LMFDB - Embedded newform 294.4.e.m.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.e (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:	$17.3465615417$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.4.e.m.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(7.41421 - 12.8418i) q^{10} +(-5.24264 + 9.08052i) q^{11} +(6.00000 + 10.3923i) q^{12} -2.78680 q^{13} +22.2426 q^{15} +(-8.00000 - 13.8564i) q^{16} +(25.2218 - 43.6855i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(62.5269 + 108.300i) q^{19} -29.6569 q^{20} +20.9706 q^{22} +(91.1249 + 157.833i) q^{23} +(12.0000 - 20.7846i) q^{24} +(35.0147 - 60.6473i) q^{25} +(2.78680 + 4.82687i) q^{26} -27.0000 q^{27} +156.132 q^{29} +(-22.2426 - 38.5254i) q^{30} +(69.8162 - 120.925i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(15.7279 + 27.2416i) q^{33} -100.887 q^{34} +36.0000 q^{36} +(197.279 + 341.698i) q^{37} +(125.054 - 216.600i) q^{38} +(-4.18019 + 7.24031i) q^{39} +(29.6569 + 51.3672i) q^{40} -197.605 q^{41} +343.294 q^{43} +(-20.9706 - 36.3221i) q^{44} +(33.3640 - 57.7881i) q^{45} +(182.250 - 315.666i) q^{46} +(-305.002 - 528.279i) q^{47} -48.0000 q^{48} -140.059 q^{50} +(-75.6655 - 131.056i) q^{51} +(5.57359 - 9.65375i) q^{52} +(68.7645 - 119.104i) q^{53} +(27.0000 + 46.7654i) q^{54} -77.7401 q^{55} +375.161 q^{57} +(-156.132 - 270.429i) q^{58} +(294.718 - 510.466i) q^{59} +(-44.4853 + 77.0508i) q^{60} +(123.609 + 214.097i) q^{61} -279.265 q^{62} +64.0000 q^{64} +(-10.3310 - 17.8937i) q^{65} +(31.4558 - 54.4831i) q^{66} +(197.823 - 342.640i) q^{67} +(100.887 + 174.742i) q^{68} +546.749 q^{69} +285.661 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-498.729 + 863.823i) q^{73} +(394.558 - 683.395i) q^{74} +(-105.044 - 181.942i) q^{75} -500.215 q^{76} +16.7208 q^{78} +(424.132 + 734.618i) q^{79} +(59.3137 - 102.734i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(197.605 + 342.262i) q^{82} +210.863 q^{83} +374.000 q^{85} +(-343.294 - 594.602i) q^{86} +(234.198 - 405.643i) q^{87} +(-41.9411 + 72.6442i) q^{88} +(-276.744 - 479.334i) q^{89} -133.456 q^{90} -728.999 q^{92} +(-209.449 - 362.776i) q^{93} +(-610.004 + 1056.56i) q^{94} +(-463.588 + 802.958i) q^{95} +(48.0000 + 83.1384i) q^{96} +903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 12 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 24 q^{10} - 4 q^{11} + 24 q^{12} - 96 q^{13} + 72 q^{15} - 32 q^{16} + 132 q^{17} - 36 q^{18} + 120 q^{19} - 96 q^{20} + 16 q^{22} + 76 q^{23} + 48 q^{24} + 174 q^{25} + 96 q^{26} - 108 q^{27} - 224 q^{29} - 72 q^{30} + 432 q^{31} - 64 q^{32} + 12 q^{33} - 528 q^{34} + 144 q^{36} + 280 q^{37} + 240 q^{38} - 144 q^{39} + 96 q^{40} - 72 q^{41} - 256 q^{43} - 16 q^{44} + 108 q^{45} + 152 q^{46} - 264 q^{47} - 192 q^{48} - 696 q^{50} - 396 q^{51} + 192 q^{52} - 268 q^{53} + 108 q^{54} - 96 q^{55} + 720 q^{57} + 224 q^{58} + 336 q^{59} - 144 q^{60} - 504 q^{61} - 1728 q^{62} + 256 q^{64} - 228 q^{65} + 24 q^{66} + 384 q^{67} + 528 q^{68} + 456 q^{69} - 792 q^{71} - 144 q^{72} - 312 q^{73} + 560 q^{74} - 522 q^{75} - 960 q^{76} + 576 q^{78} + 848 q^{79} + 192 q^{80} - 162 q^{81} + 72 q^{82} + 1296 q^{83} + 1496 q^{85} + 256 q^{86} - 336 q^{87} - 32 q^{88} - 612 q^{89} - 432 q^{90} - 608 q^{92} - 1296 q^{93} - 528 q^{94} - 904 q^{95} + 192 q^{96} + 4368 q^{97} + 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 12 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9 + 24 * q^10 - 4 * q^11 + 24 * q^12 - 96 * q^13 + 72 * q^15 - 32 * q^16 + 132 * q^17 - 36 * q^18 + 120 * q^19 - 96 * q^20 + 16 * q^22 + 76 * q^23 + 48 * q^24 + 174 * q^25 + 96 * q^26 - 108 * q^27 - 224 * q^29 - 72 * q^30 + 432 * q^31 - 64 * q^32 + 12 * q^33 - 528 * q^34 + 144 * q^36 + 280 * q^37 + 240 * q^38 - 144 * q^39 + 96 * q^40 - 72 * q^41 - 256 * q^43 - 16 * q^44 + 108 * q^45 + 152 * q^46 - 264 * q^47 - 192 * q^48 - 696 * q^50 - 396 * q^51 + 192 * q^52 - 268 * q^53 + 108 * q^54 - 96 * q^55 + 720 * q^57 + 224 * q^58 + 336 * q^59 - 144 * q^60 - 504 * q^61 - 1728 * q^62 + 256 * q^64 - 228 * q^65 + 24 * q^66 + 384 * q^67 + 528 * q^68 + 456 * q^69 - 792 * q^71 - 144 * q^72 - 312 * q^73 + 560 * q^74 - 522 * q^75 - 960 * q^76 + 576 * q^78 + 848 * q^79 + 192 * q^80 - 162 * q^81 + 72 * q^82 + 1296 * q^83 + 1496 * q^85 + 256 * q^86 - 336 * q^87 - 32 * q^88 - 612 * q^89 - 432 * q^90 - 608 * q^92 - 1296 * q^93 - 528 * q^94 - 904 * q^95 + 192 * q^96 + 4368 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	3.70711	+	6.42090i	0.331574	+	0.574303i	0.982821	−	0.184563i	$-0.0590871\pi$
$5$	3.70711	+	6.42090i	0.331574	+	0.574303i	−0.651247	+	0.758866i	$0.725754\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	7.41421	−	12.8418i	0.234458	−	0.406093i
$11$	−5.24264	+	9.08052i	−0.143701	+	0.248898i	−0.928888	−	0.370361i	$-0.879234\pi$
$11$	−5.24264	+	9.08052i	−0.143701	+	0.248898i	0.785186	+	0.619260i	$0.212567\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	−2.78680			−0.0594553			−0.0297276	−	0.999558i	$-0.509464\pi$
$13$	−2.78680			−0.0594553			−0.0297276	+	0.999558i	$0.509464\pi$
$14$		0			0
$15$	22.2426			0.382868
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	25.2218	−	43.6855i	0.359835	−	0.623252i	−0.628098	−	0.778134i	$-0.716166\pi$
$17$	25.2218	−	43.6855i	0.359835	−	0.623252i	0.987933	+	0.154882i	$0.0494997\pi$
$18$	−9.00000	+	15.5885i	−0.117851	+	0.204124i
$19$	62.5269	+	108.300i	0.754982	+	1.30767i	0.945383	+	0.325961i	$0.105688\pi$
$19$	62.5269	+	108.300i	0.754982	+	1.30767i	−0.190401	+	0.981706i	$0.560979\pi$
$20$	−29.6569			−0.331574
$21$		0			0
$22$	20.9706			0.203225
$23$	91.1249	+	157.833i	0.826124	+	1.43089i	0.901057	+	0.433700i	$0.142792\pi$
$23$	91.1249	+	157.833i	0.826124	+	1.43089i	−0.0749331	+	0.997189i	$0.523874\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	35.0147	−	60.6473i	0.280118	−	0.485178i
$26$	2.78680	+	4.82687i	0.0210206	+	0.0364088i
$27$	−27.0000			−0.192450
$28$		0			0
$29$	156.132			0.999758			0.499879	−	0.866095i	$-0.333378\pi$
$29$	156.132			0.999758			0.499879	+	0.866095i	$0.333378\pi$
$30$	−22.2426	−	38.5254i	−0.135364	−	0.234458i
$31$	69.8162	−	120.925i	0.404496	−	0.700607i	−0.589767	−	0.807573i	$-0.700780\pi$
$31$	69.8162	−	120.925i	0.404496	−	0.700607i	0.994263	+	0.106966i	$0.0341137\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	15.7279	+	27.2416i	0.0829661	+	0.143701i
$34$	−100.887			−0.508883
$35$		0			0
$36$	36.0000			0.166667
$37$	197.279	+	341.698i	0.876554	+	1.51824i	0.855098	+	0.518467i	$0.173497\pi$
$37$	197.279	+	341.698i	0.876554	+	1.51824i	0.0214563	+	0.999770i	$0.493170\pi$
$38$	125.054	−	216.600i	0.533853	−	0.924660i
$39$	−4.18019	+	7.24031i	−0.0171633	+	0.0297276i
$40$	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
$45$	33.3640	−	57.7881i	0.110525	−	0.191434i
$46$	182.250	−	315.666i	0.584158	−	1.01179i
$47$	−305.002	−	528.279i	−0.946577	−	1.63952i	−0.752562	−	0.658521i	$-0.771182\pi$
$47$	−305.002	−	528.279i	−0.946577	−	1.63952i	−0.194015	−	0.980999i	$-0.562151\pi$
$48$	−48.0000			−0.144338
$49$		0			0
$50$	−140.059			−0.396146
$51$	−75.6655	−	131.056i	−0.207751	−	0.359835i
$52$	5.57359	−	9.65375i	0.0148638	−	0.0257449i
$53$	68.7645	−	119.104i	0.178218	−	0.308682i	−0.763053	−	0.646336i	$-0.776300\pi$
$53$	68.7645	−	119.104i	0.178218	−	0.308682i	0.941270	+	0.337655i	$0.109634\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−77.7401			−0.190590
