pi$
$44$	20.9706	−	36.3221i	0.0718507	−	0.124449i
$45$		0			0
$46$	182.250	+	315.666i	0.584158	+	1.01179i
$47$	−305.002	+	528.279i	−0.946577	+	1.63952i	−0.194015	+	0.980999i	$0.562151\pi$
$47$	−305.002	+	528.279i	−0.946577	+	1.63952i	−0.752562	+	0.658521i	$0.771182\pi$
$48$		0			0
$49$		0			0
$50$	140.059			0.396146
$51$		0			0
$52$	−5.57359	−	9.65375i	−0.0148638	−	0.0257449i
$53$	−68.7645	−	119.104i	−0.178218	−	0.308682i	0.763053	−	0.646336i	$-0.223700\pi$
$53$	−68.7645	−	119.104i	−0.178218	−	0.308682i	−0.941270	+	0.337655i	$0.890366\pi$
$54$		0			0
$55$	77.7401			0.190590
$56$		0			0
$57$		0			0
$58$	−156.132	+	270.429i	−0.353468	+	0.612224i
$59$	294.718	+	510.466i	0.650322	+	1.12639i	0.983045	+	0.183366i	$0.0586993\pi$
$59$	294.718	+	510.466i	0.650322	+	1.12639i	−0.332723	+	0.943025i	$0.607967\pi$
$60$		0			0
$61$	−123.609	+	214.097i	−0.259450	+	0.449381i	−0.966095	−	0.258188i	$-0.916875\pi$
$61$	−123.609	+	214.097i	−0.259450	+	0.449381i	0.706644	+	0.707569i	$0.250208\pi$
$62$	−279.265			−0.572043
$63$		0			0
$64$	64.0000			0.125000
$65$	10.3310	−	17.8937i	0.0197138	−	0.0341453i
$66$		0			0
$67$	197.823	+	342.640i	0.360716	+	0.624778i	0.988079	−	0.153949i	$-0.0491990\pi$
$67$	197.823	+	342.640i	0.360716	+	0.624778i	−0.627363	+	0.778727i	$0.715866\pi$
$68$	100.887	−	174.742i	0.179917	−	0.311626i
$69$		0			0
$70$		0			0
$71$	−285.661			−0.477489			−0.238745	−	0.971082i	$-0.576736\pi$
$71$	−285.661			−0.477489			−0.238745	+	0.971082i	$0.576736\pi$
$72$		0			0
$73$	498.729	+	863.823i	0.799613	+	1.38497i	0.919868	+	0.392228i	$0.128295\pi$
$73$	498.729	+	863.823i	0.799613	+	1.38497i	−0.120255	+	0.992743i	$0.538371\pi$
$74$	−394.558	−	683.395i	−0.619817	−	1.07356i
$75$		0			0
$76$	500.215			0.754982
$77$		0			0
$78$		0			0
$79$	424.132	−	734.618i	0.604033	−	1.04622i	−0.388171	−	0.921587i	$-0.626893\pi$
$79$	424.132	−	734.618i	0.604033	−	1.04622i	0.992204	−	0.124628i	$-0.0397737\pi$
$80$	59.3137	+	102.734i	0.0828934	+	0.143576i
$81$		0			0
$82$	−197.605	+	342.262i	−0.266120	+	0.460933i
$83$	210.863			0.278858			0.139429	−	0.990232i	$-0.455473\pi$
$83$	210.863			0.278858			0.139429	+	0.990232i	$0.455473\pi$
$84$		0			0
$85$	374.000			0.477247
$86$	343.294	−	594.602i	0.430445	−	0.745553i
$87$		0			0
$88$	−41.9411	−	72.6442i	−0.0508061	−	0.0879988i
$89$	−276.744	+	479.334i	−0.329604	+	0.570891i	−0.982433	−	0.186614i	$-0.940249\pi$
$89$	−276.744	+	479.334i	−0.329604	+	0.570891i	0.652829	+	0.757505i	$0.273582\pi$
$90$		0			0
$91$		0			0
$92$	728.999			0.826124
$93$		0			0
$94$	610.004	+	1056.56i	0.669331	+	1.15932i
$95$	463.588	+	802.958i	0.500664	+	0.867176i
$96$		0			0
$97$	−903.910			−0.946166			−0.473083	−	0.881018i	$-0.656859\pi$
$97$	−903.910			−0.946166			−0.473083	+	0.881018i	$0.656859\pi$
$98$		0			0
$99$		0			0
$100$	140.059	−	242.589i	0.140059	−	0.242589i
$101$	−156.806	−	271.595i	−0.154482	−	0.267572i	0.778388	−	0.627784i	$-0.216038\pi$
$101$	−156.806	−	271.595i	−0.154482	−	0.267572i	−0.932870	+	0.360212i	$0.882704\pi$
$102$		0			0
$103$	−115.487	+	200.030i	−0.110479	+	0.191355i	−0.915963	−	0.401262i	$-0.868572\pi$
$103$	−115.487	+	200.030i	−0.110479	+	0.191355i	0.805485	+	0.592617i	$0.201905\pi$
$104$	−22.2944			−0.0210206
$105$		0			0
$106$	−275.058			−0.252038
$107$	62.7431	−	108.674i	0.0566879	−	0.0981863i	−0.836289	−	0.548289i	$-0.815279\pi$
$107$	62.7431	−	108.674i	0.0566879	−	0.0981863i	0.892977	+	0.450103i	$0.148613\pi$
$108$		0			0
$109$	−372.764	−	645.646i	−0.327562	−	0.567354i	0.654465	−	0.756092i	$-0.272894\pi$
$109$	−372.764	−	645.646i	−0.327562	−	0.567354i	−0.982028	+	0.188738i	$0.939560\pi$
$110$	77.7401	−	134.650i	0.0673839	−	0.116712i
$111$		0			0
$112$		0			0
$113$	1043.76			0.868929			0.434464	−	0.900689i	$-0.356938\pi$
$113$	1043.76			0.868929			0.434464	+	0.900689i	$0.356938\pi$
$114$		0			0
$115$	675.619	+	1170.21i	0.547842	+	0.948890i
$116$	312.264	+	540.857i	0.249940	+	0.432908i
$117$		0			0
$118$	1178.87			0.919694
$119$		0			0
$120$		0			0
$121$	610.529	−	1057.47i	0.458700	−	0.794491i
$122$	247.217	+	428.193i	0.183459	+	0.317760i
$123$		0			0
$124$	−279.265	+	483.701i	−0.202248	+	0.350304i
$125$	1445.99			1.03467
$126$		0			0
$127$	−2080.17			−1.45343			−0.726715	−	0.686939i	$-0.758954\pi$
$127$	−2080.17			−1.45343			−0.726715	+	0.686939i	$0.758954\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−20.6619	−	35.7875i	−0.0139398	−	0.0241444i
$131$	−634.764	+	1099.44i	−0.423355	+	0.733273i	−0.996265	−	0.0863453i	$-0.972481\pi$
$131$	−634.764	+	1099.44i	−0.423355	+	0.733273i	0.572910	+	0.819618i	$0.305814\pi$
$132$		0			0
$133$		0			0
$134$	791.294			0.510129
$135$		0			0
$136$	−201.775	−	349.484i	−0.127221	−	0.220353i
$137$	1536.59	+	2661.46i	0.958249	+	1.65974i	0.726752	+	0.686900i	$0.241029\pi$
$137$	1536.59	+	2661.46i	0.958249	+	1.65974i	0.231497	+	0.972836i	$0.425638\pi$
$138$		0			0
$139$	1013.60			0.618504			0.309252	−	0.950980i	$-0.399921\pi$
$139$	1013.60			0.618504			0.309252	+	0.950980i	$0.399921\pi$
$140$		0			0
$141$		0			0
$142$	−285.661	+	494.779i	−0.168818	+	0.292401i
$143$	14.6102	+	25.3056i	0.00854380	+	0.0147983i
$144$		0			0
$145$	−578.798	+	1002.51i	−0.331494	+	0.574164i
$146$	1994.91			1.13082
$147$		0			0
$148$	−1578.23			−0.876554
$149$	615.735	−	1066.48i	0.338544	−	0.586375i	−0.645615	−	0.763663i	$-0.723399\pi$
$149$	615.735	−	1066.48i	0.338544	−	0.586375i	0.984159	+	0.177288i	$0.0567324\pi$
$150$		0			0
$151$	1122.37	+	1944.00i	0.604881	+	1.04768i	0.992070	+	0.125684i	$0.0401125\pi$
$151$	1122.37	+	1944.00i	0.604881	+	1.04768i	−0.387190	+	0.922000i	$0.626554\pi$
$152$	500.215	−	866.398i	0.266926	−	0.462330i
$153$		0			0
$154$		0			0
$155$	−1035.26			−0.536481
$156$		0			0
$157$	1893.58	+	3279.77i	0.962573	+	1.66723i	0.715998	+	0.698102i	$0.245972\pi$
$157$	1893.58	+	3279.77i	0.962573	+	1.66723i	0.246575	+	0.969124i	$0.420695\pi$
$158$	−848.264	−	1469.24i	−0.427116	−	0.739786i
$159$		0			0
$160$	237.255			0.117229
$161$		0			0
$162$		0			0
$163$	1054.28	−	1826.07i	0.506611	−	0.877476i	−0.493360	−	0.869825i	$-0.664231\pi$
$163$	1054.28	−	1826.07i	0.506611	−	0.877476i	0.999971	−	0.00765060i	$-0.00243528\pi$
