LMFDB - Embedded newform 294.4.e.n.79.1

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:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.n.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(3.89949 + 6.75412i) q^{10} +(30.6985 + 53.1713i) q^{11} +(-6.00000 + 10.3923i) q^{12} -53.6985 q^{13} +11.6985 q^{15} +(-8.00000 + 13.8564i) q^{16} +(16.0503 + 27.7999i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-27.8995 + 48.3233i) q^{19} +15.5980 q^{20} +122.794 q^{22} +(47.3015 - 81.9286i) q^{23} +(12.0000 + 20.7846i) q^{24} +(54.8970 + 95.0843i) q^{25} +(-53.6985 + 93.0085i) q^{26} +27.0000 q^{27} +138.191 q^{29} +(11.6985 - 20.2624i) q^{30} +(66.3015 + 114.838i) q^{31} +(16.0000 + 27.7128i) q^{32} +(92.0955 - 159.514i) q^{33} +64.2010 q^{34} +36.0000 q^{36} +(-74.6030 + 129.216i) q^{37} +(55.7990 + 96.6467i) q^{38} +(80.5477 + 139.513i) q^{39} +(15.5980 - 27.0165i) q^{40} -427.497 q^{41} +437.588 q^{43} +(122.794 - 212.685i) q^{44} +(-17.5477 - 30.3936i) q^{45} +(-94.6030 - 163.857i) q^{46} +(28.5025 - 49.3678i) q^{47} +48.0000 q^{48} +219.588 q^{50} +(48.1508 - 83.3996i) q^{51} +(107.397 + 186.017i) q^{52} +(131.794 + 228.274i) q^{53} +(27.0000 - 46.7654i) q^{54} -239.417 q^{55} +167.397 q^{57} +(138.191 - 239.354i) q^{58} +(225.899 + 391.269i) q^{59} +(-23.3970 - 40.5247i) q^{60} +(289.653 - 501.694i) q^{61} +265.206 q^{62} +64.0000 q^{64} +(104.698 - 181.343i) q^{65} +(-184.191 - 319.028i) q^{66} +(-154.794 - 268.111i) q^{67} +(64.2010 - 111.199i) q^{68} -283.809 q^{69} -1058.98 q^{71} +(36.0000 - 62.3538i) q^{72} +(596.829 + 1033.74i) q^{73} +(149.206 + 258.432i) q^{74} +(164.691 - 285.253i) q^{75} +223.196 q^{76} +322.191 q^{78} +(-659.779 + 1142.77i) q^{79} +(-31.1960 - 54.0330i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-427.497 + 740.447i) q^{82} -1190.33 q^{83} -125.176 q^{85} +(437.588 - 757.924i) q^{86} +(-207.286 - 359.031i) q^{87} +(-245.588 - 425.371i) q^{88} +(-116.543 + 201.858i) q^{89} -70.1909 q^{90} -378.412 q^{92} +(198.905 - 344.513i) q^{93} +(-57.0051 - 98.7356i) q^{94} +(-108.794 - 188.437i) q^{95} +(48.0000 - 83.1384i) q^{96} +1609.44 q^{97} -552.573 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	\( 4 q + 4 q^{2} - 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} - 32 q^{8} - 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 96 q^{13} - 72 q^{15} - 32 q^{16} + 84 q^{17} + 36 q^{18} - 72 q^{19} - 96 q^{20} + 16 q^{22} + 308 q^{23} + 48 q^{24} - 18 q^{25} - 96 q^{26} + 108 q^{27} - 160 q^{29} - 72 q^{30} + 384 q^{31} + 64 q^{32} + 12 q^{33} + 336 q^{34} + 144 q^{36} - 536 q^{37} + 144 q^{38} + 144 q^{39} - 96 q^{40} - 1512 q^{41} + 800 q^{43} + 16 q^{44} + 108 q^{45} - 616 q^{46} + 312 q^{47} + 192 q^{48} - 72 q^{50} + 252 q^{51} + 192 q^{52} + 52 q^{53} + 108 q^{54} - 