$56$		0			0
$57$	375.161			0.871778
$58$	−156.132	−	270.429i	−0.353468	−	0.612224i
$59$	294.718	−	510.466i	0.650322	−	1.12639i	−0.332723	−	0.943025i	$-0.607967\pi$
$59$	294.718	−	510.466i	0.650322	−	1.12639i	0.983045	−	0.183366i	$-0.0586993\pi$
$60$	−44.4853	+	77.0508i	−0.0957171	+	0.165787i
$61$	123.609	+	214.097i	0.259450	+	0.449381i	0.966095	−	0.258188i	$-0.0831253\pi$
$61$	123.609	+	214.097i	0.259450	+	0.449381i	−0.706644	+	0.707569i	$0.749792\pi$
$62$	−279.265			−0.572043
$63$		0			0
$64$	64.0000			0.125000
$65$	−10.3310	−	17.8937i	−0.0197138	−	0.0341453i
$66$	31.4558	−	54.4831i	0.0586659	−	0.101612i
$67$	197.823	−	342.640i	0.360716	−	0.624778i	−0.627363	−	0.778727i	$-0.715866\pi$
$67$	197.823	−	342.640i	0.360716	−	0.624778i	0.988079	+	0.153949i	$0.0491990\pi$
$68$	100.887	+	174.742i	0.179917	+	0.311626i
$69$	546.749			0.953926
$70$		0			0
$71$	285.661			0.477489			0.238745	−	0.971082i	$-0.423264\pi$
$71$	285.661			0.477489			0.238745	+	0.971082i	$0.423264\pi$
$72$	−36.0000	−	62.3538i	−0.0589256	−	0.102062i
$73$	−498.729	+	863.823i	−0.799613	+	1.38497i	0.120255	+	0.992743i	$0.461629\pi$
$73$	−498.729	+	863.823i	−0.799613	+	1.38497i	−0.919868	+	0.392228i	$0.871705\pi$
$74$	394.558	−	683.395i	0.619817	−	1.07356i
$75$	−105.044	−	181.942i	−0.161726	−	0.280118i
$76$	−500.215			−0.754982
$77$		0			0
$78$	16.7208			0.0242725
$79$	424.132	+	734.618i	0.604033	+	1.04622i	0.992204	+	0.124628i	$0.0397737\pi$
$79$	424.132	+	734.618i	0.604033	+	1.04622i	−0.388171	+	0.921587i	$0.626893\pi$
$80$	59.3137	−	102.734i	0.0828934	−	0.143576i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	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
$87$	234.198	−	405.643i	0.288605	−	0.499879i
$88$	−41.9411	+	72.6442i	−0.0508061	+	0.0879988i
$89$	−276.744	−	479.334i	−0.329604	−	0.570891i	0.652829	−	0.757505i	$-0.273582\pi$
$89$	−276.744	−	479.334i	−0.329604	−	0.570891i	−0.982433	+	0.186614i	$0.940249\pi$
$90$	−133.456			−0.156305
$91$		0			0
$92$	−728.999			−0.826124
$93$	−209.449	−	362.776i	−0.233536	−	0.404496i
$94$	−610.004	+	1056.56i	−0.669331	+	1.15932i
$95$	−463.588	+	802.958i	−0.500664	+	0.867176i
$96$	48.0000	+	83.1384i	0.0510310	+	0.0883883i
$97$	903.910			0.946166			0.473083	−	0.881018i	$-0.343141\pi$
$97$	903.910			0.946166			0.473083	+	0.881018i	$0.343141\pi$
$98$		0			0
$99$	94.3675			0.0958009
$100$	140.059	+	242.589i	0.140059	+	0.242589i
$101$	−156.806	+	271.595i	−0.154482	+	0.267572i	−0.932870	−	0.360212i	$-0.882704\pi$
$101$	−156.806	+	271.595i	−0.154482	+	0.267572i	0.778388	+	0.627784i	$0.216038\pi$
$102$	−151.331	+	262.113i	−0.146902	+	0.254442i
$103$	115.487	+	200.030i	0.110479	+	0.191355i	0.915963	−	0.401262i	$-0.131428\pi$
$103$	115.487	+	200.030i	0.110479	+	0.191355i	−0.805485	+	0.592617i	$0.798095\pi$
$104$	−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	$-0.184721\pi$
$107$	−62.7431	−	108.674i	−0.0566879	−	0.0981863i	−0.892977	+	0.450103i	$0.851387\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−372.764	+	645.646i	−0.327562	+	0.567354i	−0.982028	−	0.188738i	$-0.939560\pi$
$109$	−372.764	+	645.646i	−0.327562	+	0.567354i	0.654465	+	0.756092i	$0.272894\pi$
$110$	77.7401	+	134.650i	0.0673839	+	0.116712i
$111$	1183.68			1.01216
$112$		0			0
$113$	−1043.76			−0.868929			−0.434464	−	0.900689i	$-0.643062\pi$
$113$	−1043.76			−0.868929			−0.434464	+	0.900689i	$0.643062\pi$
$114$	−375.161	−	649.799i	−0.308220	−	0.533853i
$115$	−675.619	+	1170.21i	−0.547842	+	0.948890i
$116$	−312.264	+	540.857i	−0.249940	+	0.432908i
$117$	12.5406	+	21.7209i	0.00990921	+	0.0171633i
$118$	−1178.87			−0.919694
$119$		0			0
$120$	177.941			0.135364
$121$	610.529	+	1057.47i	0.458700	+	0.794491i
$122$	247.217	−	428.193i	0.183459	−	0.317760i
$123$	−296.408	+	513.393i	−0.217286	+	0.376350i
$124$	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
$129$	514.940	−	891.903i	0.351457	−	0.608741i
$130$	−20.6619	+	35.7875i	−0.0139398	+	0.0241444i
$131$	−634.764	−	1099.44i	−0.423355	−	0.733273i	0.572910	−	0.819618i	$-0.305814\pi$
$131$	−634.764	−	1099.44i	−0.423355	−	0.733273i	−0.996265	+	0.0863453i	$0.972481\pi$
$132$	−125.823			−0.0829661
$133$		0			0
$134$	−791.294			−0.510129
$135$	−100.092	−	173.364i	−0.0638114	−	0.110525i
$136$	201.775	−	349.484i	0.127221	−	0.220353i
$137$	−1536.59	+	2661.46i	−0.958249	+	1.65974i	−0.231497	+	0.972836i	$0.574362\pi$
$137$	−1536.59	+	2661.46i	−0.958249	+	1.65974i	−0.726752	+	0.686900i	$0.758971\pi$
$138$	−546.749	−	946.998i	−0.337264	−	0.584158i
$139$	−1013.60			−0.618504			−0.309252	−	0.950980i	$-0.600079\pi$
$139$	−1013.60			−0.618504			−0.309252	+	0.950980i	$0.600079\pi$
$140$		0			0
$141$	−1830.01			−1.09301
$142$	−285.661	−	494.779i	−0.168818	−	0.292401i
$143$	14.6102	−	25.3056i	0.00854380	−	0.0147983i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	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	$-0.276601\pi$
$149$	−615.735	−	1066.48i	−0.338544	−	0.586375i	−0.984159	+	0.177288i	$0.943268\pi$
$150$	−210.088	+	363.884i	−0.114358	+	0.198073i
$151$	1122.37	−	1944.00i	0.604881	−	1.04768i	−0.387190	−	0.922000i	$-0.626554\pi$
$151$	1122.37	−	1944.00i	0.604881	−	1.04768i	0.992070	−	0.125684i	$-0.0401125\pi$
$152$	500.215	+	866.398i	0.266926	+	0.462330i
$153$	−453.993			−0.239890
$154$		0			0
$155$	1035.26			0.536481
$156$	−16.7208	−	28.9612i	−0.00858163	−	0.0148638i
$157$	−1893.58	+	3279.77i	−0.962573	+	1.66723i	−0.246575	+	0.969124i	$0.579305\pi$
$157$	−1893.58	+	3279.77i	−0.962573	+	1.66723i	−0.715998	+	0.698102i	$0.754028\pi$
$158$	848.264	−	1469.24i	0.427116	−	0.739786i
$159$	−206.294	−	357.311i	−0.102894	−	0.178218i
$160$	−237.255			−0.117229
$161$		0			0
$162$	162.000			0.0785674
$163$	1054.28	+	1826.07i	0.506611	+	0.877476i	0.999971	+	0.00765060i	$0.00243528\pi$
$163$	1054.28	+	1826.07i	0.506611	+	0.877476i	−0.493360	+	0.869825i	$0.664231\pi$
$164$	395.210	−	684.524i	0.188175	−	0.325929i
$165$	−116.610	+	201.975i	−0.0550187	+	0.0952952i
$166$	−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
$171$	562.742	−	974.698i	0.251661	−	0.435889i
$172$	−686.587	+	1189.20i	−0.304371	+	0.527186i
$173$	235.628	+	408.120i	0.103552	+	0.179357i	0.913146	−	0.407634i	$-0.133646\pi$
$173$	235.628	+	408.120i	0.103552	+	0.179357i	−0.809594	+	0.586991i	$0.800313\pi$
$174$	−936.792			−0.408150
$175$		0			0
$176$	167.765			0.0718507
$177$	−884.153	−	1531.40i	−0.375464	−	0.650322i
$178$	−553.487	+	958.668i	−0.233065	+	0.403681i
$179$	−666.244	+	1153.97i	−0.278198	+	0.481852i	−0.970937	−	0.239336i	$-0.923070\pi$
$179$	−666.244	+	1153.97i	−0.278198	+	0.481852i	0.692739	+	0.721188i	$0.256404\pi$
$180$	133.456	+	231.152i	0.0552623	+	0.0957171i
$181$	997.727			0.409726			0.204863	−	0.978791i	$-0.434325\pi$
$181$	997.727			0.409726			0.204863	+	0.978791i	$0.434325\pi$
$182$		0			0
$183$	741.652			0.299587
$184$	728.999	+	1262.66i	0.292079	+	0.505896i
$185$	−1462.67	+	2533.42i	−0.581285	+	1.00681i
$186$	−418.897	+	725.552i	−0.165135	+	0.286022i
$187$	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	$-0.241312\pi$
$191$	−613.360	−	1062.37i	−0.232362	−	0.402463i	−0.958503	+	0.285083i	$0.907979\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	1739.65	−	3013.16i	0.648821	−	1.12379i	−0.334584	−	0.942366i	$-0.608596\pi$
$193$	1739.65	−	3013.16i	0.648821	−	1.12379i	0.983405	−	0.181425i	$-0.0580709\pi$