$164$	395.210	+	684.524i	0.188175	+	0.325929i
$165$		0			0
$166$	210.863	−	365.225i	0.0985912	−	0.170765i
$167$	−1502.41			−0.696170			−0.348085	−	0.937463i	$-0.613168\pi$
$167$	−1502.41			−0.696170			−0.348085	+	0.937463i	$0.613168\pi$
$168$		0			0
$169$	−2189.23			−0.996465
$170$	374.000	−	647.787i	0.168732	−	0.292253i
$171$		0			0
$172$	−686.587	−	1189.20i	−0.304371	−	0.527186i
$173$	235.628	−	408.120i	0.103552	−	0.179357i	−0.809594	−	0.586991i	$-0.800313\pi$
$173$	235.628	−	408.120i	0.103552	−	0.179357i	0.913146	+	0.407634i	$0.133646\pi$
$174$		0			0
$175$		0			0
$176$	−167.765			−0.0718507
$177$		0			0
$178$	553.487	+	958.668i	0.233065	+	0.403681i
$179$	666.244	+	1153.97i	0.278198	+	0.481852i	0.970937	−	0.239336i	$-0.0769296\pi$
$179$	666.244	+	1153.97i	0.278198	+	0.481852i	−0.692739	+	0.721188i	$0.743596\pi$
$180$		0			0
$181$	−997.727			−0.409726			−0.204863	−	0.978791i	$-0.565675\pi$
$181$	−997.727			−0.409726			−0.204863	+	0.978791i	$0.565675\pi$
$182$		0			0
$183$		0			0
$184$	728.999	−	1262.66i	0.292079	−	0.505896i
$185$	−1462.67	−	2533.42i	−0.581285	−	1.00681i
$186$		0			0
$187$	−264.458	+	458.055i	−0.103418	+	0.179124i
$188$	2440.02			0.946577
$189$		0			0
$190$	1854.35			0.708046
$191$	613.360	−	1062.37i	0.232362	−	0.402463i	−0.726141	−	0.687546i	$-0.758688\pi$
$191$	613.360	−	1062.37i	0.232362	−	0.402463i	0.958503	+	0.285083i	$0.0920212\pi$
$192$		0			0
$193$	1739.65	+	3013.16i	0.648821	+	1.12379i	0.983405	+	0.181425i	$0.0580709\pi$
$193$	1739.65	+	3013.16i	0.648821	+	1.12379i	−0.334584	+	0.942366i	$0.608596\pi$
$194$	−903.910	+	1565.62i	−0.334520	+	0.579406i
$195$		0			0
$196$		0			0
$197$	−3193.47			−1.15495			−0.577476	−	0.816408i	$-0.695962\pi$
$197$	−3193.47			−1.15495			−0.577476	+	0.816408i	$0.695962\pi$
$198$		0			0
$199$	−532.574	−	922.446i	−0.189715	−	0.328595i	0.755440	−	0.655217i	$-0.227423\pi$
$199$	−532.574	−	922.446i	−0.189715	−	0.328595i	−0.945155	+	0.326622i	$0.894090\pi$
$200$	−280.118	−	485.178i	−0.0990366	−	0.171536i
$201$		0			0
$202$	−627.222			−0.218471
$203$		0			0
$204$		0			0
$205$	−732.543	+	1268.80i	−0.249576	+	0.432278i
$206$	230.975	+	400.060i	0.0781203	+	0.135308i
$207$		0			0
$208$	−22.2944	+	38.6150i	−0.00743191	+	0.0128724i
$209$	−1311.22			−0.433968
$210$		0			0
$211$	2057.50			0.671298			0.335649	−	0.941987i	$-0.391044\pi$
$211$	2057.50			0.671298			0.335649	+	0.941987i	$0.391044\pi$
$212$	−275.058	+	476.414i	−0.0891088	+	0.154341i
$213$		0			0
$214$	−125.486	−	217.348i	−0.0400844	−	0.0694282i
$215$	1272.63	−	2204.25i	0.403685	−	0.699204i
$216$		0			0
$217$		0			0
$218$	−1491.05			−0.463243
$219$		0			0
$220$	−155.480	−	269.300i	−0.0476476	−	0.0825281i
$221$	70.2881	+	121.743i	0.0213941	+	0.0370556i
$222$		0			0
$223$	2028.27			0.609071			0.304536	−	0.952501i	$-0.401499\pi$
$223$	2028.27			0.609071			0.304536	+	0.952501i	$0.401499\pi$
$224$		0			0
$225$		0			0
$226$	1043.76	−	1807.85i	0.307213	−	0.532108i
$227$	1211.98	+	2099.21i	0.354369	+	0.613786i	0.987010	−	0.160660i	$-0.0513622\pi$
$227$	1211.98	+	2099.21i	0.354369	+	0.613786i	−0.632640	+	0.774446i	$0.718029\pi$
$228$		0			0
$229$	983.584	−	1703.62i	0.283830	−	0.491608i	−0.688495	−	0.725241i	$-0.741728\pi$
$229$	983.584	−	1703.62i	0.283830	−	0.491608i	0.972325	+	0.233633i	$0.0750615\pi$
$230$	2702.48			0.774766
$231$		0			0
$232$	1249.06			0.353468
$233$	2239.17	−	3878.35i	0.629582	−	1.09047i	−0.358053	−	0.933701i	$-0.616559\pi$
$233$	2239.17	−	3878.35i	0.629582	−	1.09047i	0.987636	−	0.156767i	$-0.0501073\pi$
$234$		0			0
$235$	2261.35	+	3916.77i	0.627720	+	1.08724i
$236$	1178.87	−	2041.86i	0.325161	−	0.563195i
$237$		0			0
$238$		0			0
$239$	−6116.92			−1.65553			−0.827763	−	0.561078i	$-0.810387\pi$
$239$	−6116.92			−1.65553			−0.827763	+	0.561078i	$0.810387\pi$
$240$		0			0
$241$	−3114.19	−	5393.94i	−0.832376	−	1.44172i	−0.896149	−	0.443754i	$-0.853647\pi$
$241$	−3114.19	−	5393.94i	−0.832376	−	1.44172i	0.0637726	−	0.997964i	$-0.479687\pi$
$242$	−1221.06	−	2114.94i	−0.324350	−	0.561790i
$243$		0			0
$244$	988.870			0.259450
$245$		0			0
$246$		0			0
$247$	−174.250	+	301.809i	−0.0448876	+	0.0777477i
$248$	558.530	+	967.402i	0.143011	+	0.247702i
$249$		0			0
$250$	1445.99	−	2504.53i	0.365810	−	0.633601i
$251$	−5904.42			−1.48479			−0.742397	−	0.669960i	$-0.766311\pi$
$251$	−5904.42			−1.48479			−0.742397	+	0.669960i	$0.766311\pi$
$252$		0			0
$253$	−1910.94			−0.474861
$254$	−2080.17	+	3602.97i	−0.513865	+	0.890041i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−204.112	+	353.532i	−0.0495414	+	0.0858082i	−0.889733	−	0.456482i	$-0.849109\pi$
$257$	−204.112	+	353.532i	−0.0495414	+	0.0858082i	0.840191	+	0.542290i	$0.182443\pi$
$258$		0			0
$259$		0			0
$260$	−82.6476			−0.0197138
$261$		0			0
$262$	1269.53	+	2198.89i	0.299357	+	0.518502i
$263$	−2313.00	−	4006.24i	−0.542304	−	0.939298i	−0.998771	−	0.0495577i	$-0.984219\pi$
$263$	−2313.00	−	4006.24i	−0.542304	−	0.939298i	0.456467	−	0.889740i	$-0.349115\pi$
$264$		0			0
$265$	−1019.67			−0.236369
$266$		0			0
$267$		0			0
$268$	791.294	−	1370.56i	0.180358	−	0.312389i
$269$	−435.646	−	754.562i	−0.0987429	−	0.171028i	0.812422	−	0.583070i	$-0.198149\pi$
$269$	−435.646	−	754.562i	−0.0987429	−	0.171028i	−0.911165	+	0.412043i	$0.864815\pi$
$270$		0			0
$271$	−3236.17	+	5605.22i	−0.725401	+	1.25643i	0.233408	+	0.972379i	$0.425012\pi$
$271$	−3236.17	+	5605.22i	−0.725401	+	1.25643i	−0.958809	+	0.284052i	$0.908321\pi$
$272$	−807.098			−0.179917
$273$		0			0
$274$	6146.38			1.35517
$275$	−367.139	+	635.904i	−0.0805066	+	0.139442i
$276$		0			0
$277$	−2355.94	−	4080.61i	−0.511028	−	0.885126i	−0.999918	−	0.0127811i	$-0.995932\pi$
$277$	−2355.94	−	4080.61i	−0.511028	−	0.885126i	0.488890	−	0.872345i	$-0.337402\pi$
$278$	1013.60	−	1755.60i	0.218674	−	0.378755i
$279$		0			0
$280$		0			0
$281$	7165.66			1.52124			0.760618	−	0.649200i	$-0.224896\pi$
$281$	7165.66			1.52124			0.760618	+	0.649200i	$0.224896\pi$
$282$		0			0
$283$	−3173.50	−	5496.67i	−0.666590	−	1.15457i	−0.978851	−	0.204572i	$-0.934420\pi$
$283$	−3173.50	−	5496.67i	−0.666590	−	1.15457i	0.312261	−	0.949996i	$-0.398914\pi$