2304 q^{55} + 432 q^{57} - 160 q^{58} + 864 q^{59} + 144 q^{60} + 1416 q^{61} + 1536 q^{62} + 256 q^{64} + 300 q^{65} - 24 q^{66} - 144 q^{67} + 336 q^{68} - 1848 q^{69} - 3048 q^{71} + 144 q^{72} + 744 q^{73} + 1072 q^{74} - 54 q^{75} + 576 q^{76} + 576 q^{78} - 976 q^{79} + 192 q^{80} - 162 q^{81} - 1512 q^{82} + 624 q^{83} + 1400 q^{85} + 800 q^{86} + 240 q^{87} - 32 q^{88} + 108 q^{89} + 432 q^{90} - 2464 q^{92} + 1152 q^{93} - 624 q^{94} + 40 q^{95} + 192 q^{96} + 1488 q^{97} - 72 q^{99}+O(q^{100}) \) 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 + 84 * q^17 + 36 * q^18 - 72 * q^19 - 96 * q^20 + 16 * q^22 + 308 * q^23 + 48 * q^24 - 18 * q^25 - 96 * q^26 + 108 * q^27 - 160 * q^29 - 72 * q^30 + 384 * q^31 + 64 * q^32 + 12 * q^33 + 336 * q^34 + 144 * q^36 - 536 * q^37 + 144 * q^38 + 144 * q^39 - 96 * q^40 - 1512 * q^41 + 800 * q^43 + 16 * q^44 + 108 * q^45 - 616 * q^46 + 312 * q^47 + 192 * q^48 - 72 * q^50 + 252 * q^51 + 192 * q^52 + 52 * q^53 + 108 * q^54 - 2304 * q^55 + 432 * q^57 - 160 * q^58 + 864 * q^59 + 144 * q^60 + 1416 * q^61 + 1536 * q^62 + 256 * q^64 + 300 * q^65 - 24 * q^66 - 144 * q^67 + 336 * q^68 - 1848 * q^69 - 3048 * q^71 + 144 * q^72 + 744 * q^73 + 1072 * q^74 - 54 * q^75 + 576 * q^76 + 576 * q^78 - 976 * q^79 + 192 * q^80 - 162 * q^81 - 1512 * q^82 + 624 * q^83 + 1400 * q^85 + 800 * q^86 + 240 * q^87 - 32 * q^88 + 108 * q^89 + 432 * q^90 - 2464 * q^92 + 1152 * q^93 - 624 * q^94 + 40 * q^95 + 192 * q^96 + 1488 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.94975	+	3.37706i	−0.174391	+	0.302054i	−0.939950	−	0.341311i	$-0.889129\pi$
$5$	−1.94975	+	3.37706i	−0.174391	+	0.302054i	0.765560	+	0.643365i	$0.222462\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	3.89949	+	6.75412i	0.123313	+	0.213584i
$11$	30.6985	+	53.1713i	0.841449	+	1.45743i	0.888669	+	0.458548i	$0.151630\pi$
$11$	30.6985	+	53.1713i	0.841449	+	1.45743i	−0.0472203	+	0.998885i	$0.515036\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	−53.6985			−1.14564			−0.572818	−	0.819682i	$-0.694150\pi$
$13$	−53.6985			−1.14564			−0.572818	+	0.819682i	$0.694150\pi$
$14$		0			0
$15$	11.6985			0.201369
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	16.0503	+	27.7999i	0.228986	+	0.396615i	0.957508	−	0.288407i	$-0.0931257\pi$
$17$	16.0503	+	27.7999i	0.228986	+	0.396615i	−0.728522	+	0.685022i	$0.759792\pi$
$18$	9.00000	+	15.5885i	0.117851	+	0.204124i
$19$	−27.8995	+	48.3233i	−0.336873	+	0.583481i	−0.983843	−	0.179035i	$-0.942703\pi$
$19$	−27.8995	+	48.3233i	−0.336873	+	0.583481i	0.646970	+	0.762515i	$0.276036\pi$
$20$	15.5980			0.174391
$21$		0			0
$22$	122.794			1.18999
$23$	47.3015	−	81.9286i	0.428828	−	0.742752i	−0.567941	−	0.823069i	$-0.692260\pi$