$194$	−903.910	−	1565.62i	−0.334520	−	0.579406i
$195$	−61.9857			−0.0227635
$196$		0			0
$197$	3193.47			1.15495			0.577476	−	0.816408i	$-0.304038\pi$
$197$	3193.47			1.15495			0.577476	+	0.816408i	$0.304038\pi$
$198$	−94.3675	−	163.449i	−0.0338708	−	0.0586659i
$199$	532.574	−	922.446i	0.189715	−	0.328595i	−0.755440	−	0.655217i	$-0.772577\pi$
$199$	532.574	−	922.446i	0.189715	−	0.328595i	0.945155	+	0.326622i	$0.105910\pi$
$200$	280.118	−	485.178i	0.0990366	−	0.171536i
$201$	−593.470	−	1027.92i	−0.208259	−	0.360716i
$202$	627.222			0.218471
$203$		0			0
$204$	605.324			0.207751
$205$	−732.543	−	1268.80i	−0.249576	−	0.432278i
$206$	230.975	−	400.060i	0.0781203	−	0.135308i
$207$	820.124	−	1420.50i	0.275375	−	0.476963i
$208$	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
$213$	428.492	−	742.169i	0.137839	−	0.238745i
$214$	−125.486	+	217.348i	−0.0400844	+	0.0694282i
$215$	1272.63	+	2204.25i	0.403685	+	0.699204i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	1491.05			0.463243
$219$	1496.19	+	2591.47i	0.461657	+	0.799613i
$220$	155.480	−	269.300i	0.0476476	−	0.0825281i
$221$	−70.2881	+	121.743i	−0.0213941	+	0.0370556i
$222$	−1183.68	−	2050.19i	−0.357852	−	0.619817i
$223$	−2028.27			−0.609071			−0.304536	−	0.952501i	$-0.598501\pi$
$223$	−2028.27			−0.609071			−0.304536	+	0.952501i	$0.598501\pi$
$224$		0			0
$225$	−630.265			−0.186745
$226$	1043.76	+	1807.85i	0.307213	+	0.532108i
$227$	1211.98	−	2099.21i	0.354369	−	0.613786i	−0.632640	−	0.774446i	$-0.718029\pi$
$227$	1211.98	−	2099.21i	0.354369	−	0.613786i	0.987010	+	0.160660i	$0.0513622\pi$
$228$	−750.323	+	1299.60i	−0.217945	+	0.377491i
$229$	−983.584	−	1703.62i	−0.283830	−	0.491608i	0.688495	−	0.725241i	$-0.258272\pi$
$229$	−983.584	−	1703.62i	−0.283830	−	0.491608i	−0.972325	+	0.233633i	$0.924938\pi$
$230$	2702.48			0.774766
$231$		0			0
$232$	1249.06			0.353468
$233$	−2239.17	−	3878.35i	−0.629582	−	1.09047i	−0.987636	−	0.156767i	$-0.949893\pi$
$233$	−2239.17	−	3878.35i	−0.629582	−	1.09047i	0.358053	−	0.933701i	$-0.383441\pi$
$234$	25.0812	−	43.4419i	0.00700687	−	0.0121363i
$235$	2261.35	−	3916.77i	0.627720	−	1.08724i
$236$	1178.87	+	2041.86i	0.325161	+	0.563195i
$237$	2544.79			0.697477
$238$		0			0
$239$	6116.92			1.65553			0.827763	−	0.561078i	$-0.189613\pi$
$239$	6116.92			1.65553			0.827763	+	0.561078i	$0.189613\pi$
$240$	−177.941	−	308.203i	−0.0478585	−	0.0828934i
$241$	3114.19	−	5393.94i	0.832376	−	1.44172i	−0.0637726	−	0.997964i	$-0.520313\pi$
$241$	3114.19	−	5393.94i	0.832376	−	1.44172i	0.896149	−	0.443754i	$-0.146353\pi$
$242$	1221.06	−	2114.94i	0.324350	−	0.561790i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−988.870			−0.259450
$245$		0			0
$246$	1185.63			0.307289
$247$	−174.250	−	301.809i	−0.0448876	−	0.0777477i
$248$	558.530	−	967.402i	0.143011	−	0.247702i
$249$	316.294	−	547.838i	0.0804994	−	0.139429i
$250$	−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
$255$	561.000	−	971.681i	0.137769	−	0.238624i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−204.112	−	353.532i	−0.0495414	−	0.0858082i	0.840191	−	0.542290i	$-0.182443\pi$
$257$	−204.112	−	353.532i	−0.0495414	−	0.0858082i	−0.889733	+	0.456482i	$0.849109\pi$
$258$	−2059.76			−0.497035
$259$		0			0
$260$	82.6476			0.0197138
$261$	−702.594	−	1216.93i	−0.166626	−	0.288605i
$262$	−1269.53	+	2198.89i	−0.299357	+	0.518502i
$263$	2313.00	−	4006.24i	0.542304	−	0.939298i	−0.456467	−	0.889740i	$-0.650885\pi$
$263$	2313.00	−	4006.24i	0.542304	−	0.939298i	0.998771	−	0.0495577i	$-0.0157812\pi$
$264$	125.823	+	217.932i	0.0293329	+	0.0508061i
$265$	1019.67			0.236369
$266$		0			0
$267$	−1660.46			−0.380594
$268$	791.294	+	1370.56i	0.180358	+	0.312389i
$269$	−435.646	+	754.562i	−0.0987429	+	0.171028i	−0.911165	−	0.412043i	$-0.864815\pi$
$269$	−435.646	+	754.562i	−0.0987429	+	0.171028i	0.812422	+	0.583070i	$0.198149\pi$
$270$	−200.184	+	346.728i	−0.0451215	+	0.0781527i
$271$	3236.17	+	5605.22i	0.725401	+	1.25643i	0.958809	+	0.284052i	$0.0916788\pi$
$271$	3236.17	+	5605.22i	0.725401	+	1.25643i	−0.233408	+	0.972379i	$0.574988\pi$
$272$	−807.098			−0.179917
$273$		0			0
$274$	6146.38			1.35517
$275$	367.139	+	635.904i	0.0805066	+	0.139442i
$276$	−1093.50	+	1894.00i	−0.238481	+	0.413062i
$277$	−2355.94	+	4080.61i	−0.511028	+	0.885126i	0.488890	+	0.872345i	$0.337402\pi$
$277$	−2355.94	+	4080.61i	−0.511028	+	0.885126i	−0.999918	+	0.0127811i	$0.995932\pi$
$278$	1013.60	+	1755.60i	0.218674	+	0.378755i
$279$	−1256.69			−0.269664
$280$		0			0
$281$	−7165.66			−1.52124			−0.760618	−	0.649200i	$-0.775104\pi$
$281$	−7165.66			−1.52124			−0.760618	+	0.649200i	$0.775104\pi$
$282$	1830.01	+	3169.67i	0.386439	+	0.669331i
$283$	3173.50	−	5496.67i	0.666590	−	1.15457i	−0.312261	−	0.949996i	$-0.601086\pi$
$283$	3173.50	−	5496.67i	0.666590	−	1.15457i	0.978851	−	0.204572i	$-0.0655803\pi$
$284$	−571.322	+	989.559i	−0.119372	+	0.206759i
$285$	1390.76	+	2408.87i	0.289059	+	0.500664i
$286$	−58.4407			−0.0120828
$287$		0			0
$288$	288.000			0.0589256
$289$	1184.22	+	2051.13i	0.241038	+	0.417490i
$290$	1157.60	−	2005.02i	0.234401	−	0.405995i
$291$	1355.86	−	2348.43i	0.273135	−	0.473083i
$292$	−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
$297$	141.551	−	245.174i	0.0276554	−	0.0479005i
$298$	−1231.47	+	2132.97i	−0.239386	+	0.414629i
$299$	−253.947	−	439.848i	−0.0491174	−	0.0850739i
$300$	840.353			0.161726
$301$		0			0
$302$	−4489.47			−0.855430
$303$	470.417	+	814.785i	0.0891905	+	0.154482i
$304$	1000.43	−	1732.80i	0.188745	−	0.326917i
$305$	−916.461	+	1587.36i	−0.172054	+	0.298006i
$306$	453.993	+	786.339i	0.0848139	+	0.146902i
$307$	−6786.53			−1.26165			−0.630827	−	0.775923i	$-0.717284\pi$
$307$	−6786.53			−1.26165			−0.630827	+	0.775923i	$0.717284\pi$
$308$		0			0
$309$	692.924			0.127570
$310$	−1035.26	−	1793.13i	−0.189675	−	0.328526i
$311$	2568.38	−	4448.57i	0.468295	−	0.811111i	−0.531048	−	0.847341i	$-0.678202\pi$
$311$	2568.38	−	4448.57i	0.468295	−	0.811111i	0.999343	+	0.0362307i	$0.0115351\pi$
$312$	−33.4416	+	57.9225i	−0.00606813	+	0.0105103i
$313$	−1881.78	−	3259.34i	−0.339822	−	0.588590i	0.644577	−	0.764540i	$-0.277034\pi$
$313$	−1881.78	−	3259.34i	−0.339822	−	0.588590i	−0.984399	+	0.175950i	$0.943700\pi$
$314$	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	$-0.137441\pi$
$317$	517.473	+	896.289i	0.0916851	+	0.158803i	−0.816535	+	0.577296i	$0.804108\pi$
$318$	−412.587	+	714.622i	−0.0727570	+	0.126019i
$319$	−818.544	+	1417.76i	−0.143667	+	0.248838i
$320$	237.255	+	410.937i	0.0414467	+	0.0717878i
$321$	−376.458			−0.0654575
$322$		0			0
$323$	6308.17			1.08668
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	−97.5789	+	169.012i	−0.0166545	+	0.0288464i
$326$	2108.56	−	3652.13i	0.358228	−	0.620469i
$327$	1118.29	+	1936.94i	0.189118	+	0.327562i
$328$	−1580.84			−0.266120
$329$		0			0
$330$	466.441			0.0778082
$331$	−4400.03	−	7621.08i	−0.730657	−	1.26554i	−0.956603	−	0.291395i	$-0.905880\pi$
$331$	−4400.03	−	7621.08i	−0.730657	−	1.26554i	0.225945	−	0.974140i	$-0.427453\pi$
$332$	−421.726	+	730.451i	−0.0697145	+	0.120749i
$333$	1775.51	−	3075.28i	0.292185	−	0.506079i
$334$	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
$339$	−1565.64	+	2711.78i	−0.250838	+	0.434464i
$340$	−748.000	+	1295.57i	−0.119312	+	0.206654i
$341$	732.043	+	1267.94i	0.116253	+	0.201356i
$342$	−2250.97			−0.355902