$284$	571.322	+	989.559i	0.119372	+	0.206759i
$285$		0			0
$286$	58.4407			0.0120828
$287$		0			0
$288$		0			0
$289$	1184.22	−	2051.13i	0.241038	−	0.417490i
$290$	1157.60	+	2005.02i	0.234401	+	0.405995i
$291$		0			0
$292$	1994.91	−	3455.29i	0.399807	−	0.692485i
$293$	−9233.78			−1.84110			−0.920552	−	0.390621i	$-0.872260\pi$
$293$	−9233.78			−1.84110			−0.920552	+	0.390621i	$0.872260\pi$
$294$		0			0
$295$	4370.20			0.862519
$296$	−1578.23	+	2733.58i	−0.309909	+	0.536778i
$297$		0			0
$298$	−1231.47	−	2132.97i	−0.239386	−	0.414629i
$299$	−253.947	+	439.848i	−0.0491174	+	0.0850739i
$300$		0			0
$301$		0			0
$302$	4489.47			0.855430
$303$		0			0
$304$	−1000.43	−	1732.80i	−0.188745	−	0.326917i
$305$	916.461	+	1587.36i	0.172054	+	0.298006i
$306$		0			0
$307$	6786.53			1.26165			0.630827	−	0.775923i	$-0.282716\pi$
$307$	6786.53			1.26165			0.630827	+	0.775923i	$0.282716\pi$
$308$		0			0
$309$		0			0
$310$	−1035.26	+	1793.13i	−0.189675	+	0.328526i
$311$	2568.38	+	4448.57i	0.468295	+	0.811111i	0.999343	−	0.0362307i	$-0.0115351\pi$
$311$	2568.38	+	4448.57i	0.468295	+	0.811111i	−0.531048	+	0.847341i	$0.678202\pi$
$312$		0			0
$313$	1881.78	−	3259.34i	0.339822	−	0.588590i	−0.644577	−	0.764540i	$-0.722966\pi$
$313$	1881.78	−	3259.34i	0.339822	−	0.588590i	0.984399	+	0.175950i	$0.0562997\pi$
$314$	7574.31			1.36128
$315$		0			0
$316$	−3393.06			−0.604033
$317$	−517.473	+	896.289i	−0.0916851	+	0.158803i	−0.908220	−	0.418492i	$-0.862559\pi$
$317$	−517.473	+	896.289i	−0.0916851	+	0.158803i	0.816535	+	0.577296i	$0.195892\pi$
$318$		0			0
$319$	−818.544	−	1417.76i	−0.143667	−	0.248838i
$320$	237.255	−	410.937i	0.0414467	−	0.0717878i
$321$		0			0
$322$		0			0
$323$	−6308.17			−1.08668
$324$		0			0
$325$	97.5789	+	169.012i	0.0166545	+	0.0288464i
$326$	−2108.56	−	3652.13i	−0.358228	−	0.620469i
$327$		0			0
$328$	1580.84			0.266120
$329$		0			0
$330$		0			0
$331$	−4400.03	+	7621.08i	−0.730657	+	1.26554i	0.225945	+	0.974140i	$0.427453\pi$
$331$	−4400.03	+	7621.08i	−0.730657	+	1.26554i	−0.956603	+	0.291395i	$0.905880\pi$
$332$	−421.726	−	730.451i	−0.0697145	−	0.120749i
$333$		0			0
$334$	−1502.41	+	2602.26i	−0.246133	+	0.426315i
$335$	2933.41			0.478416
$336$		0			0
$337$	−5859.78			−0.947189			−0.473595	−	0.880743i	$-0.657044\pi$
$337$	−5859.78			−0.947189			−0.473595	+	0.880743i	$0.657044\pi$
$338$	−2189.23	+	3791.86i	−0.352304	+	0.610208i
$339$		0			0
$340$	−748.000	−	1295.57i	−0.119312	−	0.206654i
$341$	732.043	−	1267.94i	0.116253	−	0.201356i
$342$		0			0
$343$		0			0
$344$	−2746.35			−0.430445
$345$		0			0
$346$	−471.256	−	816.239i	−0.0732222	−	0.126825i
$347$	3969.27	+	6874.98i	0.614068	+	1.06360i	0.990547	+	0.137172i	$0.0438013\pi$
$347$	3969.27	+	6874.98i	0.614068	+	1.06360i	−0.376479	+	0.926425i	$0.622865\pi$
$348$		0			0
$349$	−9927.75			−1.52269			−0.761347	−	0.648344i	$-0.775462\pi$
$349$	−9927.75			−1.52269			−0.761347	+	0.648344i	$0.775462\pi$
$350$		0			0
$351$		0			0
$352$	−167.765	+	290.577i	−0.0254031	+	0.0439994i
$353$	−5051.52	−	8749.49i	−0.761658	−	1.31923i	−0.941996	−	0.335625i	$-0.891052\pi$
$353$	−5051.52	−	8749.49i	−0.761658	−	1.31923i	0.180338	−	0.983605i	$-0.442281\pi$
$354$		0			0
$355$	−1058.98	+	1834.20i	−0.158323	+	0.274223i
$356$	2213.95			0.329604
$357$		0			0
$358$	2664.97			0.393431
$359$	−2412.64	+	4178.81i	−0.354691	+	0.614343i	−0.987065	−	0.160320i	$-0.948747\pi$
$359$	−2412.64	+	4178.81i	−0.354691	+	0.614343i	0.632374	+	0.774663i	$0.282081\pi$
$360$		0			0
$361$	−4389.73	−	7603.23i	−0.639996	−	1.10850i
$362$	−997.727	+	1728.11i	−0.144860	+	0.250905i
$363$		0			0
$364$		0			0
$365$	7395.36			1.06052
$366$		0			0
$367$	−3467.65	−	6006.15i	−0.493215	−	0.854274i	0.506754	−	0.862091i	$-0.330845\pi$
$367$	−3467.65	−	6006.15i	−0.493215	−	0.854274i	−0.999969	+	0.00781688i	$0.997512\pi$
$368$	−1458.00	−	2525.33i	−0.206531	−	0.357722i
$369$		0			0
$370$	−5850.68			−0.822061
$371$		0			0
$372$		0			0
$373$	−7046.55	+	12205.0i	−0.978168	+	1.69424i	−0.309110	+	0.951026i	$0.600031\pi$
$373$	−7046.55	+	12205.0i	−0.978168	+	1.69424i	−0.669058	+	0.743210i	$0.733302\pi$
$374$	528.916	+	916.109i	0.0731272	+	0.126660i
$375$		0			0
$376$	2440.02	−	4226.23i	0.334666	−	0.579658i
$377$	−435.108			−0.0594409
$378$		0			0
$379$	5354.17			0.725661			0.362830	−	0.931855i	$-0.381810\pi$
$379$	5354.17			0.725661			0.362830	+	0.931855i	$0.381810\pi$
$380$	1854.35	−	3211.83i	0.250332	−	0.433588i
$381$		0			0
$382$	−1226.72	−	2124.74i	−0.164305	−	0.284585i
$383$	−4485.24	+	7768.66i	−0.598394	+	1.03645i	0.394664	+	0.918825i	$0.370861\pi$
$383$	−4485.24	+	7768.66i	−0.598394	+	1.03645i	−0.993058	+	0.117623i	$0.962472\pi$
$384$		0			0
$385$		0			0
$386$	6958.58			0.917571
$387$		0			0
$388$	1807.82	+	3131.23i	0.236542	+	0.409702i
$389$	−1851.29	−	3206.53i	−0.241296	−	0.417937i	0.719788	−	0.694194i	$-0.244239\pi$
$389$	−1851.29	−	3206.53i	−0.241296	−	0.417937i	−0.961084	+	0.276257i	$0.910906\pi$
$390$		0			0
$391$	−9193.34			−1.18907
$392$		0			0
$393$		0			0
$394$	−3193.47	+	5531.26i	−0.408337	+	0.707260i
$395$	−3144.61	−	5446.62i	−0.400563	−	0.693795i
$396$		0			0
$397$	1041.62	−	1804.13i	0.131681	−	0.228078i	−0.792644	−	0.609685i	$-0.791296\pi$
$397$	1041.62	−	1804.13i	0.131681	−	0.228078i	0.924325	+	0.381607i	$0.124629\pi$
$398$	−2130.30			−0.268297
$399$		0			0
$400$	−1120.47			−0.140059
$401$	−5317.01	+	9209.33i	−0.662141	+	1.14686i	0.317910	+	0.948121i	$0.397019\pi$
$401$	−5317.01	+	9209.33i	−0.662141	+	1.14686i	−0.980052	+	0.198742i	$0.936314\pi$
$402$		0			0
$403$	−194.564	−	336.994i	−0.0240494	−	0.0416548i
$404$	−627.222	+	1086.38i	−0.0772412	+	0.133786i
$405$		0			0
$406$		0			0
$407$	4137.06			0.503848
$408$		0			0
$409$	3258.18	+	5643.34i	0.393904	+	0.682262i	0.992961	−	0.118445i	$-0.0377908\pi$
$409$	3258.18	+	5643.34i	0.393904	+	0.682262i	−0.599056	+	0.800707i	$0.704458\pi$
$410$	1465.09	+	2537.60i	0.176477	+	0.305667i
$411$		0			0
$412$	923.899			0.110479
$413$		0			0
$414$		0			0
$415$	781.691	−	1353.93i	0.0924620	−	0.160149i
$416$	44.5887	+	77.2300i	0.00525515	+	0.00910219i
$417$		0			0
$418$	−1311.22	+	2271.11i	−0.153431	+	0.265750i
$419$	−6079.92			−0.708887			−0.354443	−	0.935077i	$-0.615330\pi$