$23$	47.3015	−	81.9286i	0.428828	−	0.742752i	0.996769	+	0.0803170i	$0.0255932\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	54.8970	+	95.0843i	0.439176	+	0.760675i
$26$	−53.6985	+	93.0085i	−0.405044	+	0.701556i
$27$	27.0000			0.192450
$28$		0			0
$29$	138.191			0.884876			0.442438	−	0.896799i	$-0.354114\pi$
$29$	138.191			0.884876			0.442438	+	0.896799i	$0.354114\pi$
$30$	11.6985	−	20.2624i	0.0711947	−	0.123313i
$31$	66.3015	+	114.838i	0.384132	+	0.665337i	0.991648	−	0.128971i	$-0.0411673\pi$
$31$	66.3015	+	114.838i	0.384132	+	0.665337i	−0.607516	+	0.794307i	$0.707834\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	92.0955	−	159.514i	0.485811	−	0.841449i
$34$	64.2010			0.323835
$35$		0			0
$36$	36.0000			0.166667
$37$	−74.6030	+	129.216i	−0.331477	+	0.574136i	−0.982802	−	0.184664i	$-0.940880\pi$
$37$	−74.6030	+	129.216i	−0.331477	+	0.574136i	0.651324	+	0.758799i	$0.274214\pi$
$38$	55.7990	+	96.6467i	0.238205	+	0.412583i
$39$	80.5477	+	139.513i	0.330717	+	0.572818i
$40$	15.5980	−	27.0165i	0.0616564	−	0.106792i
$41$	−427.497			−1.62839			−0.814194	−	0.580593i	$-0.802821\pi$
$41$	−427.497			−1.62839			−0.814194	+	0.580593i	$0.802821\pi$
$42$		0			0
$43$	437.588			1.55190			0.775948	−	0.630797i	$-0.217272\pi$
$43$	437.588			1.55190			0.775948	+	0.630797i	$0.217272\pi$
$44$	122.794	−	212.685i	0.420725	−	0.728716i
$45$	−17.5477	−	30.3936i	−0.0581302	−	0.100685i
$46$	−94.6030	−	163.857i	−0.303227	−	0.525205i
$47$	28.5025	−	49.3678i	0.0884579	−	0.153214i	−0.818402	−	0.574647i	$-0.805139\pi$
$47$	28.5025	−	49.3678i	0.0884579	−	0.153214i	0.906859	+	0.421433i	$0.138473\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	219.588			0.621088
$51$	48.1508	−	83.3996i	0.132205	−	0.228986i
$52$	107.397	+	186.017i	0.286409	+	0.496075i
$53$	131.794	+	228.274i	0.341572	+	0.591619i	0.984725	−	0.174118i	$-0.0557075\pi$
$53$	131.794	+	228.274i	0.341572	+	0.591619i	−0.643153	+	0.765737i	$0.722374\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−239.417			−0.586964
$56$		0			0
$57$	167.397			0.388987
$58$	138.191	−	239.354i	0.312851	−	0.541874i
$59$	225.899	+	391.269i	0.498468	+	0.863372i	0.999998	−	0.00176815i	$-0.000562821\pi$
$59$	225.899	+	391.269i	0.498468	+	0.863372i	−0.501530	+	0.865140i	$0.667229\pi$
$60$	−23.3970	−	40.5247i	−0.0503423	−	0.0871954i
$61$	289.653	−	501.694i	0.607972	−	1.05304i	−0.383602	−	0.923499i	$-0.625317\pi$
$61$	289.653	−	501.694i	0.607972	−	1.05304i	0.991574	−	0.129540i	$-0.0413501\pi$
$62$	265.206			0.543245
$63$		0			0
$64$	64.0000			0.125000
$65$	104.698	−	181.343i	0.199788	−	0.346044i
$66$	−184.191	−	319.028i	−0.343520	−	0.594994i
$67$	−154.794	−	268.111i	−0.282255	−	0.488880i	0.689685	−	0.724110i	$-0.257749\pi$
$67$	−154.794	−	268.111i	−0.282255	−	0.488880i	−0.971940	+	0.235230i	$0.924416\pi$
$68$	64.2010	−	111.199i	0.114493	−	0.198307i
$69$	−283.809			−0.495168
$70$		0			0