$343$		0			0
$344$	2746.35			0.430445
$345$	2026.86	+	3510.62i	0.316297	+	0.547842i
$346$	471.256	−	816.239i	0.0732222	−	0.126825i
$347$	−3969.27	+	6874.98i	−0.614068	+	1.06360i	0.376479	+	0.926425i	$0.377135\pi$
$347$	−3969.27	+	6874.98i	−0.614068	+	1.06360i	−0.990547	+	0.137172i	$0.956199\pi$
$348$	936.792	+	1622.57i	0.144303	+	0.249940i
$349$	9927.75			1.52269			0.761347	−	0.648344i	$-0.224538\pi$
$349$	9927.75			1.52269			0.761347	+	0.648344i	$0.224538\pi$
$350$		0			0
$351$	75.2435			0.0114422
$352$	−167.765	−	290.577i	−0.0254031	−	0.0439994i
$353$	−5051.52	+	8749.49i	−0.761658	+	1.31923i	0.180338	+	0.983605i	$0.442281\pi$
$353$	−5051.52	+	8749.49i	−0.761658	+	1.31923i	−0.941996	+	0.335625i	$0.891052\pi$
$354$	−1768.31	+	3062.80i	−0.265493	+	0.459847i
$355$	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	$-0.0512527\pi$
$359$	2412.64	+	4178.81i	0.354691	+	0.614343i	−0.632374	+	0.774663i	$0.717919\pi$
$360$	266.912	−	462.305i	0.0390763	−	0.0676822i
$361$	−4389.73	+	7603.23i	−0.639996	+	1.10850i
$362$	−997.727	−	1728.11i	−0.144860	−	0.250905i
$363$	3663.18			0.529661
$364$		0			0
$365$	−7395.36			−1.06052
$366$	−741.652	−	1284.58i	−0.105920	−	0.183459i
$367$	3467.65	−	6006.15i	0.493215	−	0.854274i	−0.506754	−	0.862091i	$-0.669155\pi$
$367$	3467.65	−	6006.15i	0.493215	−	0.854274i	0.999969	+	0.00781688i	$0.00248822\pi$
$368$	1458.00	−	2525.33i	0.206531	−	0.357722i
$369$	889.223	+	1540.18i	0.125450	+	0.217286i
$370$	5850.68			0.822061
$371$		0			0
$372$	1675.59			0.233536
$373$	−7046.55	−	12205.0i	−0.978168	−	1.69424i	−0.669058	−	0.743210i	$-0.733302\pi$
$373$	−7046.55	−	12205.0i	−0.978168	−	1.69424i	−0.309110	−	0.951026i	$-0.600031\pi$
$374$	528.916	−	916.109i	0.0731272	−	0.126660i
$375$	2168.98	−	3756.79i	0.298682	−	0.517333i
$376$	−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
$381$	−3120.26	+	5404.45i	−0.419569	+	0.726715i
$382$	−1226.72	+	2124.74i	−0.164305	+	0.284585i
$383$	−4485.24	−	7768.66i	−0.598394	−	1.03645i	−0.993058	−	0.117623i	$-0.962472\pi$
$383$	−4485.24	−	7768.66i	−0.598394	−	1.03645i	0.394664	−	0.918825i	$-0.370861\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	−6958.58			−0.917571
$387$	−1544.82	−	2675.71i	−0.202914	−	0.351457i
$388$	−1807.82	+	3131.23i	−0.236542	+	0.409702i
$389$	1851.29	−	3206.53i	0.241296	−	0.417937i	−0.719788	−	0.694194i	$-0.755761\pi$
$389$	1851.29	−	3206.53i	0.241296	−	0.417937i	0.961084	+	0.276257i	$0.0890942\pi$
$390$	61.9857	+	107.362i	0.00804812	+	0.0139398i
$391$	9193.34			1.18907
$392$		0			0
$393$	−3808.58			−0.488849
$394$	−3193.47	−	5531.26i	−0.408337	−	0.707260i
$395$	−3144.61	+	5446.62i	−0.400563	+	0.693795i
$396$	−188.735	+	326.899i	−0.0239502	+	0.0414830i
$397$	−1041.62	−	1804.13i	−0.131681	−	0.228078i	0.792644	−	0.609685i	$-0.208704\pi$
$397$	−1041.62	−	1804.13i	−0.131681	−	0.228078i	−0.924325	+	0.381607i	$0.875371\pi$
$398$	−2130.30			−0.268297
$399$		0			0
$400$	−1120.47			−0.140059
$401$	5317.01	+	9209.33i	0.662141	+	1.14686i	0.980052	+	0.198742i	$0.0636855\pi$
$401$	5317.01	+	9209.33i	0.662141	+	1.14686i	−0.317910	+	0.948121i	$0.602981\pi$
$402$	−1186.94	+	2055.84i	−0.147262	+	0.255065i
$403$	−194.564	+	336.994i	−0.0240494	+	0.0416548i
$404$	−627.222	−	1086.38i	−0.0772412	−	0.133786i
$405$	−600.551			−0.0736830
$406$		0			0
$407$	−4137.06			−0.503848
$408$	−605.324	−	1048.45i	−0.0734510	−	0.127221i
$409$	−3258.18	+	5643.34i	−0.393904	+	0.682262i	−0.992961	−	0.118445i	$-0.962209\pi$
$409$	−3258.18	+	5643.34i	−0.393904	+	0.682262i	0.599056	+	0.800707i	$0.295542\pi$
$410$	−1465.09	+	2537.60i	−0.176477	+	0.305667i
$411$	4609.78	+	7984.38i	0.553245	+	0.958249i
$412$	−923.899			−0.110479
$413$		0			0
$414$	−3280.50			−0.389439
$415$	781.691	+	1353.93i	0.0924620	+	0.160149i
$416$	44.5887	−	77.2300i	0.00525515	−	0.00910219i
$417$	−1520.39	+	2633.40i	−0.178547	+	0.309252i
$418$	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
$423$	−2745.02	+	4754.51i	−0.315526	+	0.546507i
$424$	550.116	−	952.829i	0.0630094	−	0.109136i
$425$	−1766.27	−	3059.27i	−0.201592	−	0.349168i
$426$	−1713.97			−0.194934
$427$		0			0
$428$	501.945			0.0566879
$429$	−43.8305	−	75.9167i	−0.00493277	−	0.00854380i
$430$	2545.25	−	4408.50i	0.285449	−	0.494412i
$431$	1868.45	−	3236.25i	0.208817	−	0.361681i	−0.742525	−	0.669818i	$-0.766372\pi$
$431$	1868.45	−	3236.25i	0.208817	−	0.361681i	0.951342	+	0.308137i	$0.0997055\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	5757.46			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$433$	5757.46			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$434$		0			0
$435$	3472.79			0.382776
$436$	−1491.05	−	2582.58i	−0.163781	−	0.283677i
$437$	−11395.5	+	19737.6i	−1.24742	+	2.16059i
$438$	2992.37	−	5182.94i	0.326441	−	0.565412i
$439$	−4906.38	−	8498.10i	−0.533414	−	0.923900i	−0.999238	−	0.0390229i	$-0.987575\pi$
$439$	−4906.38	−	8498.10i	−0.533414	−	0.923900i	0.465824	−	0.884877i	$-0.345758\pi$
$440$	−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	$-0.267883\pi$
$443$	−2915.15	−	5049.19i	−0.312648	−	0.541522i	−0.978935	+	0.204174i	$0.934549\pi$
$444$	−2367.35	+	4100.37i	−0.253039	+	0.438277i
$445$	2051.84	−	3553.89i	0.218576	−	0.378585i
$446$	2028.27	+	3513.06i	0.215339	+	0.372978i
$447$	−3694.41			−0.390916
$448$		0			0
$449$	−8674.94			−0.911794			−0.455897	−	0.890033i	$-0.650681\pi$
$449$	−8674.94			−0.911794			−0.455897	+	0.890033i	$0.650681\pi$
$450$	630.265	+	1091.65i	0.0660244	+	0.114358i
$451$	1035.97	−	1794.36i	0.108164	−	0.187346i
$452$	2087.53	−	3615.70i	0.217232	−	0.376257i
$453$	−3367.10	−	5831.99i	−0.349228	−	0.604881i
$454$	−4847.91			−0.501154
$455$		0			0
$456$	3001.29			0.308220
$457$	−4553.41	−	7886.74i	−0.466082	−	0.807278i	0.533167	−	0.846010i	$-0.321002\pi$
$457$	−4553.41	−	7886.74i	−0.466082	−	0.807278i	−0.999250	+	0.0387315i	$0.987668\pi$
$458$	−1967.17	+	3407.24i	−0.200698	+	0.347619i
$459$	−680.989	+	1179.51i	−0.0692502	+	0.119945i
$460$	−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
$465$	1552.90	−	2689.70i	0.154869	−	0.268240i
$466$	−4478.33	+	7756.70i	−0.445182	+	0.771078i
$467$	65.2797	+	113.068i	0.00646849	+	0.0112038i	0.869242	−	0.494388i	$-0.164608\pi$
$467$	65.2797	+	113.068i	0.00646849	+	0.0112038i	−0.862773	+	0.505591i	$0.831274\pi$
$468$	−100.325			−0.00990921
$469$		0			0
$470$	−9045.40			−0.887730
$471$	5680.74	+	9839.32i	0.555742	+	0.962573i
$472$	2357.74	−	4083.73i	0.229924	−	0.398239i
$473$	−1799.76	+	3117.28i	−0.174954	+	0.303029i
$474$	−2544.79	−	4407.71i	−0.246595	−	0.427116i
$475$	8757.45			0.845935
$476$		0			0
$477$	−1237.76			−0.118812
$478$	−6116.92	−	10594.8i	−0.585317	−	1.01380i
$479$	5922.90	−	10258.8i	0.564978	−	0.978570i	−0.432074	−	0.901838i	$-0.642218\pi$
$479$	5922.90	−	10258.8i	0.564978	−	0.978570i	0.997052	−	0.0767319i	$-0.0244485\pi$
$480$	−355.882	+	616.406i	−0.0338411	+	0.0586145i
$481$	−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
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	2403.61	−	4163.17i	0.223650	−	0.387374i	−0.732263	−	0.681022i	$-0.761536\pi$
$487$	2403.61	−	4163.17i	0.223650	−	0.387374i	0.955914	+	0.293648i	$0.0948693\pi$
$488$	988.870	+	1712.77i	0.0917296	+	0.158880i
$489$	6325.68			0.584984
$490$		0			0
$491$	6068.04			0.557733			0.278866	−	0.960330i	$-0.410041\pi$
$491$	6068.04			0.557733			0.278866	+	0.960330i	$0.410041\pi$