$419$	−6079.92			−0.708887			−0.354443	+	0.935077i	$0.615330\pi$
$420$		0			0
$421$	−5631.58			−0.651939			−0.325969	−	0.945380i	$-0.605691\pi$
$421$	−5631.58			−0.651939			−0.325969	+	0.945380i	$0.605691\pi$
$422$	2057.50	−	3563.69i	0.237340	−	0.411084i
$423$		0			0
$424$	550.116	+	952.829i	0.0630094	+	0.109136i
$425$	−1766.27	+	3059.27i	−0.201592	+	0.349168i
$426$		0			0
$427$		0			0
$428$	−501.945			−0.0566879
$429$		0			0
$430$	−2545.25	−	4408.50i	−0.285449	−	0.494412i
$431$	−1868.45	−	3236.25i	−0.208817	−	0.361681i	0.742525	−	0.669818i	$-0.233628\pi$
$431$	−1868.45	−	3236.25i	−0.208817	−	0.361681i	−0.951342	+	0.308137i	$0.900295\pi$
$432$		0			0
$433$	−5757.46			−0.638998			−0.319499	−	0.947587i	$-0.603515\pi$
$433$	−5757.46			−0.638998			−0.319499	+	0.947587i	$0.603515\pi$
$434$		0			0
$435$		0			0
$436$	−1491.05	+	2582.58i	−0.163781	+	0.283677i
$437$	−11395.5	−	19737.6i	−1.24742	−	2.16059i
$438$		0			0
$439$	4906.38	−	8498.10i	0.533414	−	0.923900i	−0.465824	−	0.884877i	$-0.654242\pi$
$439$	4906.38	−	8498.10i	0.533414	−	0.923900i	0.999238	−	0.0390229i	$-0.0124245\pi$
$440$	−621.921			−0.0673839
$441$		0			0
$442$	281.152			0.0302558
$443$	2915.15	−	5049.19i	0.312648	−	0.541522i	−0.666287	−	0.745695i	$-0.732117\pi$
$443$	2915.15	−	5049.19i	0.312648	−	0.541522i	0.978935	+	0.204174i	$0.0654507\pi$
$444$		0			0
$445$	2051.84	+	3553.89i	0.218576	+	0.378585i
$446$	2028.27	−	3513.06i	0.215339	−	0.372978i
$447$		0			0
$448$		0			0
$449$	8674.94			0.911794			0.455897	−	0.890033i	$-0.349319\pi$
$449$	8674.94			0.911794			0.455897	+	0.890033i	$0.349319\pi$
$450$		0			0
$451$	−1035.97	−	1794.36i	−0.108164	−	0.187346i
$452$	−2087.53	−	3615.70i	−0.217232	−	0.376257i
$453$		0			0
$454$	4847.91			0.501154
$455$		0			0
$456$		0			0
$457$	−4553.41	+	7886.74i	−0.466082	+	0.807278i	−0.999250	−	0.0387315i	$-0.987668\pi$
$457$	−4553.41	+	7886.74i	−0.466082	+	0.807278i	0.533167	+	0.846010i	$0.321002\pi$
$458$	−1967.17	−	3407.24i	−0.200698	−	0.347619i
$459$		0			0
$460$	2702.48	−	4680.83i	0.273921	−	0.474445i
$461$	8729.69			0.881957			0.440979	−	0.897518i	$-0.354631\pi$
$461$	8729.69			0.881957			0.440979	+	0.897518i	$0.354631\pi$
$462$		0			0
$463$	−1795.62			−0.180237			−0.0901184	−	0.995931i	$-0.528725\pi$
$463$	−1795.62			−0.180237			−0.0901184	+	0.995931i	$0.528725\pi$
$464$	1249.06	−	2163.43i	0.124970	−	0.216454i
$465$		0			0
$466$	−4478.33	−	7756.70i	−0.445182	−	0.771078i
$467$	65.2797	−	113.068i	0.00646849	−	0.0112038i	−0.862773	−	0.505591i	$-0.831274\pi$
$467$	65.2797	−	113.068i	0.00646849	−	0.0112038i	0.869242	+	0.494388i	$0.164608\pi$
$468$		0			0
$469$		0			0
$470$	9045.40			0.887730
$471$		0			0
$472$	−2357.74	−	4083.73i	−0.229924	−	0.398239i
$473$	1799.76	+	3117.28i	0.174954	+	0.303029i
$474$		0			0
$475$	−8757.45			−0.845935
$476$		0			0
$477$		0			0
$478$	−6116.92	+	10594.8i	−0.585317	+	1.01380i
$479$	5922.90	+	10258.8i	0.564978	+	0.978570i	0.997052	+	0.0767319i	$0.0244485\pi$
$479$	5922.90	+	10258.8i	0.564978	+	0.978570i	−0.432074	+	0.901838i	$0.642218\pi$
$480$		0			0
$481$	549.777	−	952.242i	0.0521158	−	0.0902671i
$482$	−12456.8			−1.17716
$483$		0			0
$484$	−4884.24			−0.458700
$485$	−3350.89	+	5803.91i	−0.313724	+	0.543386i
$486$		0			0
$487$	2403.61	+	4163.17i	0.223650	+	0.387374i	0.955914	−	0.293648i	$-0.0948693\pi$
$487$	2403.61	+	4163.17i	0.223650	+	0.387374i	−0.732263	+	0.681022i	$0.761536\pi$
$488$	988.870	−	1712.77i	0.0917296	−	0.158880i
$489$		0			0
$490$		0			0
$491$	−6068.04			−0.557733			−0.278866	−	0.960330i	$-0.589959\pi$
$491$	−6068.04			−0.557733			−0.278866	+	0.960330i	$0.589959\pi$
$492$		0			0
$493$	−3937.93	−	6820.70i	−0.359748	−	0.623101i
$494$	348.500	+	603.619i	0.0317404	+	0.0549759i
$495$		0			0
$496$	2234.12			0.202248
$497$		0			0
$498$		0			0
$499$	7753.21	−	13429.0i	0.695554	−	1.20473i	−0.274440	−	0.961604i	$-0.588492\pi$
$499$	7753.21	−	13429.0i	0.695554	−	1.20473i	0.969994	−	0.243130i	$-0.0781742\pi$
$500$	−2891.98	−	5009.06i	−0.258667	−	0.448024i
$501$		0			0
$502$	−5904.42	+	10226.7i	−0.524954	+	0.909247i
$503$	1496.79			0.132681			0.0663405	−	0.997797i	$-0.478868\pi$
$503$	1496.79			0.132681			0.0663405	+	0.997797i	$0.478868\pi$
$504$		0			0
$505$	−2325.18			−0.204889
$506$	−1910.94	+	3309.85i	−0.167889	+	0.290792i
$507$		0			0
$508$	4160.35	+	7205.94i	0.363358	+	0.629354i
$509$	−2526.87	+	4376.66i	−0.220042	+	0.381124i	−0.954821	−	0.297183i	$-0.903953\pi$
$509$	−2526.87	+	4376.66i	−0.220042	+	0.381124i	0.734778	+	0.678307i	$0.237286\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	408.223	+	707.063i	0.0350310	+	0.0606755i
$515$	856.248	+	1483.07i	0.0732637	+	0.126896i
$516$		0			0
$517$	−6396.07			−0.544098
$518$		0			0
$519$		0			0
$520$	−82.6476	+	143.150i	−0.00696988	+	0.0120722i
$521$	4868.36	+	8432.25i	0.409380	+	0.709067i	0.994820	−	0.101649i	$-0.0324118\pi$
$521$	4868.36	+	8432.25i	0.409380	+	0.709067i	−0.585441	+	0.810715i	$0.699078\pi$
$522$		0			0
$523$	5898.34	−	10216.2i	0.493148	−	0.854157i	−0.506821	−	0.862051i	$-0.669180\pi$
$523$	5898.34	−	10216.2i	0.493148	−	0.854157i	0.999969	+	0.00789446i	$0.00251291\pi$
$524$	5078.11			0.423355
$525$		0			0
$526$	−9252.01			−0.766933
$527$	3521.79	−	6099.91i	0.291103	−	0.504206i
$528$		0			0
$529$	−10524.0	−	18228.1i	−0.864962	−	1.49816i
$530$	−1019.67	+	1766.12i	−0.0835691	+	0.144746i
$531$		0			0
$532$		0			0
$533$	−550.685			−0.0447520
$534$		0			0
$535$	−465.191	−	805.734i	−0.0375924	−	0.0651120i
$536$	−1582.59	−	2741.12i	−0.127532	−	0.220893i
$537$		0			0
$538$	−1742.59			−0.139644
$539$		0			0
$540$		0			0
$541$	2155.41	−	3733.28i	0.171291	−	0.296684i	−0.767581	−	0.640952i	$-0.778540\pi$
$541$	2155.41	−	3733.28i	0.171291	−	0.296684i	0.938871	+	0.344268i	$0.111873\pi$
$542$	6472.35	+	11210.4i	0.512936	+	0.888431i
$543$		0			0
$544$	−807.098	+	1397.94i	−0.0636104	+	0.110176i
$545$	−5527.50			−0.434444
$546$		0			0
$547$	17015.9			1.33007			0.665034	−	0.746813i	$-0.268417\pi$
$547$	17015.9			1.33007			0.665034	+	0.746813i	$0.268417\pi$
$548$	6146.38	−	10645.8i	0.479124	−	0.829868i
$549$		0			0
$550$	734.278	+	1271.81i	0.0569268	+	0.0986001i