$71$	−1058.98			−1.77012			−0.885059	−	0.465479i	$-0.845882\pi$
$71$	−1058.98			−1.77012			−0.885059	+	0.465479i	$0.845882\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	596.829	+	1033.74i	0.956898	+	1.65740i	0.729964	+	0.683486i	$0.239537\pi$
$73$	596.829	+	1033.74i	0.956898	+	1.65740i	0.226934	+	0.973910i	$0.427130\pi$
$74$	149.206	+	258.432i	0.234390	+	0.405975i
$75$	164.691	−	285.253i	0.253558	−	0.439176i
$76$	223.196			0.336873
$77$		0			0
$78$	322.191			0.467704
$79$	−659.779	+	1142.77i	−0.939632	+	1.62749i	−0.173473	+	0.984839i	$0.555499\pi$
$79$	−659.779	+	1142.77i	−0.939632	+	1.62749i	−0.766159	+	0.642651i	$0.777834\pi$
$80$	−31.1960	−	54.0330i	−0.0435977	−	0.0755134i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−427.497	+	740.447i	−0.575722	+	0.997180i
$83$	−1190.33			−1.57417			−0.787083	−	0.616847i	$-0.788410\pi$
$83$	−1190.33			−1.57417			−0.787083	+	0.616847i	$0.788410\pi$
$84$		0			0
$85$	−125.176			−0.159732
$86$	437.588	−	757.924i	0.548678	−	0.950338i
$87$	−207.286	−	359.031i	−0.255442	−	0.442438i
$88$	−245.588	−	425.371i	−0.297497	−	0.515280i
$89$	−116.543	+	201.858i	−0.138803	+	0.240414i	−0.927044	−	0.374953i	$-0.877659\pi$
$89$	−116.543	+	201.858i	−0.138803	+	0.240414i	0.788241	+	0.615367i	$0.210992\pi$
$90$	−70.1909			−0.0822086
$91$		0			0
$92$	−378.412			−0.428828
$93$	198.905	−	344.513i	0.221779	−	0.384132i
$94$	−57.0051	−	98.7356i	−0.0625492	−	0.108338i
$95$	−108.794	−	188.437i	−0.117495	−	0.203507i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	1609.44			1.68468			0.842338	−	0.538950i	$-0.181179\pi$
$97$	1609.44			1.68468			0.842338	+	0.538950i	$0.181179\pi$
$98$		0			0
$99$	−552.573			−0.560966
$100$	219.588	−	380.337i	0.219588	−	0.380337i
$101$	−739.628	−	1281.07i	−0.728671	−	1.26209i	−0.957445	−	0.288615i	$-0.906805\pi$
$101$	−739.628	−	1281.07i	−0.728671	−	1.26209i	0.228774	−	0.973479i	$-0.426528\pi$
$102$	−96.3015	−	166.799i	−0.0934830	−	0.161917i
$103$	−572.673	+	991.899i	−0.547837	+	0.948881i	0.450586	+	0.892733i	$0.351215\pi$
$103$	−572.673	+	991.899i	−0.547837	+	0.948881i	−0.998422	+	0.0561477i	$0.982118\pi$
$104$	429.588			0.405044
$105$		0			0
$106$	527.176			0.483055
$107$	−218.477	+	378.414i	−0.197392	+	0.341894i	−0.947682	−	0.319215i	$-0.896581\pi$
$107$	−218.477	+	378.414i	−0.197392	+	0.341894i	0.750290	+	0.661109i	$0.229914\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	83.1758	+	144.065i	0.0730898	+	0.126595i	0.900254	−	0.435365i	$-0.143381\pi$
$109$	83.1758	+	144.065i	0.0730898	+	0.126595i	−0.827164	+	0.561960i	$0.810047\pi$
$110$	−239.417	+	414.683i	−0.207523	+	0.359440i
$111$	447.618			0.382757
$112$		0			0
$113$	490.824			0.408609			0.204305	−	0.978907i	$-0.434507\pi$
$113$	490.824			0.408609			0.204305	+	0.978907i	$0.434507\pi$
$114$	167.397	−	289.940i	0.137528	−	0.238205i