$492$	−1185.63	−	2053.57i	−0.108643	−	0.188175i
$493$	3937.93	−	6820.70i	0.359748	−	0.623101i
$494$	−348.500	+	603.619i	−0.0317404	+	0.0549759i
$495$	349.831	+	605.924i	0.0317651	+	0.0550187i
$496$	−2234.12			−0.202248
$497$		0			0
$498$	−1265.18			−0.113843
$499$	7753.21	+	13429.0i	0.695554	+	1.20473i	0.969994	+	0.243130i	$0.0781742\pi$
$499$	7753.21	+	13429.0i	0.695554	+	1.20473i	−0.274440	+	0.961604i	$0.588492\pi$
$500$	−2891.98	+	5009.06i	−0.258667	+	0.448024i
$501$	−2253.62	+	3903.39i	−0.200967	+	0.348085i
$502$	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
$507$	−3283.85	+	5687.80i	−0.287655	+	0.498233i
$508$	4160.35	−	7205.94i	0.363358	−	0.629354i
$509$	−2526.87	−	4376.66i	−0.220042	−	0.381124i	0.734778	−	0.678307i	$-0.237286\pi$
$509$	−2526.87	−	4376.66i	−0.220042	−	0.381124i	−0.954821	+	0.297183i	$0.903953\pi$
$510$	−2244.00			−0.194835
$511$		0			0
$512$	512.000			0.0441942
$513$	−1688.23	−	2924.09i	−0.145296	−	0.251661i
$514$	−408.223	+	707.063i	−0.0350310	+	0.0606755i
$515$	−856.248	+	1483.07i	−0.0732637	+	0.126896i
$516$	2059.76	+	3567.61i	0.175729	+	0.304371i
$517$	6396.07			0.544098
$518$		0			0
$519$	1413.77			0.119571
$520$	−82.6476	−	143.150i	−0.00696988	−	0.0120722i
$521$	4868.36	−	8432.25i	0.409380	−	0.709067i	−0.585441	−	0.810715i	$-0.699078\pi$
$521$	4868.36	−	8432.25i	0.409380	−	0.709067i	0.994820	+	0.101649i	$0.0324118\pi$
$522$	−1405.19	+	2433.86i	−0.117823	+	0.204075i
$523$	−5898.34	−	10216.2i	−0.493148	−	0.854157i	0.506821	−	0.862051i	$-0.330820\pi$
$523$	−5898.34	−	10216.2i	−0.493148	−	0.854157i	−0.999969	+	0.00789446i	$0.997487\pi$
$524$	5078.11			0.423355
$525$		0			0
$526$	−9252.01			−0.766933
$527$	−3521.79	−	6099.91i	−0.291103	−	0.504206i
$528$	251.647	−	435.865i	0.0207415	−	0.0359254i
$529$	−10524.0	+	18228.1i	−0.864962	+	1.49816i
$530$	−1019.67	−	1766.12i	−0.0835691	−	0.144746i
$531$	−5304.92			−0.433548
$532$		0			0
$533$	550.685			0.0447520
$534$	1660.46	+	2876.00i	0.134560	+	0.233065i
$535$	465.191	−	805.734i	0.0375924	−	0.0651120i
$536$	1582.59	−	2741.12i	0.127532	−	0.220893i
$537$	1998.73	+	3461.90i	0.160617	+	0.278198i
$538$	1742.59			0.139644
$539$		0			0
$540$	800.735			0.0638114
$541$	2155.41	+	3733.28i	0.171291	+	0.296684i	0.938871	−	0.344268i	$-0.111873\pi$
$541$	2155.41	+	3733.28i	0.171291	+	0.296684i	−0.767581	+	0.640952i	$0.778540\pi$
$542$	6472.35	−	11210.4i	0.512936	−	0.888431i
$543$	1496.59	−	2592.17i	0.118278	−	0.204863i
$544$	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
$549$	1112.48	−	1926.87i	0.0864835	−	0.149794i
$550$	734.278	−	1271.81i	0.0569268	−	0.0986001i
$551$	9762.45	+	16909.1i	0.754799	+	1.30735i
$552$	4373.99			0.337264
$553$		0			0
$554$	9423.76			0.722703
$555$	4388.01	+	7600.26i	0.335605	+	0.581285i
$556$	2027.19	−	3511.20i	0.154626	−	0.267820i
$557$	−870.588	+	1507.90i	−0.0662262	+	0.114707i	−0.897237	−	0.441549i	$-0.854429\pi$
$557$	−870.588	+	1507.90i	−0.0662262	+	0.114707i	0.831011	+	0.556256i	$0.187763\pi$
$558$	1256.69	+	2176.65i	0.0953405	+	0.165135i
$559$	−956.689			−0.0723858
$560$		0			0
$561$	1586.75			0.119416
$562$	7165.66	+	12411.3i	0.537838	+	0.931563i
$563$	5673.42	−	9826.66i	0.424700	−	0.735602i	−0.571692	−	0.820468i	$-0.693713\pi$
$563$	5673.42	−	9826.66i	0.424700	−	0.735602i	0.996392	+	0.0848658i	$0.0270461\pi$
$564$	3660.03	−	6339.35i	0.273253	−	0.473289i
$565$	−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	0.975442	+	0.220258i	$0.0706900\pi$
$569$	9208.72	+	15950.0i	0.678470	+	1.17514i	−0.296972	+	0.954886i	$0.595977\pi$
$570$	2781.53	−	4817.75i	0.204395	−	0.354023i
$571$	−4999.25	+	8658.95i	−0.366396	+	0.634616i	−0.988999	−	0.147922i	$-0.952742\pi$
$571$	−4999.25	+	8658.95i	−0.366396	+	0.634616i	0.622603	+	0.782538i	$0.286075\pi$
$572$	58.4407	+	101.222i	0.00427190	+	0.00739915i
$573$	−3680.16			−0.268309
$574$		0			0
$575$	12762.8			0.925648
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−700.855	+	1213.92i	−0.0505667	+	0.0875840i	−0.890201	−	0.455568i	$-0.849436\pi$
$577$	−700.855	+	1213.92i	−0.0505667	+	0.0875840i	0.839634	+	0.543152i	$0.182769\pi$
$578$	2368.44	−	4102.26i	0.170440	−	0.295210i
$579$	−5218.94	−	9039.47i	−0.374597	−	0.648821i
$580$	−4630.38			−0.331494
$581$		0			0
$582$	−5423.46			−0.386271
$583$	721.015	+	1248.83i	0.0512202	+	0.0887160i
$584$	−3989.83	+	6910.59i	−0.282706	+	0.489661i
$585$	−92.9786	+	161.044i	−0.00657127	+	0.0113818i
$586$	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
$591$	4790.21	−	8296.88i	0.333406	−	0.577476i
$592$	3156.47	−	5467.16i	0.219139	−	0.379559i
$593$	10231.0	+	17720.6i	0.708493	+	1.22715i	0.965416	+	0.260715i	$0.0839581\pi$
$593$	10231.0	+	17720.6i	0.708493	+	1.22715i	−0.256923	+	0.966432i	$0.582709\pi$
$594$	−566.205			−0.0391106
$595$		0			0
$596$	4925.88			0.338544
$597$	−1597.72	−	2767.34i	−0.109532	−	0.189715i
$598$	−507.893	+	879.697i	−0.0347313	+	0.0601563i
$599$	−4995.21	+	8651.96i	−0.340733	+	0.590166i	−0.984569	−	0.174997i	$-0.944008\pi$
$599$	−4995.21	+	8651.96i	−0.340733	+	0.590166i	0.643836	+	0.765163i	$0.277342\pi$
$600$	−840.353	−	1455.53i	−0.0571788	−	0.0990366i
$601$	−17435.9			−1.18341			−0.591703	−	0.806156i	$-0.701544\pi$
$601$	−17435.9			−1.18341			−0.591703	+	0.806156i	$0.701544\pi$
$602$		0			0
$603$	−3560.82			−0.240477
$604$	4489.47	+	7775.99i	0.302440	+	0.523842i
$605$	−4526.60	+	7840.29i	−0.304186	+	0.526865i
$606$	940.833	−	1629.57i	0.0630672	−	0.109236i
$607$	8350.16	+	14462.9i	0.558356	+	0.967102i	0.997634	+	0.0687503i	$0.0219012\pi$
$607$	8350.16	+	14462.9i	0.558356	+	0.967102i	−0.439277	+	0.898351i	$0.644766\pi$
$608$	−4001.72			−0.266926
$609$		0			0
$610$	3665.85			0.243321
$611$	849.979	+	1472.21i	0.0562790	+	0.0974781i
$612$	907.986	−	1572.68i	0.0599725	−	0.103875i
$613$	13351.5	−	23125.4i	0.879707	−	1.52370i	0.0280452	−	0.999607i	$-0.491072\pi$
$613$	13351.5	−	23125.4i	0.879707	−	1.52370i	0.851662	−	0.524091i	$-0.175595\pi$
$614$	6786.53	+	11754.6i	0.446062	+	0.772602i
$615$	−4395.26			−0.288185
$616$		0			0
$617$	27790.4			1.81329			0.906645	−	0.421894i	$-0.138635\pi$
$617$	27790.4			1.81329			0.906645	+	0.421894i	$0.138635\pi$
$618$	−692.924	−	1200.18i	−0.0451028	−	0.0781203i
$619$	868.040	−	1503.49i	0.0563642	−	0.0976257i	−0.836467	−	0.548018i	$-0.815383\pi$
$619$	868.040	−	1503.49i	0.0563642	−	0.0976257i	0.892831	+	0.450392i	$0.148716\pi$
$620$	−2070.53	+	3586.26i	−0.134120	+	0.232303i
$621$	−2460.37	−	4261.49i	−0.158988	−	0.275375i
$622$	−10273.5			−0.662269
$623$		0			0
$624$	133.766			0.00858163
$625$	983.599	+	1703.64i	0.0629503	+	0.109033i
$626$	−3763.56	+	6518.67i	−0.240291	+	0.416196i
$627$	−1966.84	+	3406.66i	−0.125276	+	0.216984i
$628$	−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
$633$	3086.24	−	5345.53i	0.193787	−	0.335649i
$634$	1034.95	−	1792.58i	0.0648311	−	0.112291i
$635$	−7711.43	−	13356.6i	−0.481919	−	0.834709i
$636$	1650.35			0.102894
$637$		0			0
$638$	3274.18			0.203175
$639$	−1285.47	−	2226.51i	−0.0795815	−	0.137839i
$640$	474.510	−	821.875i	0.0293073	−	0.0507617i
$641$	6884.81	−	11924.8i	0.424233	−	0.734794i	−0.572115	−	0.820173i	$-0.693877\pi$
$641$	6884.81	−	11924.8i	0.424233	−	0.734794i	0.996348	+	0.0853796i	$0.0272103\pi$
$642$	376.458	+	652.045i	0.0231427	+	0.0400844i
$643$	−26969.9			−1.65411			−0.827053	−	0.562124i	$-0.809985\pi$
$643$	−26969.9			−1.65411			−0.827053	+	0.562124i	$0.809985\pi$