$551$	9762.45	−	16909.1i	0.754799	−	1.30735i
$552$		0			0
$553$		0			0
$554$	−9423.76			−0.722703
$555$		0			0
$556$	−2027.19	−	3511.20i	−0.154626	−	0.267820i
$557$	870.588	+	1507.90i	0.0662262	+	0.114707i	0.897237	−	0.441549i	$-0.145571\pi$
$557$	870.588	+	1507.90i	0.0662262	+	0.114707i	−0.831011	+	0.556256i	$0.812237\pi$
$558$		0			0
$559$	956.689			0.0723858
$560$		0			0
$561$		0			0
$562$	7165.66	−	12411.3i	0.537838	−	0.931563i
$563$	5673.42	+	9826.66i	0.424700	+	0.735602i	0.996392	−	0.0848658i	$-0.0270461\pi$
$563$	5673.42	+	9826.66i	0.424700	+	0.735602i	−0.571692	+	0.820468i	$0.693713\pi$
$564$		0			0
$565$	3869.34	−	6701.89i	0.288114	−	0.499028i
$566$	−12694.0			−0.942701
$567$		0			0
$568$	2285.29			0.168818
$569$	−9208.72	+	15950.0i	−0.678470	+	1.17514i	0.296972	+	0.954886i	$0.404023\pi$
$569$	−9208.72	+	15950.0i	−0.678470	+	1.17514i	−0.975442	+	0.220258i	$0.929310\pi$
$570$		0			0
$571$	−4999.25	−	8658.95i	−0.366396	−	0.634616i	0.622603	−	0.782538i	$-0.286075\pi$
$571$	−4999.25	−	8658.95i	−0.366396	−	0.634616i	−0.988999	+	0.147922i	$0.952742\pi$
$572$	58.4407	−	101.222i	0.00427190	−	0.00739915i
$573$		0			0
$574$		0			0
$575$	−12762.8			−0.925648
$576$		0			0
$577$	700.855	+	1213.92i	0.0505667	+	0.0875840i	0.890201	−	0.455568i	$-0.150564\pi$
$577$	700.855	+	1213.92i	0.0505667	+	0.0875840i	−0.839634	+	0.543152i	$0.817231\pi$
$578$	−2368.44	−	4102.26i	−0.170440	−	0.295210i
$579$		0			0
$580$	4630.38			0.331494
$581$		0			0
$582$		0			0
$583$	721.015	−	1248.83i	0.0512202	−	0.0887160i
$584$	−3989.83	−	6910.59i	−0.282706	−	0.489661i
$585$		0			0
$586$	−9233.78	+	15993.4i	−0.650928	+	1.12744i
$587$	10851.3			0.763001			0.381500	−	0.924369i	$-0.375407\pi$
$587$	10851.3			0.763001			0.381500	+	0.924369i	$0.375407\pi$
$588$		0			0
$589$	17461.6			1.22155
$590$	4370.20	−	7569.41i	0.304946	−	0.528183i
$591$		0			0
$592$	3156.47	+	5467.16i	0.219139	+	0.379559i
$593$	10231.0	−	17720.6i	0.708493	−	1.22715i	−0.256923	−	0.966432i	$-0.582709\pi$
$593$	10231.0	−	17720.6i	0.708493	−	1.22715i	0.965416	−	0.260715i	$-0.0839581\pi$
$594$		0			0
$595$		0			0
$596$	−4925.88			−0.338544
$597$		0			0
$598$	507.893	+	879.697i	0.0347313	+	0.0601563i
$599$	4995.21	+	8651.96i	0.340733	+	0.590166i	0.984569	−	0.174997i	$-0.0559916\pi$
$599$	4995.21	+	8651.96i	0.340733	+	0.590166i	−0.643836	+	0.765163i	$0.722658\pi$
$600$		0			0
$601$	17435.9			1.18341			0.591703	−	0.806156i	$-0.298456\pi$
$601$	17435.9			1.18341			0.591703	+	0.806156i	$0.298456\pi$
$602$		0			0
$603$		0			0
$604$	4489.47	−	7775.99i	0.302440	−	0.523842i
$605$	−4526.60	−	7840.29i	−0.304186	−	0.526865i
$606$		0			0
$607$	−8350.16	+	14462.9i	−0.558356	+	0.967102i	0.439277	+	0.898351i	$0.355234\pi$
$607$	−8350.16	+	14462.9i	−0.558356	+	0.967102i	−0.997634	+	0.0687503i	$0.978099\pi$
$608$	−4001.72			−0.266926
$609$		0			0
$610$	3665.85			0.243321
$611$	−849.979	+	1472.21i	−0.0562790	+	0.0974781i
$612$		0			0
$613$	13351.5	+	23125.4i	0.879707	+	1.52370i	0.851662	+	0.524091i	$0.175595\pi$
$613$	13351.5	+	23125.4i	0.879707	+	1.52370i	0.0280452	+	0.999607i	$0.491072\pi$
$614$	6786.53	−	11754.6i	0.446062	−	0.772602i
$615$		0			0
$616$		0			0
$617$	−27790.4			−1.81329			−0.906645	−	0.421894i	$-0.861365\pi$
$617$	−27790.4			−1.81329			−0.906645	+	0.421894i	$0.861365\pi$
$618$		0			0
$619$	−868.040	−	1503.49i	−0.0563642	−	0.0976257i	0.836467	−	0.548018i	$-0.184617\pi$
$619$	−868.040	−	1503.49i	−0.0563642	−	0.0976257i	−0.892831	+	0.450392i	$0.851284\pi$
$620$	2070.53	+	3586.26i	0.134120	+	0.232303i
$621$		0			0
$622$	10273.5			0.662269
$623$		0			0
$624$		0			0
$625$	983.599	−	1703.64i	0.0629503	−	0.109033i
$626$	−3763.56	−	6518.67i	−0.240291	−	0.416196i
$627$		0			0
$628$	7574.31	−	13119.1i	0.481287	−	0.833613i
$629$	19903.0			1.26166
$630$		0			0
$631$	−8990.27			−0.567190			−0.283595	−	0.958944i	$-0.591527\pi$
$631$	−8990.27			−0.567190			−0.283595	+	0.958944i	$0.591527\pi$
$632$	−3393.06	+	5876.95i	−0.213558	+	0.369893i
$633$		0			0
$634$	1034.95	+	1792.58i	0.0648311	+	0.112291i
$635$	−7711.43	+	13356.6i	−0.481919	+	0.834709i
$636$		0			0
$637$		0			0
$638$	−3274.18			−0.203175
$639$		0			0
$640$	−474.510	−	821.875i	−0.0293073	−	0.0507617i
$641$	−6884.81	−	11924.8i	−0.424233	−	0.734794i	0.572115	−	0.820173i	$-0.306123\pi$
$641$	−6884.81	−	11924.8i	−0.424233	−	0.734794i	−0.996348	+	0.0853796i	$0.972790\pi$
$642$		0			0
$643$	26969.9			1.65411			0.827053	−	0.562124i	$-0.190015\pi$
$643$	26969.9			1.65411			0.827053	+	0.562124i	$0.190015\pi$
$644$		0			0
$645$		0			0
$646$	−6308.17	+	10926.1i	−0.384198	+	0.665450i
$647$	12200.9	+	21132.5i	0.741368	+	1.28409i	0.951872	+	0.306495i	$0.0991562\pi$
$647$	12200.9	+	21132.5i	0.741368	+	1.28409i	−0.210504	+	0.977593i	$0.567510\pi$
$648$		0			0
$649$	−3090.20	+	5352.38i	−0.186904	+	0.323728i
$650$	390.316			0.0235530
$651$		0			0
$652$	−8434.24			−0.506611
$653$	7984.79	−	13830.1i	0.478513	−	0.828809i	−0.521183	−	0.853445i	$-0.674509\pi$
$653$	7984.79	−	13830.1i	0.478513	−	0.828809i	0.999696	+	0.0246357i	$0.00784257\pi$
$654$		0			0
$655$	4706.27	+	8151.50i	0.280747	+	0.486268i
$656$	1580.84	−	2738.10i	0.0940876	−	0.162965i
$657$		0			0
$658$		0			0
$659$	11596.2			0.685467			0.342733	−	0.939433i	$-0.388647\pi$
$659$	11596.2			0.685467			0.342733	+	0.939433i	$0.388647\pi$
$660$		0			0
$661$	−6301.11	−	10913.8i	−0.370779	−	0.642208i	0.618907	−	0.785464i	$-0.287576\pi$
$661$	−6301.11	−	10913.8i	−0.370779	−	0.642208i	−0.989686	+	0.143257i	$0.954243\pi$
$662$	8800.06	+	15242.2i	0.516653	+	0.894869i
$663$		0			0
$664$	−1686.90			−0.0985912
$665$		0			0
$666$		0			0
$667$	14227.5	−	24642.8i	0.825924	−	1.43054i
$668$	3004.83	+	5204.52i	0.174042	+	0.301450i
$669$		0			0
$670$	2933.41	−	5080.81i	0.169146	−	0.292969i
$671$	−2592.14			−0.149134
$672$		0			0
$673$	2126.29			0.121787			0.0608934	−	0.998144i	$-0.480605\pi$
$673$	2126.29			0.121787			0.0608934	+	0.998144i	$0.480605\pi$
$674$	−5859.78	+	10149.4i	−0.334882	+	0.580032i
$675$		0			0
$676$	4378.47	+	7583.73i	0.249116	+	0.431482i
$677$	1309.69	−	2268.45i	0.0743508	−	0.128779i	−0.826453	−	0.563006i	$-0.809645\pi$