$115$	184.452	+	319.480i	0.149567	+	0.259058i
$116$	−276.382	−	478.707i	−0.221219	−	0.383163i
$117$	241.643	−	418.538i	0.190939	−	0.330717i
$118$	903.598			0.704940
$119$		0			0
$120$	−93.5879			−0.0711947
$121$	−1219.29	+	2111.88i	−0.916074	+	1.58669i
$122$	−579.307	−	1003.39i	−0.429901	−	0.744611i
$123$	641.246	+	1110.67i	0.470075	+	0.814194i
$124$	265.206	−	459.350i	0.192066	−	0.332668i
$125$	−915.578			−0.655134
$126$		0			0
$127$	−2616.70			−1.82831			−0.914153	−	0.405369i	$-0.867143\pi$
$127$	−2616.70			−1.82831			−0.914153	+	0.405369i	$0.867143\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−656.382	−	1136.89i	−0.447994	−	0.775948i
$130$	−209.397	−	362.686i	−0.141272	−	0.244690i
$131$	88.7939	−	153.796i	0.0592211	−	0.102574i	−0.834895	−	0.550409i	$-0.814472\pi$
$131$	88.7939	−	153.796i	0.0592211	−	0.102574i	0.894116	+	0.447835i	$0.147805\pi$
$132$	−736.764			−0.485811
$133$		0			0
$134$	−619.176			−0.399169
$135$	−52.6432	+	91.1807i	−0.0335615	+	0.0581302i
$136$	−128.402	−	222.399i	−0.0809587	−	0.140225i
$137$	−13.5076	−	23.3958i	−0.00842358	−	0.0145901i	0.861783	−	0.507277i	$-0.169348\pi$
$137$	−13.5076	−	23.3958i	−0.00842358	−	0.0145901i	−0.870206	+	0.492687i	$0.836015\pi$
$138$	−283.809	+	491.572i	−0.175068	+	0.303227i
$139$	922.754			0.563071			0.281536	−	0.959551i	$-0.409156\pi$
$139$	922.754			0.563071			0.281536	+	0.959551i	$0.409156\pi$
$140$		0			0
$141$	−171.015			−0.102142
$142$	−1058.98	+	1834.22i	−0.625831	+	1.08397i
$143$	−1648.46	−	2855.22i	−0.963995	−	1.66969i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−269.437	+	466.679i	−0.154314	+	0.267280i
$146$	2387.32			1.35326
$147$		0			0
$148$	596.824			0.331477
$149$	−373.352	+	646.664i	−0.205276	+	0.355549i	−0.950221	−	0.311578i	$-0.899143\pi$
$149$	−373.352	+	646.664i	−0.205276	+	0.355549i	0.744945	+	0.667126i	$0.232476\pi$
$150$	−329.382	−	570.506i	−0.179293	−	0.310544i
$151$	−1036.57	−	1795.40i	−0.558643	−	0.967598i	−0.997610	−	0.0690949i	$-0.977989\pi$
$151$	−1036.57	−	1795.40i	−0.558643	−	0.967598i	0.438967	−	0.898503i	$-0.355344\pi$
$152$	223.196	−	386.587i	0.119103	−	0.206292i
$153$	−288.905			−0.152657
$154$		0			0
$155$	−517.085			−0.267956
$156$	322.191	−	558.051i	0.165358	−	0.286409i
$157$	783.110	+	1356.39i	0.398083	+	0.689500i	0.993489	−	0.113925i	$-0.0363423\pi$
$157$	783.110	+	1356.39i	0.398083	+	0.689500i	−0.595407	+	0.803425i	$0.703009\pi$
$158$	1319.56	+	2285.54i	0.664420	+	1.15081i
$159$	395.382	−	684.821i	0.197206	−	0.341572i
$160$	−124.784			−0.0616564
$161$		0			0
$162$	−162.000			−0.0785674
$163$	−49.3667	+	85.5056i	−0.0237221	+	0.0410878i	−0.877643	−	0.479315i	$-0.840885\pi$
$163$	−49.3667	+	85.5056i	−0.0237221	+	0.0410878i	0.853921	+	0.520403i	$0.174218\pi$
$164$	854.995	+	1480.89i	0.407097	+	0.705112i