$644$		0			0
$645$	7635.75			0.466136
$646$	−6308.17	−	10926.1i	−0.384198	−	0.665450i
$647$	12200.9	−	21132.5i	0.741368	−	1.28409i	−0.210504	−	0.977593i	$-0.567510\pi$
$647$	12200.9	−	21132.5i	0.741368	−	1.28409i	0.951872	−	0.306495i	$-0.0991562\pi$
$648$	−324.000	+	561.184i	−0.0196419	+	0.0340207i
$649$	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	$-0.325491\pi$
$653$	−7984.79	−	13830.1i	−0.478513	−	0.828809i	−0.999696	+	0.0246357i	$0.992157\pi$
$654$	2236.58	−	3873.87i	0.133727	−	0.231621i
$655$	4706.27	−	8151.50i	0.280747	−	0.486268i
$656$	1580.84	+	2738.10i	0.0940876	+	0.162965i
$657$	8977.11			0.533075
$658$		0			0
$659$	−11596.2			−0.685467			−0.342733	−	0.939433i	$-0.611353\pi$
$659$	−11596.2			−0.685467			−0.342733	+	0.939433i	$0.611353\pi$
$660$	−466.441	−	807.899i	−0.0275094	−	0.0476476i
$661$	6301.11	−	10913.8i	0.370779	−	0.642208i	−0.618907	−	0.785464i	$-0.712424\pi$
$661$	6301.11	−	10913.8i	0.370779	−	0.642208i	0.989686	+	0.143257i	$0.0457575\pi$
$662$	−8800.06	+	15242.2i	−0.516653	+	0.894869i
$663$	210.864	+	365.228i	0.0123519	+	0.0213941i
$664$	1686.90			0.0985912
$665$		0			0
$666$	−7102.05			−0.413212
$667$	14227.5	+	24642.8i	0.825924	+	1.43054i
$668$	3004.83	−	5204.52i	0.174042	−	0.301450i
$669$	−3042.40	+	5269.59i	−0.175824	+	0.304536i
$670$	−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
$675$	−945.397	+	1637.48i	−0.0539087	+	0.0933726i
$676$	4378.47	−	7583.73i	0.249116	−	0.431482i
$677$	1309.69	+	2268.45i	0.0743508	+	0.128779i	0.900804	−	0.434226i	$-0.142978\pi$
$677$	1309.69	+	2268.45i	0.0743508	+	0.128779i	−0.826453	+	0.563006i	$0.809645\pi$
$678$	6262.58			0.354739
$679$		0			0
$680$	2992.00			0.168732
$681$	−3635.94	−	6297.63i	−0.204595	−	0.354369i
$682$	1464.09	−	2535.87i	0.0822034	−	0.142381i
$683$	14964.9	−	25919.9i	0.838383	−	1.45212i	−0.0528633	−	0.998602i	$-0.516835\pi$
$683$	14964.9	−	25919.9i	0.838383	−	1.45212i	0.891246	−	0.453520i	$-0.149832\pi$
$684$	2250.97	+	3898.79i	0.125830	+	0.217945i
$685$	−22785.3			−1.27092
$686$		0			0
$687$	−5901.51			−0.327739
$688$	−2746.35	−	4756.81i	−0.152185	−	0.263593i
$689$	−191.633	+	331.918i	−0.0105960	+	0.0183528i
$690$	4053.72	−	7021.24i	0.223656	−	0.387383i
$691$	3380.45	+	5855.11i	0.186105	+	0.322343i	0.943948	−	0.330094i	$-0.107080\pi$
$691$	3380.45	+	5855.11i	0.186105	+	0.322343i	−0.757844	+	0.652436i	$0.773747\pi$
$692$	−1885.02			−0.103552
$693$		0			0
$694$	15877.1			0.868423
$695$	−3757.51	−	6508.20i	−0.205080	−	0.355209i
$696$	1873.58	−	3245.14i	0.102037	−	0.176734i
$697$	−4983.96	+	8632.48i	−0.270848	+	0.469122i
$698$	−9927.75	−	17195.4i	−0.538354	−	0.932456i
$699$	−13435.0			−0.726979
$700$		0			0
$701$	467.205			0.0251727			0.0125864	−	0.999921i	$-0.495994\pi$
$701$	467.205			0.0251727			0.0125864	+	0.999921i	$0.495994\pi$
$702$	−75.2435	−	130.326i	−0.00404542	−	0.00700687i
$703$	−24670.5	+	42730.6i	−1.32357	+	2.29248i
$704$	−335.529	+	581.153i	−0.0179627	+	0.0311123i
$705$	−6784.05	−	11750.3i	−0.362414	−	0.627720i
$706$	20206.1			1.07715
$707$		0			0
$708$	7073.23			0.375464
$709$	−4412.32	−	7642.36i	−0.233721	−	0.404816i	0.725179	−	0.688560i	$-0.241757\pi$
$709$	−4412.32	−	7642.36i	−0.233721	−	0.404816i	−0.958900	+	0.283744i	$0.908424\pi$
$710$	2117.95	−	3668.40i	0.111951	−	0.193905i
$711$	3817.19	−	6611.56i	0.201344	−	0.348738i
$712$	−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
$717$	9175.38	−	15892.2i	0.477909	−	0.827763i
$718$	4825.27	−	8357.62i	0.250804	−	0.434406i
$719$	−10549.4	−	18272.2i	−0.547188	−	0.947757i	−0.998466	−	0.0553733i	$-0.982365\pi$
$719$	−10549.4	−	18272.2i	−0.547188	−	0.947757i	0.451278	−	0.892383i	$-0.350968\pi$
$720$	−1067.65			−0.0552623
$721$		0			0
$722$	17558.9			0.905090
$723$	−9342.57	−	16181.8i	−0.480573	−	0.832376i
$724$	−1995.45	+	3456.23i	−0.102432	+	0.177417i
$725$	5466.92	−	9468.98i	0.280050	−	0.485061i
$726$	−3663.18	−	6344.81i	−0.187263	−	0.324350i
$727$	4616.48			0.235510			0.117755	−	0.993043i	$-0.462430\pi$
$727$	4616.48			0.235510			0.117755	+	0.993043i	$0.462430\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	7395.36	+	12809.1i	0.374951	+	0.649435i
$731$	8658.49	−	14996.9i	0.438093	−	0.758799i
$732$	−1483.30	+	2569.16i	−0.0748969	+	0.129725i
$733$	−5344.03	−	9256.13i	−0.269285	−	0.466416i	0.699392	−	0.714738i	$-0.253454\pi$
$733$	−5344.03	−	9256.13i	−0.269285	−	0.466416i	−0.968678	+	0.248322i	$0.920121\pi$
$734$	−13870.6			−0.697511
$735$		0			0
$736$	−5831.99			−0.292079
$737$	2074.23	+	3592.68i	0.103671	+	0.179563i
$738$	1778.45	−	3080.36i	0.0887066	−	0.153644i
$739$	7683.78	−	13308.7i	0.382480	−	0.662474i	−0.608936	−	0.793219i	$-0.708404\pi$
$739$	7683.78	−	13308.7i	0.382480	−	0.662474i	0.991416	+	0.130745i	$0.0417369\pi$
$740$	−5850.68	−	10133.7i	−0.290642	−	0.503407i
$741$	−1045.50			−0.0518318
$742$		0			0
$743$	6502.58			0.321072			0.160536	−	0.987030i	$-0.448678\pi$
$743$	6502.58			0.321072			0.160536	+	0.987030i	$0.448678\pi$
$744$	−1675.59	−	2902.21i	−0.0825673	−	0.143011i
$745$	4565.19	−	7907.14i	0.224504	−	0.388853i
$746$	−14093.1	+	24410.0i	−0.691669	+	1.19801i
$747$	−948.883	−	1643.51i	−0.0464763	−	0.0804994i
$748$	−2115.66			−0.103418
$749$		0			0
$750$	−8675.94			−0.422401
$751$	9937.07	+	17211.5i	0.482835	+	0.836295i	0.999806	−	0.0197085i	$-0.00627380\pi$
$751$	9937.07	+	17211.5i	0.482835	+	0.836295i	−0.516971	+	0.856003i	$0.672940\pi$
$752$	−4880.03	+	8452.47i	−0.236644	+	0.409880i
$753$	−8856.62	+	15340.1i	−0.428623	+	0.742397i
$754$	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
$759$	−2866.41	+	4964.77i	−0.137081	+	0.237430i
$760$	−3708.70	+	6423.66i	−0.177012	+	0.306593i
$761$	17609.9	+	30501.3i	0.838842	+	1.45292i	0.890863	+	0.454271i	$0.150100\pi$
$761$	17609.9	+	30501.3i	0.838842	+	1.45292i	−0.0520212	+	0.998646i	$0.516566\pi$
$762$	12481.0			0.593361
$763$		0			0
$764$	4906.88			0.232362
$765$	−1683.00	−	2915.04i	−0.0795412	−	0.137769i
$766$	−8970.47	+	15537.3i	−0.423128	+	0.732880i
$767$	−821.319	+	1422.57i	−0.0386651	+	0.0669698i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	2264.35			0.106183			0.0530915	−	0.998590i	$-0.483093\pi$
$769$	2264.35			0.106183			0.0530915	+	0.998590i	$0.483093\pi$
$770$		0			0
$771$	−1224.67			−0.0572054
$772$	6958.58	+	12052.6i	0.324410	+	0.561895i
$773$	−4766.39	+	8255.64i	−0.221779	+	0.384133i	−0.955348	−	0.295482i	$-0.904520\pi$
$773$	−4766.39	+	8255.64i	−0.221779	+	0.384133i	0.733569	+	0.679615i	$0.237853\pi$
$774$	−3089.64	+	5351.42i	−0.143482	+	0.248518i
$775$	−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
$780$	123.971	−	214.725i	0.00569088	−	0.00985690i
$781$	−1497.62	+	2593.95i	−0.0686159	+	0.118846i
$782$	−9193.34	−	15923.3i	−0.420401	−	0.728155i
$783$	−4215.56			−0.192404
$784$		0			0
$785$	−28078.8			−1.27666
$786$	3808.58	+	6596.66i	0.172834	+	0.299357i
$787$	−16606.5	+	28763.3i	−0.752170	+	1.30280i	0.194599	+	0.980883i	$0.437659\pi$
$787$	−16606.5	+	28763.3i	−0.752170	+	1.30280i	−0.946769	+	0.321913i	$0.895674\pi$
$788$	−6386.94	+	11062.5i	−0.288738	+	0.500109i
$789$	−6939.01	−	12018.7i	−0.313099	−	0.542304i
$790$	12578.4			0.566481
$791$		0			0
$792$	754.940			0.0338708
$793$	−344.472	−	596.643i	−0.0154257	−	0.0267181i
$794$	−2083.24	+	3608.27i	−0.0931124	+	0.161275i
$795$	1529.50	−	2649.18i	0.0682339	−	0.118185i
$796$	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