$677$	1309.69	−	2268.45i	0.0743508	−	0.128779i	0.900804	+	0.434226i	$0.142978\pi$
$678$		0			0
$679$		0			0
$680$	−2992.00			−0.168732
$681$		0			0
$682$	−1464.09	−	2535.87i	−0.0822034	−	0.142381i
$683$	−14964.9	−	25919.9i	−0.838383	−	1.45212i	−0.891246	−	0.453520i	$-0.850168\pi$
$683$	−14964.9	−	25919.9i	−0.838383	−	1.45212i	0.0528633	−	0.998602i	$-0.483165\pi$
$684$		0			0
$685$	22785.3			1.27092
$686$		0			0
$687$		0			0
$688$	−2746.35	+	4756.81i	−0.152185	+	0.263593i
$689$	−191.633	−	331.918i	−0.0105960	−	0.0183528i
$690$		0			0
$691$	−3380.45	+	5855.11i	−0.186105	+	0.322343i	−0.943948	−	0.330094i	$-0.892920\pi$
$691$	−3380.45	+	5855.11i	−0.186105	+	0.322343i	0.757844	+	0.652436i	$0.226253\pi$
$692$	−1885.02			−0.103552
$693$		0			0
$694$	15877.1			0.868423
$695$	3757.51	−	6508.20i	0.205080	−	0.355209i
$696$		0			0
$697$	−4983.96	−	8632.48i	−0.270848	−	0.469122i
$698$	−9927.75	+	17195.4i	−0.538354	+	0.932456i
$699$		0			0
$700$		0			0
$701$	−467.205			−0.0251727			−0.0125864	−	0.999921i	$-0.504006\pi$
$701$	−467.205			−0.0251727			−0.0125864	+	0.999921i	$0.504006\pi$
$702$		0			0
$703$	24670.5	+	42730.6i	1.32357	+	2.29248i
$704$	335.529	+	581.153i	0.0179627	+	0.0311123i
$705$		0			0
$706$	−20206.1			−1.07715
$707$		0			0
$708$		0			0
$709$	−4412.32	+	7642.36i	−0.233721	+	0.404816i	−0.958900	−	0.283744i	$-0.908424\pi$
$709$	−4412.32	+	7642.36i	−0.233721	+	0.404816i	0.725179	+	0.688560i	$0.241757\pi$
$710$	2117.95	+	3668.40i	0.111951	+	0.193905i
$711$		0			0
$712$	2213.95	−	3834.67i	0.116533	−	0.201841i
$713$	25448.0			1.33665
$714$		0			0
$715$	216.646			0.0113316
$716$	2664.97	−	4615.87i	0.139099	−	0.240926i
$717$		0			0
$718$	4825.27	+	8357.62i	0.250804	+	0.434406i
$719$	−10549.4	+	18272.2i	−0.547188	+	0.947757i	0.451278	+	0.892383i	$0.350968\pi$
$719$	−10549.4	+	18272.2i	−0.547188	+	0.947757i	−0.998466	+	0.0553733i	$0.982365\pi$
$720$		0			0
$721$		0			0
$722$	−17558.9			−0.905090
$723$		0			0
$724$	1995.45	+	3456.23i	0.102432	+	0.177417i
$725$	−5466.92	−	9468.98i	−0.280050	−	0.485061i
$726$		0			0
$727$	−4616.48			−0.235510			−0.117755	−	0.993043i	$-0.537570\pi$
$727$	−4616.48			−0.235510			−0.117755	+	0.993043i	$0.537570\pi$
$728$		0			0
$729$		0			0
$730$	7395.36	−	12809.1i	0.374951	−	0.649435i
$731$	8658.49	+	14996.9i	0.438093	+	0.758799i
$732$		0			0
$733$	5344.03	−	9256.13i	0.269285	−	0.466416i	−0.699392	−	0.714738i	$-0.746546\pi$
$733$	5344.03	−	9256.13i	0.269285	−	0.466416i	0.968678	+	0.248322i	$0.0798791\pi$
$734$	−13870.6			−0.697511
$735$		0			0
$736$	−5831.99			−0.292079
$737$	−2074.23	+	3592.68i	−0.103671	+	0.179563i
$738$		0			0
$739$	7683.78	+	13308.7i	0.382480	+	0.662474i	0.991416	−	0.130745i	$-0.0417369\pi$
$739$	7683.78	+	13308.7i	0.382480	+	0.662474i	−0.608936	+	0.793219i	$0.708404\pi$
$740$	−5850.68	+	10133.7i	−0.290642	+	0.503407i
$741$		0			0
$742$		0			0
$743$	−6502.58			−0.321072			−0.160536	−	0.987030i	$-0.551322\pi$
$743$	−6502.58			−0.321072			−0.160536	+	0.987030i	$0.551322\pi$
$744$		0			0
$745$	−4565.19	−	7907.14i	−0.224504	−	0.388853i
$746$	14093.1	+	24410.0i	0.691669	+	1.19801i
$747$		0			0
$748$	2115.66			0.103418
$749$		0			0
$750$		0			0
$751$	9937.07	−	17211.5i	0.482835	−	0.836295i	−0.516971	−	0.856003i	$-0.672940\pi$
$751$	9937.07	−	17211.5i	0.482835	−	0.836295i	0.999806	+	0.0197085i	$0.00627380\pi$
$752$	−4880.03	−	8452.47i	−0.236644	−	0.409880i
$753$		0			0
$754$	−435.108	+	753.630i	−0.0210155	+	0.0364000i
$755$	16642.9			0.802250
$756$		0			0
$757$	−15157.8			−0.727765			−0.363883	−	0.931445i	$-0.618549\pi$
$757$	−15157.8			−0.727765			−0.363883	+	0.931445i	$0.618549\pi$
$758$	5354.17	−	9273.70i	0.256560	−	0.444375i
$759$		0			0
$760$	−3708.70	−	6423.66i	−0.177012	−	0.306593i
$761$	17609.9	−	30501.3i	0.838842	−	1.45292i	−0.0520212	−	0.998646i	$-0.516566\pi$
$761$	17609.9	−	30501.3i	0.838842	−	1.45292i	0.890863	−	0.454271i	$-0.150100\pi$
$762$		0			0
$763$		0			0
$764$	−4906.88			−0.232362
$765$		0			0
$766$	8970.47	+	15537.3i	0.423128	+	0.732880i
$767$	821.319	+	1422.57i	0.0386651	+	0.0669698i
$768$		0			0
$769$	−2264.35			−0.106183			−0.0530915	−	0.998590i	$-0.516907\pi$
$769$	−2264.35			−0.106183			−0.0530915	+	0.998590i	$0.516907\pi$
$770$		0			0
$771$		0			0
$772$	6958.58	−	12052.6i	0.324410	−	0.561895i
$773$	−4766.39	−	8255.64i	−0.221779	−	0.384133i	0.733569	−	0.679615i	$-0.237853\pi$
$773$	−4766.39	−	8255.64i	−0.221779	−	0.384133i	−0.955348	+	0.295482i	$0.904520\pi$
$774$		0			0
$775$	4889.19	−	8468.33i	0.226613	−	0.392505i
$776$	7231.28			0.334520
$777$		0			0
$778$	−7405.16			−0.341244
$779$	12355.6	−	21400.6i	0.568276	−	0.984282i
$780$		0			0
$781$	−1497.62	−	2593.95i	−0.0686159	−	0.118846i
$782$	−9193.34	+	15923.3i	−0.420401	+	0.728155i
$783$		0			0
$784$		0			0
$785$	28078.8			1.27666
$786$		0			0
$787$	16606.5	+	28763.3i	0.752170	+	1.30280i	0.946769	+	0.321913i	$0.104326\pi$
$787$	16606.5	+	28763.3i	0.752170	+	1.30280i	−0.194599	+	0.980883i	$0.562341\pi$
$788$	6386.94	+	11062.5i	0.288738	+	0.500109i
$789$		0			0
$790$	−12578.4			−0.566481
$791$		0			0
$792$		0			0
$793$	−344.472	+	596.643i	−0.0154257	+	0.0267181i
$794$	−2083.24	−	3608.27i	−0.0931124	−	0.161275i
$795$		0			0
$796$	−2130.30	+	3689.78i	−0.0948573	+	0.164298i
$797$	−42065.6			−1.86956			−0.934781	−	0.355223i	$-0.884405\pi$
$797$	−42065.6			−1.86956			−0.934781	+	0.355223i	$0.884405\pi$
$798$		0			0
$799$	−30770.8			−1.36245
$800$	−1120.47	+	1940.71i	−0.0495183	+	0.0857682i
$801$		0			0
$802$	10634.0	+	18418.7i	0.468205	+	0.810954i
$803$	−5229.31	+	9057.43i	−0.229811	+	0.398044i
$804$		0			0
$805$		0			0
$806$	−778.255			−0.0340110
$807$		0			0
$808$	1254.44	+	2172.76i	0.0546178	+	0.0946008i
$809$	−388.780	−	673.387i	−0.0168959	−	0.0292646i	0.857454	−	0.514561i	$-0.172045\pi$
$809$	−388.780	−	673.387i	−0.0168959	−	0.0292646i	−0.874350	+	0.485296i	$0.838712\pi$
$810$		0			0
$811$	16559.4			0.716991			0.358496	−	0.933531i	$-0.383290\pi$
$811$	16559.4			0.716991			0.358496	+	0.933531i	$0.383290\pi$
$812$		0			0
$813$		0			0
$814$	4137.06	−	7165.59i	0.178137	−	0.308543i
$815$	−7816.66	−	13538.8i	−0.335958	−	0.581896i
$816$		0			0