$165$	359.126	+	622.024i	0.169442	+	0.293482i
$166$	−1190.33	+	2061.71i	−0.556552	+	0.963976i
$167$	2231.36			1.03394			0.516969	−	0.856004i	$-0.327060\pi$
$167$	2231.36			1.03394			0.516969	+	0.856004i	$0.327060\pi$
$168$		0			0
$169$	686.527			0.312484
$170$	−125.176	+	216.811i	−0.0564738	+	0.0978155i
$171$	−251.095	−	434.910i	−0.112291	−	0.194494i
$172$	−875.176	−	1515.85i	−0.387974	−	0.671991i
$173$	1050.42	−	1819.38i	0.461631	−	0.799568i	−0.537412	−	0.843320i	$-0.680598\pi$
$173$	1050.42	−	1819.38i	0.461631	−	0.799568i	0.999042	+	0.0437522i	$0.0139312\pi$
$174$	−829.145			−0.361249
$175$		0			0
$176$	−982.352			−0.420725
$177$	677.698	−	1173.81i	0.287791	−	0.498468i
$178$	233.085	+	403.716i	0.0981488	+	0.169999i
$179$	−861.271	−	1491.77i	−0.359634	−	0.622904i	0.628266	−	0.777999i	$-0.283765\pi$
$179$	−861.271	−	1491.77i	−0.359634	−	0.622904i	−0.987900	+	0.155095i	$0.950432\pi$
$180$	−70.1909	+	121.574i	−0.0290651	+	0.0503423i
$181$	−1655.00			−0.679644			−0.339822	−	0.940490i	$-0.610367\pi$
$181$	−1655.00			−0.679644			−0.339822	+	0.940490i	$0.610367\pi$
$182$		0			0
$183$	−1737.92			−0.702026
$184$	−378.412	+	655.429i	−0.151614	+	0.262603i
$185$	−290.914	−	503.878i	−0.115613	−	0.200248i
$186$	−397.809	−	689.026i	−0.156821	−	0.271623i
$187$	−985.437	+	1706.83i	−0.385360	+	0.667463i
$188$	−228.020			−0.0884579
$189$		0			0
$190$	−435.176			−0.166163
$191$	503.844	−	872.683i	0.190874	−	0.330603i	−0.754666	−	0.656109i	$-0.772201\pi$
$191$	503.844	−	872.683i	0.190874	−	0.330603i	0.945540	+	0.325506i	$0.105535\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	3.82424	+	6.62378i	0.00142630	+	0.00247042i	0.866738	−	0.498764i	$-0.166213\pi$
$193$	3.82424	+	6.62378i	0.00142630	+	0.00247042i	−0.865311	+	0.501235i	$0.832879\pi$
$194$	1609.44	−	2787.63i	0.595623	−	1.03165i
$195$	−628.191			−0.230696
$196$		0			0
$197$	2689.88			0.972822			0.486411	−	0.873730i	$-0.338306\pi$
$197$	2689.88			0.972822			0.486411	+	0.873730i	$0.338306\pi$
$198$	−552.573	+	957.084i	−0.198331	+	0.343520i
$199$	433.748	+	751.274i	0.154511	+	0.267620i	0.932881	−	0.360185i	$-0.117287\pi$
$199$	433.748	+	751.274i	0.154511	+	0.267620i	−0.778370	+	0.627806i	$0.783953\pi$
$200$	−439.176	−	760.675i	−0.155272	−	0.268939i
$201$	−464.382	+	804.333i	−0.162960	+	0.282255i
$202$	−2958.51			−1.03050
$203$		0			0
$204$	−385.206			−0.132205
$205$	833.512	−	1443.69i	0.283976	−	0.491860i
$206$	1145.35	+	1983.80i	0.387379	+	0.670960i
$207$	425.714	+	737.358i	0.142943	+	0.247584i
$208$	429.588	−	744.068i	0.143205	−	0.248038i
$209$	−3425.89			−1.13385
$210$		0			0
$211$	162.030			0.0528655			0.0264328	−	0.999651i	$-0.491585\pi$
$211$	162.030			0.0528655			0.0264328	+	0.999651i	$0.491585\pi$
$212$	527.176	−	913.095i	0.170786	−	0.295810i
$213$	1588.48	+	2751.32i	0.510989	+	0.885059i