$801$	−2490.69	+	4314.01i	−0.109868	+	0.190297i
$802$	10634.0	−	18418.7i	0.468205	−	0.810954i
$803$	−5229.31	−	9057.43i	−0.229811	−	0.398044i
$804$	4747.76			0.208259
$805$		0			0
$806$	778.255			0.0340110
$807$	1306.94	+	2263.69i	0.0570092	+	0.0987429i
$808$	−1254.44	+	2172.76i	−0.0546178	+	0.0946008i
$809$	388.780	−	673.387i	0.0168959	−	0.0292646i	−0.857454	−	0.514561i	$-0.827955\pi$
$809$	388.780	−	673.387i	0.0168959	−	0.0292646i	0.874350	+	0.485296i	$0.161288\pi$
$810$	600.551	+	1040.19i	0.0260509	+	0.0451215i
$811$	−16559.4			−0.716991			−0.358496	−	0.933531i	$-0.616710\pi$
$811$	−16559.4			−0.716991			−0.358496	+	0.933531i	$0.616710\pi$
$812$		0			0
$813$	19417.0			0.837620
$814$	4137.06	+	7165.59i	0.178137	+	0.308543i
$815$	−7816.66	+	13538.8i	−0.335958	+	0.581896i
$816$	−1210.65	+	2096.90i	−0.0519377	+	0.0899587i
$817$	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	$-0.168231\pi$
$821$	−115.612	−	200.246i	−0.00491460	−	0.00851235i	−0.868472	+	0.495738i	$0.834898\pi$
$822$	9219.56	−	15968.8i	0.391203	−	0.677584i
$823$	2611.43	−	4523.13i	0.110606	−	0.191575i	−0.805409	−	0.592720i	$-0.798054\pi$
$823$	2611.43	−	4523.13i	0.110606	−	0.191575i	0.916015	+	0.401145i	$0.131388\pi$
$824$	923.899	+	1600.24i	0.0390601	+	0.0676541i
$825$	2202.84			0.0929611
$826$		0			0
$827$	−46225.5			−1.94367			−0.971836	−	0.235658i	$-0.924275\pi$
$827$	−46225.5			−1.94367			−0.971836	+	0.235658i	$0.924275\pi$
$828$	3280.50	+	5681.99i	0.137687	+	0.238481i
$829$	−19797.1	+	34289.6i	−0.829410	+	1.43658i	0.0690913	+	0.997610i	$0.477990\pi$
$829$	−19797.1	+	34289.6i	−0.829410	+	1.43658i	−0.898502	+	0.438970i	$0.855343\pi$
$830$	1563.38	−	2707.86i	0.0653805	−	0.113242i
$831$	7067.82	+	12241.8i	0.295042	+	0.511028i
$832$	−178.355			−0.00743191
$833$		0			0
$834$	6081.58			0.252503
$835$	−5569.61	−	9646.85i	−0.230832	−	0.399812i
$836$	2622.45	−	4542.22i	0.108492	−	0.187914i
$837$	−1885.04	+	3264.98i	−0.0778452	+	0.134832i
$838$	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
$843$	−10748.5	+	18616.9i	−0.439143	+	0.760618i
$844$	−4114.99	+	7127.37i	−0.167824	+	0.290680i
$845$	−8115.72	−	14056.8i	−0.330402	−	0.572272i
$846$	10980.1			0.446221
$847$		0			0
$848$	−2200.46			−0.0891088
$849$	−9520.50	−	16490.0i	−0.384856	−	0.666590i
$850$	−3532.54	+	6118.54i	−0.142547	+	0.246899i
$851$	−35954.1	+	62274.3i	−1.44828	+	2.50850i
$852$	1713.97	+	2968.68i	0.0689196	+	0.119372i
$853$	8795.55			0.353053			0.176526	−	0.984296i	$-0.443514\pi$
$853$	8795.55			0.353053			0.176526	+	0.984296i	$0.443514\pi$
$854$		0			0
$855$	8344.58			0.333776
$856$	−501.945	−	869.394i	−0.0200422	−	0.0347141i
$857$	15127.5	−	26201.6i	0.602969	−	1.04437i	−0.389400	−	0.921069i	$-0.627317\pi$
$857$	15127.5	−	26201.6i	0.602969	−	1.04437i	0.992369	−	0.123305i	$-0.0393492\pi$
$858$	−87.6610	+	151.833i	−0.00348799	+	0.00604138i
$859$	22496.7	+	38965.5i	0.893573	+	1.54771i	0.835561	+	0.549398i	$0.185143\pi$
$859$	22496.7	+	38965.5i	0.893573	+	1.54771i	0.0580118	+	0.998316i	$0.481524\pi$
$860$	−10181.0			−0.403685
$861$		0			0
$862$	−7473.79			−0.295311
$863$	−22333.9	−	38683.5i	−0.880946	−	1.52584i	−0.850291	−	0.526313i	$-0.823574\pi$
$863$	−22333.9	−	38683.5i	−0.880946	−	1.52584i	−0.0306555	−	0.999530i	$-0.509759\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−1747.00	+	3025.89i	−0.0686701	+	0.118940i
$866$	−5757.46	−	9972.22i	−0.225920	−	0.391305i
$867$	7105.31			0.278327
$868$		0			0
$869$	−8894.29			−0.347201
$870$	−3472.79	−	6015.05i	−0.135332	−	0.234401i
$871$	−551.294	+	954.868i	−0.0214465	+	0.0371464i
$872$	−2982.11	+	5165.16i	−0.115811	+	0.200590i
$873$	−4067.59	−	7045.28i	−0.157694	−	0.273135i
$874$	45582.1			1.76411
$875$		0			0
$876$	−11969.5			−0.461657
$877$	−2993.42	−	5184.76i	−0.115257	−	0.199631i	0.802625	−	0.596484i	$-0.203436\pi$
$877$	−2993.42	−	5184.76i	−0.115257	−	0.199631i	−0.917883	+	0.396852i	$0.870103\pi$
$878$	−9812.76	+	16996.2i	−0.377181	+	0.653296i
$879$	−13850.7	+	23990.1i	−0.531481	+	0.920552i
$880$	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
$885$	6555.30	−	11354.1i	0.248988	−	0.431259i
$886$	−5830.30	+	10098.4i	−0.221075	+	0.382914i
$887$	4426.71	+	7667.28i	0.167570	+	0.290239i	0.937565	−	0.347811i	$-0.113075\pi$
$887$	4426.71	+	7667.28i	0.167570	+	0.290239i	−0.769995	+	0.638050i	$0.779741\pi$
$888$	9469.40			0.357852
$889$		0			0
$890$	−8207.35			−0.309113
$891$	−424.654	−	735.522i	−0.0159668	−	0.0276554i
$892$	4056.54	−	7026.12i	0.152268	−	0.263735i
$893$	38141.7	−	66063.3i	1.42930	−	2.47562i
$894$	3694.41	+	6398.91i	0.138210	+	0.239386i
$895$	−9879.34			−0.368972
$896$		0			0
$897$	−1523.68			−0.0567159
$898$	8674.94	+	15025.4i	0.322368	+	0.558358i
$899$	10900.6	−	18880.3i	0.404398	−	0.700438i
$900$	1260.53	−	2183.30i	0.0466863	−	0.0808630i
$901$	−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
$906$	−6734.21	+	11664.0i	−0.246941	+	0.427715i
$907$	−8331.23	+	14430.1i	−0.304999	+	0.528274i	−0.977261	−	0.212039i	$-0.931989\pi$
$907$	−8331.23	+	14430.1i	−0.304999	+	0.528274i	0.672262	+	0.740313i	$0.265323\pi$
$908$	4847.91	+	8396.83i	0.177185	+	0.306893i
$909$	2822.50			0.102988
$910$		0			0
$911$	−29071.2			−1.05727			−0.528635	−	0.848849i	$-0.677296\pi$
$911$	−29071.2			−1.05727			−0.528635	+	0.848849i	$0.677296\pi$
$912$	−3001.29	−	5198.39i	−0.108972	−	0.188745i
$913$	−1105.48	+	1914.74i	−0.0400723	+	0.0694072i
$914$	−9106.82	+	15773.5i	−0.329570	+	0.570832i
$915$	2749.38	+	4762.07i	0.0993353	+	0.172054i
$916$	7868.67			0.283830
$917$		0			0
$918$	2723.96			0.0979346
$919$	−3986.70	−	6905.16i	−0.143100	−	0.247857i	0.785562	−	0.618782i	$-0.212374\pi$
$919$	−3986.70	−	6905.16i	−0.143100	−	0.247857i	−0.928663	+	0.370926i	$0.879040\pi$
$920$	−5404.96	+	9361.66i	−0.193691	+	0.335483i
$921$	−10179.8	+	17631.9i	−0.364208	+	0.630827i
$922$	−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
$927$	1039.39	−	1800.27i	0.0368262	−	0.0637849i
$928$	−2498.11	+	4326.86i	−0.0883670	+	0.153056i
$929$	15070.7	+	26103.3i	0.532244	+	0.921874i	0.999291	+	0.0376418i	$0.0119846\pi$
$929$	15070.7	+	26103.3i	0.532244	+	0.921874i	−0.467047	+	0.884233i	$0.654682\pi$
$930$	−6211.59			−0.219017
$931$		0			0
$932$	17913.3			0.629582
$933$	−7705.15	−	13345.7i	−0.270370	−	0.468295i
$934$	130.559	−	226.136i	0.00457391	−	0.00792225i
$935$	−1960.75	+	3396.11i	−0.0685811	+	0.118786i
$936$	100.325	+	173.767i	0.00350343	+	0.00606813i
$937$	−1126.37			−0.0392709			−0.0196354	−	0.999807i	$-0.506251\pi$
$937$	−1126.37			−0.0392709			−0.0196354	+	0.999807i	$0.506251\pi$
$938$		0			0
$939$	−11290.7			−0.392393
$940$	9045.40	+	15667.1i	0.313860	+	0.543622i
$941$	−5166.64	+	8948.89i	−0.178988	+	0.310016i	−0.941534	−	0.336917i	$-0.890616\pi$
$941$	−5166.64	+	8948.89i	−0.178988	+	0.310016i	0.762546	+	0.646934i	$0.223949\pi$
$942$	11361.5	−	19678.6i	0.392969	−	0.680642i
$943$	−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	$-0.306629\pi$
$947$	−12405.1	−	21486.3i	−0.425673	−	0.737288i	−0.996483	+	0.0837944i	$0.973296\pi$
$948$	−5089.58	+	8815.42i	−0.174369	+	0.302016i
$949$	1389.85	−	2407.30i	0.0475412	−	0.0823438i
$950$	−8757.45	−	15168.3i	−0.299083	−	0.518028i
$951$	3104.84			0.105869
$952$		0			0
$953$	−15048.6			−0.511513			−0.255757	−	0.966741i	$-0.582325\pi$
$953$	−15048.6			−0.511513			−0.255757	+	0.966741i	$0.582325\pi$
$954$	1237.76	+	2143.87i	0.0420063	+	0.0727570i