$817$	−21465.1	+	37178.6i	−0.919178	+	1.59206i
$818$	13032.7			0.557065
$819$		0			0
$820$	5860.35			0.249576
$821$	115.612	−	200.246i	0.00491460	−	0.00851235i	−0.863558	−	0.504250i	$-0.831769\pi$
$821$	115.612	−	200.246i	0.00491460	−	0.00851235i	0.868472	+	0.495738i	$0.165102\pi$
$822$		0			0
$823$	2611.43	+	4523.13i	0.110606	+	0.191575i	0.916015	−	0.401145i	$-0.131388\pi$
$823$	2611.43	+	4523.13i	0.110606	+	0.191575i	−0.805409	+	0.592720i	$0.798054\pi$
$824$	923.899	−	1600.24i	0.0390601	−	0.0676541i
$825$		0			0
$826$		0			0
$827$	46225.5			1.94367			0.971836	−	0.235658i	$-0.0757246\pi$
$827$	46225.5			1.94367			0.971836	+	0.235658i	$0.0757246\pi$
$828$		0			0
$829$	19797.1	+	34289.6i	0.829410	+	1.43658i	0.898502	+	0.438970i	$0.144657\pi$
$829$	19797.1	+	34289.6i	0.829410	+	1.43658i	−0.0690913	+	0.997610i	$0.522010\pi$
$830$	−1563.38	−	2707.86i	−0.0653805	−	0.113242i
$831$		0			0
$832$	178.355			0.00743191
$833$		0			0
$834$		0			0
$835$	−5569.61	+	9646.85i	−0.230832	+	0.399812i
$836$	2622.45	+	4542.22i	0.108492	+	0.187914i
$837$		0			0
$838$	−6079.92	+	10530.7i	−0.250629	+	0.434103i
$839$	45737.6			1.88205			0.941023	−	0.338344i	$-0.109867\pi$
$839$	45737.6			1.88205			0.941023	+	0.338344i	$0.109867\pi$
$840$		0			0
$841$	−11.7878			−0.000483326
$842$	−5631.58	+	9754.18i	−0.230495	+	0.399229i
$843$		0			0
$844$	−4114.99	−	7127.37i	−0.167824	−	0.290680i
$845$	−8115.72	+	14056.8i	−0.330402	+	0.572272i
$846$		0			0
$847$		0			0
$848$	2200.46			0.0891088
$849$		0			0
$850$	3532.54	+	6118.54i	0.142547	+	0.246899i
$851$	35954.1	+	62274.3i	1.44828	+	2.50850i
$852$		0			0
$853$	−8795.55			−0.353053			−0.176526	−	0.984296i	$-0.556486\pi$
$853$	−8795.55			−0.353053			−0.176526	+	0.984296i	$0.556486\pi$
$854$		0			0
$855$		0			0
$856$	−501.945	+	869.394i	−0.0200422	+	0.0347141i
$857$	15127.5	+	26201.6i	0.602969	+	1.04437i	0.992369	+	0.123305i	$0.0393492\pi$
$857$	15127.5	+	26201.6i	0.602969	+	1.04437i	−0.389400	+	0.921069i	$0.627317\pi$
$858$		0			0
$859$	−22496.7	+	38965.5i	−0.893573	+	1.54771i	−0.0580118	+	0.998316i	$0.518476\pi$
$859$	−22496.7	+	38965.5i	−0.893573	+	1.54771i	−0.835561	+	0.549398i	$0.814857\pi$
$860$	−10181.0			−0.403685
$861$		0			0
$862$	−7473.79			−0.295311
$863$	22333.9	−	38683.5i	0.880946	−	1.52584i	0.0306555	−	0.999530i	$-0.490241\pi$
$863$	22333.9	−	38683.5i	0.880946	−	1.52584i	0.850291	−	0.526313i	$-0.176426\pi$
$864$		0			0
$865$	−1747.00	−	3025.89i	−0.0686701	−	0.118940i
$866$	−5757.46	+	9972.22i	−0.225920	+	0.391305i
$867$		0			0
$868$		0			0
$869$	8894.29			0.347201
$870$		0			0
$871$	551.294	+	954.868i	0.0214465	+	0.0371464i
$872$	2982.11	+	5165.16i	0.115811	+	0.200590i
$873$		0			0
$874$	−45582.1			−1.76411
$875$		0			0
$876$		0			0
$877$	−2993.42	+	5184.76i	−0.115257	+	0.199631i	−0.917883	−	0.396852i	$-0.870103\pi$
$877$	−2993.42	+	5184.76i	−0.115257	+	0.199631i	0.802625	+	0.596484i	$0.203436\pi$
$878$	−9812.76	−	16996.2i	−0.377181	−	0.653296i
$879$		0			0
$880$	−621.921	+	1077.20i	−0.0238238	+	0.0412640i
$881$	−37911.8			−1.44981			−0.724904	−	0.688850i	$-0.758116\pi$
$881$	−37911.8			−1.44981			−0.724904	+	0.688850i	$0.758116\pi$
$882$		0			0
$883$	−16293.6			−0.620978			−0.310489	−	0.950577i	$-0.600493\pi$
$883$	−16293.6			−0.620978			−0.310489	+	0.950577i	$0.600493\pi$
$884$	281.152	−	486.970i	0.0106970	−	0.0185278i
$885$		0			0
$886$	−5830.30	−	10098.4i	−0.221075	−	0.382914i
$887$	4426.71	−	7667.28i	0.167570	−	0.290239i	−0.769995	−	0.638050i	$-0.779741\pi$
$887$	4426.71	−	7667.28i	0.167570	−	0.290239i	0.937565	+	0.347811i	$0.113075\pi$
$888$		0			0
$889$		0			0
$890$	8207.35			0.309113
$891$		0			0
$892$	−4056.54	−	7026.12i	−0.152268	−	0.263735i
$893$	−38141.7	−	66063.3i	−1.42930	−	2.47562i
$894$		0			0
$895$	9879.34			0.368972
$896$		0			0
$897$		0			0
$898$	8674.94	−	15025.4i	0.322368	−	0.558358i
$899$	10900.6	+	18880.3i	0.404398	+	0.700438i
$900$		0			0
$901$	3468.73	−	6008.02i	0.128258	−	0.222149i
$902$	−4143.89			−0.152967
$903$		0			0
$904$	−8350.10			−0.307213
$905$	−3698.68	+	6406.30i	−0.135854	+	0.235307i
$906$		0			0
$907$	−8331.23	−	14430.1i	−0.304999	−	0.528274i	0.672262	−	0.740313i	$-0.265323\pi$
$907$	−8331.23	−	14430.1i	−0.304999	−	0.528274i	−0.977261	+	0.212039i	$0.931989\pi$
$908$	4847.91	−	8396.83i	0.177185	−	0.306893i
$909$		0			0
$910$		0			0
$911$	29071.2			1.05727			0.528635	−	0.848849i	$-0.322704\pi$
$911$	29071.2			1.05727			0.528635	+	0.848849i	$0.322704\pi$
$912$		0			0
$913$	1105.48	+	1914.74i	0.0400723	+	0.0694072i
$914$	9106.82	+	15773.5i	0.329570	+	0.570832i
$915$		0			0
$916$	−7868.67			−0.283830
$917$		0			0
$918$		0			0
$919$	−3986.70	+	6905.16i	−0.143100	+	0.247857i	−0.928663	−	0.370926i	$-0.879040\pi$
$919$	−3986.70	+	6905.16i	−0.143100	+	0.247857i	0.785562	+	0.618782i	$0.212374\pi$
$920$	−5404.96	−	9361.66i	−0.193691	−	0.335483i
$921$		0			0
$922$	8729.69	−	15120.3i	0.311819	−	0.540086i
$923$	−796.079			−0.0283892
$924$		0			0
$925$	27630.7			0.982154
$926$	−1795.62	+	3110.11i	−0.0637233	+	0.110372i
$927$		0			0
$928$	−2498.11	−	4326.86i	−0.0883670	−	0.153056i
$929$	15070.7	−	26103.3i	0.532244	−	0.921874i	−0.467047	−	0.884233i	$-0.654682\pi$
$929$	15070.7	−	26103.3i	0.532244	−	0.921874i	0.999291	−	0.0376418i	$-0.0119846\pi$
$930$		0			0
$931$		0			0
$932$	−17913.3			−0.629582
$933$		0			0
$934$	−130.559	−	226.136i	−0.00457391	−	0.00792225i
$935$	1960.75	+	3396.11i	0.0685811	+	0.118786i
$936$		0			0
$937$	1126.37			0.0392709			0.0196354	−	0.999807i	$-0.493749\pi$
$937$	1126.37			0.0392709			0.0196354	+	0.999807i	$0.493749\pi$
$938$		0			0
$939$		0			0
$940$	9045.40	−	15667.1i	0.313860	−	0.543622i
$941$	−5166.64	−	8948.89i	−0.178988	−	0.310016i	0.762546	−	0.646934i	$-0.223949\pi$
$941$	−5166.64	−	8948.89i	−0.178988	−	0.310016i	−0.941534	+	0.336917i	$0.890616\pi$
$942$		0			0
$943$	18006.7	−	31188.6i	0.621824	−	1.07703i
$944$	−9430.97			−0.325161
$945$		0			0
$946$	7199.06			0.247422
$947$	12405.1	−	21486.3i	0.425673	−	0.737288i	−0.570810	−	0.821082i	$-0.693371\pi$
$947$	12405.1	−	21486.3i	0.425673	−	0.737288i	0.996483	+	0.0837944i	$0.0267039\pi$
$948$		0			0