$214$	436.955	+	756.827i	0.139578	+	0.241755i
$215$	−853.186	+	1477.76i	−0.270636	+	0.468756i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	332.703			0.103365
$219$	1790.49	−	3101.21i	0.552465	−	0.956898i
$220$	478.834	+	829.365i	0.146741	+	0.254163i
$221$	−861.874	−	1492.81i	−0.262335	−	0.454377i
$222$	447.618	−	775.297i	0.135325	−	0.234390i
$223$	4577.85			1.37469			0.687344	−	0.726332i	$-0.258777\pi$
$223$	4577.85			1.37469			0.687344	+	0.726332i	$0.258777\pi$
$224$		0			0
$225$	−988.145			−0.292784
$226$	490.824	−	850.133i	0.144465	−	0.250221i
$227$	−1109.10	−	1921.01i	−0.324287	−	0.561682i	0.657080	−	0.753820i	$-0.271791\pi$
$227$	−1109.10	−	1921.01i	−0.324287	−	0.561682i	−0.981368	+	0.192138i	$0.938458\pi$
$228$	−334.794	−	579.880i	−0.0972468	−	0.168436i
$229$	392.608	−	680.018i	0.113294	−	0.196231i	−0.803803	−	0.594896i	$-0.797193\pi$
$229$	392.608	−	680.018i	0.113294	−	0.196231i	0.917096	+	0.398665i	$0.130527\pi$
$230$	737.808			0.211520
$231$		0			0
$232$	−1105.53			−0.312851
$233$	2684.56	−	4649.80i	0.754813	−	1.30738i	−0.190654	−	0.981657i	$-0.561061\pi$
$233$	2684.56	−	4649.80i	0.754813	−	1.30738i	0.945467	−	0.325718i	$-0.105606\pi$
$234$	−483.286	−	837.077i	−0.135015	−	0.233852i
$235$	111.145	+	192.510i	0.0308525	+	0.0534380i
$236$	903.598	−	1565.08i	0.249234	−	0.431686i
$237$	3958.67			1.08499
$238$		0			0
$239$	3713.28			1.00499			0.502493	−	0.864581i	$-0.332416\pi$
$239$	3713.28			1.00499			0.502493	+	0.864581i	$0.332416\pi$
$240$	−93.5879	+	162.099i	−0.0251711	+	0.0435977i
$241$	3499.31	+	6060.99i	0.935313	+	1.62001i	0.774075	+	0.633094i	$0.218215\pi$
$241$	3499.31	+	6060.99i	0.935313	+	1.62001i	0.161238	+	0.986915i	$0.448451\pi$
$242$	2438.59	+	4223.76i	0.647762	+	1.12196i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−2317.23			−0.607972
$245$		0			0
$246$	2564.98			0.664786
$247$	1498.16	−	2594.89i	0.385934	−	0.668457i
$248$	−530.412	−	918.701i	−0.135811	−	0.235232i
$249$	1785.50	+	3092.57i	0.454423	+	0.787083i
$250$	−915.578	+	1585.83i	−0.231625	+	0.401186i
$251$	−3722.75			−0.936168			−0.468084	−	0.883684i	$-0.655055\pi$
$251$	−3722.75			−0.936168			−0.468084	+	0.883684i	$0.655055\pi$
$252$		0			0
$253$	5808.34			1.44335
$254$	−2616.70	+	4532.26i	−0.646404	+	1.11960i
$255$	187.764	+	325.216i	0.0461106	+	0.0798660i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	615.075	−	1065.34i	0.149289	−	0.258576i	−0.781676	−	0.623685i	$-0.785635\pi$
$257$	615.075	−	1065.34i	0.149289	−	0.258576i	0.930965	+	0.365109i	$0.118968\pi$
$258$	−2625.53			−0.633559
$259$		0			0
$260$	−837.588			−0.199788
$261$	−621.859	+	1077.09i	−0.147479	+	0.255442i
$262$	−177.588	−	307.591i	−0.0418756	−	0.0725307i
$263$	−1194.32	−	2068.62i	−0.280018	−	0.485005i	0.691371	−	0.722500i	$-0.257007\pi$