$955$	4547.58	−	7876.65i	0.154090	−	0.266893i
$956$	−12233.8	+	21189.6i	−0.413881	+	0.716864i
$957$	2455.63	+	4253.28i	0.0829460	+	0.143667i
$958$	−23691.6			−0.798999
$959$		0			0
$960$	1423.53			0.0478585
$961$	5146.89	+	8914.67i	0.172767	+	0.299240i
$962$	−1099.55	+	1904.48i	−0.0368514	+	0.0638285i
$963$	−564.688	+	978.068i	−0.0188960	+	0.0327288i
$964$	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
$969$	9462.26	−	16389.1i	0.313696	−	0.543338i
$970$	6701.78	−	11607.8i	0.221836	−	0.384232i
$971$	−12416.5	−	21506.0i	−0.410365	−	0.710773i	0.584565	−	0.811347i	$-0.301265\pi$
$971$	−12416.5	−	21506.0i	−0.410365	−	0.710773i	−0.994930	+	0.100574i	$0.967932\pi$
$972$	−972.000			−0.0320750
$973$		0			0
$974$	−9614.42			−0.316289
$975$	292.737	+	507.035i	0.00961546	+	0.0166545i
$976$	1977.74	−	3425.54i	0.0648626	−	0.112345i
$977$	−19328.4	+	33477.8i	−0.632928	+	1.09626i	0.354022	+	0.935237i	$0.384814\pi$
$977$	−19328.4	+	33477.8i	−0.632928	+	1.09626i	−0.986950	+	0.161026i	$0.948520\pi$
$978$	−6325.68	−	10956.4i	−0.206823	−	0.358228i
$979$	5803.47			0.189458
$980$		0			0
$981$	6709.75			0.218375
$982$	−6068.04	−	10510.2i	−0.197188	−	0.341540i
$983$	13332.1	−	23091.8i	0.432581	−	0.749252i	−0.564514	−	0.825424i	$-0.690936\pi$
$983$	13332.1	−	23091.8i	0.432581	−	0.749252i	0.997095	+	0.0761716i	$0.0242697\pi$
$984$	−2371.26	+	4107.15i	−0.0768222	+	0.133060i
$985$	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
$990$	699.661	−	1211.85i	0.0224613	−	0.0389041i
$991$	−13614.1	+	23580.3i	−0.436393	+	0.755855i	−0.997408	−	0.0719507i	$-0.977078\pi$
$991$	−13614.1	+	23580.3i	−0.436393	+	0.755855i	0.561015	+	0.827806i	$0.310411\pi$
$992$	2234.12	+	3869.61i	0.0715054	+	0.123851i
$993$	−26400.2			−0.843690
$994$		0			0
$995$	7897.24			0.251617
$996$	1265.18	+	2191.35i	0.0402497	+	0.0697145i
$997$	2581.46	−	4471.22i	0.0820016	−	0.142031i	−0.822108	−	0.569332i	$-0.807202\pi$
$997$	2581.46	−	4471.22i	0.0820016	−	0.142031i	0.904110	+	0.427301i	$0.140535\pi$
$998$	15506.4	−	26857.9i	0.491831	−	0.851876i
$999$	−5326.54	−	9225.84i	−0.168693	−	0.292185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.m.67.2		4
3.2	odd	2		882.4.g.be.361.1		4
7.2	even	3	inner	294.4.e.m.79.2		4
7.3	odd	6		294.4.a.o.1.2	yes	2
7.4	even	3		294.4.a.l.1.1	✓	2
7.5	odd	6		294.4.e.k.79.1		4
7.6	odd	2		294.4.e.k.67.1		4
21.2	odd	6		882.4.g.be.667.1		4
21.5	even	6		882.4.g.bk.667.2		4
21.11	odd	6		882.4.a.bb.1.2		2
21.17	even	6		882.4.a.t.1.1		2
21.20	even	2		882.4.g.bk.361.2		4
28.3	even	6		2352.4.a.bu.1.2		2
28.11	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	7.4	even	3
294.4.a.o.1.2	yes	2	7.3	odd	6
294.4.e.k.67.1		4	7.6	odd	2
294.4.e.k.79.1		4	7.5	odd	6
294.4.e.m.67.2		4	1.1	even	1	trivial
294.4.e.m.79.2		4	7.2	even	3	inner
882.4.a.t.1.1		2	21.17	even	6
882.4.a.bb.1.2		2	21.11	odd	6
882.4.g.be.361.1		4	3.2	odd	2
882.4.g.be.667.1		4	21.2	odd	6
882.4.g.bk.361.2		4	21.20	even	2
882.4.g.bk.667.2		4	21.5	even	6
2352.4.a.bu.1.2		2	28.3	even	6
2352.4.a.bw.1.1		2	28.11	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(7.41421 - 12.8418i) q^{10} +(-5.24264 + 9.08052i) q^{11} +(6.00000 + 10.3923i) q^{12} -2.78680 q^{13} +22.2426 q^{15} +(-8.00000 - 13.8564i) q^{16} +(25.2218 - 43.6855i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(62.5269 + 108.300i) q^{19} -29.6569 q^{20} +20.9706 q^{22} +(91.1249 + 157.833i) q^{23} +(12.0000 - 20.7846i) q^{24} +(35.0147 - 60.6473i) q^{25} +(2.78680 + 4.82687i) q^{26} -27.0000 q^{27} +156.132 q^{29} +(-22.2426 - 38.5254i) q^{30} +(69.8162 - 120.925i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(15.7279 + 27.2416i) q^{33} -100.887 q^{34} +36.0000 q^{36} +(197.279 + 341.698i) q^{37} +(125.054 - 216.600i) q^{38} +(-4.18019 + 7.24031i) q^{39} +(29.6569 + 51.3672i) q^{40} -197.605 q^{41} +343.294 q^{43} +(-20.9706 - 36.3221i) q^{44} +(33.3640 - 57.7881i) q^{45} +(182.250 - 315.666i) q^{46} +(-305.002 - 528.279i) q^{47} -48.0000 q^{48} -140.059 q^{50} +(-75.6655 - 131.056i) q^{51} +(5.57359 - 9.65375i) q^{52} +(68.7645 - 119.104i) q^{53} +(27.0000 + 46.7654i) q^{54} -77.7401 q^{55} +375.161 q^{57} +(-156.132 - 270.429i) q^{58} +(294.718 - 510.466i) q^{59} +(-44.4853 + 77.0508i) q^{60} +(123.609 + 214.097i) q^{61} -279.265 q^{62} +64.0000 q^{64} +(-10.3310 - 17.8937i) q^{65} +(31.4558 - 54.4831i) q^{66} +(197.823 - 342.640i) q^{67} +(100.887 + 174.742i) q^{68} +546.749 q^{69} +285.661 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-498.729 + 863.823i) q^{73} +(394.558 - 683.395i) q^{74} +(-105.044 - 181.942i) q^{75} -500.215 q^{76} +16.7208 q^{78} +(424.132 + 734.618i) q^{79} +(59.3137 - 102.734i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(197.605 + 342.262i) q^{82} +210.863 q^{83} +374.000 q^{85} +(-343.294 - 594.602i) q^{86} +(234.198 - 405.643i) q^{87} +(-41.9411 + 72.6442i) q^{88} +(-276.744 - 479.334i) q^{89} -133.456 q^{90} -728.999 q^{92} +(-209.449 - 362.776i) q^{93} +(-610.004 + 1056.56i) q^{94} +(-463.588 + 802.958i) q^{95} +(48.0000 + 83.1384i) q^{96} +903.910 q^{97} +94.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 12 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} + 32 q^{8} - 18 q^{9} + 24 q^{10} - 4 q^{11} + 24 q^{12} - 96 q^{13} + 72 q^{15} - 32 q^{16} + 132 q^{17} - 36 q^{18} + 120 q^{19} - 96 q^{20} + 16 q^{22} + 76 q^{23} + 48 q^{24} + 174 q^{25} + 96 q^{26} - 108 q^{27} - 224 q^{29} - 72 q^{30} + 432 q^{31} - 64 q^{32} + 12 q^{33} - 528 q^{34} + 144 q^{36} + 280 q^{37} + 240 q^{38} - 144 q^{39} + 96 q^{40} - 72 q^{41} - 256 q^{43} - 16 q^{44} + 108 q^{45} + 152 q^{46} - 264 q^{47} - 192 q^{48} - 696 q^{50} - 396 q^{51} + 192 q^{52} - 268 q^{53} + 108 q^{54} - 96 q^{55} + 720 q^{57} + 224 q^{58} + 336 q^{59} - 144 q^{60} - 504 q^{61} - 1728 q^{62} + 256 q^{64} - 228 q^{65} + 24 q^{66} + 384 q^{67} + 528 q^{68} + 456 q^{69} - 792 q^{71} - 144 q^{72} - 312 q^{73} + 560 q^{74} - 522 q^{75} - 960 q^{76} + 576 q^{78} + 848 q^{79} + 192 q^{80} - 162 q^{81} + 72 q^{82} + 1296 q^{83} + 1496 q^{85} + 256 q^{86} - 336 q^{87} - 32 q^{88} - 612 q^{89} - 432 q^{90} - 608 q^{92} - 1296 q^{93} - 528 q^{94} - 904 q^{95} + 192 q^{96} + 4368 q^{97} + 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 12 * q^5 - 24 * q^6 + 32 * q^8 - 18 * q^9 + 24 * q^10 - 4 * q^11 + 24 * q^12 - 96 * q^13 + 72 * q^15 - 32 * q^16 + 132 * q^17 - 36 * q^18 + 120 * q^19 - 96 * q^20 + 16 * q^22 + 76 * q^23 + 48 * q^24 + 174 * q^25 + 96 * q^26 - 108 * q^27 - 224 * q^29 - 72 * q^30 + 432 * q^31 - 64 * q^32 + 12 * q^33 - 528 * q^34 + 144 * q^36 + 280 * q^37 + 240 * q^38 - 144 * q^39 + 96 * q^40 - 72 * q^41 - 256 * q^43 - 16 * q^44 + 108 * q^45 + 152 * q^46 - 264 * q^47 - 192 * q^48 - 696 * q^50 - 396 * q^51 + 192 * q^52 - 268 * q^53 + 108 * q^54 - 96 * q^55 + 720 * q^57 + 224 * q^58 + 336 * q^59 - 144 * q^60 - 504 * q^61 - 1728 * q^62 + 256 * q^64 - 228 * q^65 + 24 * q^66 + 384 * q^67 + 528 * q^68 + 456 * q^69 - 792 * q^71 - 144 * q^72 - 312 * q^73 + 560 * q^74 - 522 * q^75 - 960 * q^76 + 576 * q^78 + 848 * q^79 + 192 * q^80 - 162 * q^81 + 72 * q^82 + 1296 * q^83 + 1496 * q^85 + 256 * q^86 - 336 * q^87 - 32 * q^88 - 612 * q^89 - 432 * q^90 - 608 * q^92 - 1296 * q^93 - 528 * q^94 - 904 * q^95 + 192 * q^96 + 4368 * q^97 + 72 * q^99

Introduction

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