$949$	1389.85	+	2407.30i	0.0475412	+	0.0823438i
$950$	−8757.45	+	15168.3i	−0.299083	+	0.518028i
$951$		0			0
$952$		0			0
$953$	15048.6			0.511513			0.255757	−	0.966741i	$-0.417675\pi$
$953$	15048.6			0.511513			0.255757	+	0.966741i	$0.417675\pi$
$954$		0			0
$955$	−4547.58	−	7876.65i	−0.154090	−	0.266893i
$956$	12233.8	+	21189.6i	0.413881	+	0.716864i
$957$		0			0
$958$	23691.6			0.798999
$959$		0			0
$960$		0			0
$961$	5146.89	−	8914.67i	0.172767	−	0.299240i
$962$	−1099.55	−	1904.48i	−0.0368514	−	0.0638285i
$963$		0			0
$964$	−12456.8	+	21575.7i	−0.416188	+	0.720859i
$965$	25796.2			0.860528
$966$		0			0
$967$	−15619.9			−0.519442			−0.259721	−	0.965684i	$-0.583631\pi$
$967$	−15619.9			−0.519442			−0.259721	+	0.965684i	$0.583631\pi$
$968$	−4884.24	+	8459.74i	−0.162175	+	0.280895i
$969$		0			0
$970$	6701.78	+	11607.8i	0.221836	+	0.384232i
$971$	−12416.5	+	21506.0i	−0.410365	+	0.710773i	−0.994930	−	0.100574i	$-0.967932\pi$
$971$	−12416.5	+	21506.0i	−0.410365	+	0.710773i	0.584565	+	0.811347i	$0.301265\pi$
$972$		0			0
$973$		0			0
$974$	9614.42			0.316289
$975$		0			0
$976$	−1977.74	−	3425.54i	−0.0648626	−	0.112345i
$977$	19328.4	+	33477.8i	0.632928	+	1.09626i	0.986950	+	0.161026i	$0.0514804\pi$
$977$	19328.4	+	33477.8i	0.632928	+	1.09626i	−0.354022	+	0.935237i	$0.615186\pi$
$978$		0			0
$979$	−5803.47			−0.189458
$980$		0			0
$981$		0			0
$982$	−6068.04	+	10510.2i	−0.197188	+	0.341540i
$983$	13332.1	+	23091.8i	0.432581	+	0.749252i	0.997095	−	0.0761716i	$-0.0242697\pi$
$983$	13332.1	+	23091.8i	0.432581	+	0.749252i	−0.564514	+	0.825424i	$0.690936\pi$
$984$		0			0
$985$	−11838.5	+	20505.0i	−0.382952	+	0.663292i
$986$	−15751.7			−0.508760
$987$		0			0
$988$	1394.00			0.0448876
$989$	−31282.6	+	54183.0i	−1.00579	+	1.74208i
$990$		0			0
$991$	−13614.1	−	23580.3i	−0.436393	−	0.755855i	0.561015	−	0.827806i	$-0.310411\pi$
$991$	−13614.1	−	23580.3i	−0.436393	−	0.755855i	−0.997408	+	0.0719507i	$0.977078\pi$
$992$	2234.12	−	3869.61i	0.0715054	−	0.123851i
$993$		0			0
$994$		0			0
$995$	−7897.24			−0.251617
$996$		0			0
$997$	−2581.46	−	4471.22i	−0.0820016	−	0.142031i	0.822108	−	0.569332i	$-0.192798\pi$
$997$	−2581.46	−	4471.22i	−0.0820016	−	0.142031i	−0.904110	+	0.427301i	$0.859465\pi$
$998$	−15506.4	−	26857.9i	−0.491831	−	0.851876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bk.667.2		4
3.2	odd	2		294.4.e.k.79.1		4
7.2	even	3		882.4.a.t.1.1		2
7.3	odd	6		882.4.g.be.361.1		4
7.4	even	3	inner	882.4.g.bk.361.2		4
7.5	odd	6		882.4.a.bb.1.2		2
7.6	odd	2		882.4.g.be.667.1		4
21.2	odd	6		294.4.a.o.1.2	yes	2
21.5	even	6		294.4.a.l.1.1	✓	2
21.11	odd	6		294.4.e.k.67.1		4
21.17	even	6		294.4.e.m.67.2		4
21.20	even	2		294.4.e.m.79.2		4
84.23	even	6		2352.4.a.bu.1.2		2
84.47	odd	6		2352.4.a.bw.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.l.1.1	✓	2	21.5	even	6
294.4.a.o.1.2	yes	2	21.2	odd	6
294.4.e.k.67.1		4	21.11	odd	6
294.4.e.k.79.1		4	3.2	odd	2
294.4.e.m.67.2		4	21.17	even	6
294.4.e.m.79.2		4	21.20	even	2
882.4.a.t.1.1		2	7.2	even	3
882.4.a.bb.1.2		2	7.5	odd	6
882.4.g.be.361.1		4	7.3	odd	6
882.4.g.be.667.1		4	7.6	odd	2
882.4.g.bk.361.2		4	7.4	even	3	inner
882.4.g.bk.667.2		4	1.1	even	1	trivial
2352.4.a.bu.1.2		2	84.23	even	6
2352.4.a.bw.1.1		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.70711 - 6.42090i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.70711 - 6.42090i) q^{5} -8.00000 q^{8} +(-7.41421 - 12.8418i) q^{10} +(5.24264 + 9.08052i) q^{11} +2.78680 q^{13} +(-8.00000 + 13.8564i) q^{16} +(25.2218 + 43.6855i) q^{17} +(-62.5269 + 108.300i) q^{19} -29.6569 q^{20} +20.9706 q^{22} +(-91.1249 + 157.833i) q^{23} +(35.0147 + 60.6473i) q^{25} +(2.78680 - 4.82687i) q^{26} -156.132 q^{29} +(-69.8162 - 120.925i) q^{31} +(16.0000 + 27.7128i) q^{32} +100.887 q^{34} +(197.279 - 341.698i) q^{37} +(125.054 + 216.600i) q^{38} +(-29.6569 + 51.3672i) q^{40} -197.605 q^{41} +343.294 q^{43} +(20.9706 - 36.3221i) q^{44} +(182.250 + 315.666i) q^{46} +(-305.002 + 528.279i) q^{47} +140.059 q^{50} +(-5.57359 - 9.65375i) q^{52} +(-68.7645 - 119.104i) q^{53} +77.7401 q^{55} +(-156.132 + 270.429i) q^{58} +(294.718 + 510.466i) q^{59} +(-123.609 + 214.097i) q^{61} -279.265 q^{62} +64.0000 q^{64} +(10.3310 - 17.8937i) q^{65} +(197.823 + 342.640i) q^{67} +(100.887 - 174.742i) q^{68} -285.661 q^{71} +(498.729 + 863.823i) q^{73} +(-394.558 - 683.395i) q^{74} +500.215 q^{76} +(424.132 - 734.618i) q^{79} +(59.3137 + 102.734i) q^{80} +(-197.605 + 342.262i) q^{82} +210.863 q^{83} +374.000 q^{85} +(343.294 - 594.602i) q^{86} +(-41.9411 - 72.6442i) q^{88} +(-276.744 + 479.334i) q^{89} +728.999 q^{92} +(610.004 + 1056.56i) q^{94} +(463.588 + 802.958i) q^{95} -903.910 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8} - 24 q^{10} + 4 q^{11} + 96 q^{13} - 32 q^{16} + 132 q^{17} - 120 q^{19} - 96 q^{20} + 16 q^{22} - 76 q^{23} + 174 q^{25} + 96 q^{26} + 224 q^{29} - 432 q^{31} + 64 q^{32} + 528 q^{34} + 280 q^{37} + 240 q^{38} - 96 q^{40} - 72 q^{41} - 256 q^{43} + 16 q^{44} + 152 q^{46} - 264 q^{47} + 696 q^{50} - 192 q^{52} + 268 q^{53} + 96 q^{55} + 224 q^{58} + 336 q^{59} + 504 q^{61} - 1728 q^{62} + 256 q^{64} + 228 q^{65} + 384 q^{67} + 528 q^{68} + 792 q^{71} + 312 q^{73} - 560 q^{74} + 960 q^{76} + 848 q^{79} + 192 q^{80} - 72 q^{82} + 1296 q^{83} + 1496 q^{85} - 256 q^{86} - 32 q^{88} - 612 q^{89} + 608 q^{92} + 528 q^{94} + 904 q^{95} - 4368 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8 - 24 * q^10 + 4 * q^11 + 96 * q^13 - 32 * q^16 + 132 * q^17 - 120 * q^19 - 96 * q^20 + 16 * q^22 - 76 * q^23 + 174 * q^25 + 96 * q^26 + 224 * q^29 - 432 * q^31 + 64 * q^32 + 528 * q^34 + 280 * q^37 + 240 * q^38 - 96 * q^40 - 72 * q^41 - 256 * q^43 + 16 * q^44 + 152 * q^46 - 264 * q^47 + 696 * q^50 - 192 * q^52 + 268 * q^53 + 96 * q^55 + 224 * q^58 + 336 * q^59 + 504 * q^61 - 1728 * q^62 + 256 * q^64 + 228 * q^65 + 384 * q^67 + 528 * q^68 + 792 * q^71 + 312 * q^73 - 560 * q^74 + 960 * q^76 + 848 * q^79 + 192 * q^80 - 72 * q^82 + 1296 * q^83 + 1496 * q^85 - 256 * q^86 - 32 * q^88 - 612 * q^89 + 608 * q^92 + 528 * q^94 + 904 * q^95 - 4368 * q^97

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