$263$	−1194.32	−	2068.62i	−0.280018	−	0.485005i	−0.971389	+	0.237495i	$0.923674\pi$
$264$	−736.764	+	1276.11i	−0.171760	+	0.297497i
$265$	−1027.86			−0.238268
$266$		0			0
$267$	699.256			0.160276
$268$	−619.176	+	1072.44i	−0.141128	+	0.244440i
$269$	3351.16	+	5804.37i	0.759567	+	1.31561i	0.943071	+	0.332590i	$0.107923\pi$
$269$	3351.16	+	5804.37i	0.759567	+	1.31561i	−0.183504	+	0.983019i	$0.558744\pi$
$270$	105.286	+	182.361i	0.0237316	+	0.0411043i
$271$	2475.19	−	4287.15i	0.554822	−	0.960980i	−0.443095	−	0.896475i	$-0.646120\pi$
$271$	2475.19	−	4287.15i	0.554822	−	0.960980i	0.997917	−	0.0645056i	$-0.0205470\pi$
$272$	−513.608			−0.114493
$273$		0			0
$274$	−54.0303			−0.0119127
$275$	−3370.51	+	5837.89i	−0.739088	+	1.28014i
$276$	567.618	+	983.144i	0.123792	+	0.214414i
$277$	1852.59	+	3208.78i	0.401846	+	0.696017i	0.993949	−	0.109845i	$-0.0350355\pi$
$277$	1852.59	+	3208.78i	0.401846	+	0.696017i	−0.592103	+	0.805862i	$0.701702\pi$
$278$	922.754	−	1598.26i	0.199076	−	0.344809i
$279$	−1193.43			−0.256088
$280$		0			0
$281$	9324.74			1.97960			0.989800	−	0.142465i	$-0.0455029\pi$
$281$	9324.74			1.97960			0.989800	+	0.142465i	$0.0455029\pi$
$282$	−171.015	+	296.207i	−0.0361128	+	0.0625492i
$283$	−2784.74	−	4823.32i	−0.584932	−	1.01313i	−0.994884	−	0.101025i	$-0.967788\pi$
$283$	−2784.74	−	4823.32i	−0.584932	−	1.01313i	0.409952	−	0.912107i	$-0.365546\pi$
$284$	2117.97	+	3668.43i	0.442530	+	0.766484i
$285$	−326.382	+	565.310i	−0.0678358	+	0.117495i
$286$	−6593.85			−1.36330
$287$		0			0
$288$	−288.000			−0.0589256
$289$	1941.28	−	3362.39i	0.395131	−	0.684387i
$290$	538.875	+	933.358i	0.109117	+	0.188996i
$291$	−2414.16	−	4181.44i	−0.486324	−	0.842338i
$292$	2387.32	−	4134.95i	0.478449	−	0.828698i
$293$	1665.31			0.332042			0.166021	−	0.986122i	$-0.446908\pi$
$293$	1665.31			0.332042			0.166021	+	0.986122i	$0.446908\pi$
$294$		0			0
$295$	−1761.79			−0.347713
$296$	596.824	−	1033.73i	0.117195	−	0.202988i
$297$	828.859	+	1435.63i	0.161937	+	0.280483i
$298$	746.703	+	1293.33i	0.145152	+	0.251411i
$299$	−2540.02	+	4399.44i	−0.491281	+	0.850924i
$300$	−1317.53			−0.253558
$301$		0			0
$302$	−4146.29			−0.790040
$303$	−2218.88	+	3843.22i	−0.420698	+	0.728671i
$304$	−446.392	−	773.173i	−0.0842182	−	0.145870i
$305$	1129.50	+	1956.35i	0.212049	+	0.367280i
$306$	−288.905	+	500.397i	−0.0539725	+	0.0934830i
$307$	5303.32			0.985916			0.492958	−	0.870053i	$-0.335916\pi$
$307$	5303.32			0.985916			0.492958	+	0.870053i	$0.335916\pi$
$308$		0			0
$309$	3436.04			0.632587
$310$	−517.085	+	895.617i	−0.0947369	+	0.164089i
$311$	562.994	+	975.135i	0.102651	+	0.177797i	0.912776	−	0.408460i	$-0.133934\pi$
$311$	562.994	+	975.135i	0.102651	+	0.177797i	−0.810125	+	0.586257i	$0.800601\pi$
$312$	−644.382	−	1116.10i	−0.116926	−	0.202522i
$313$	−4149.75	+	7187.58i	−0.749386	+	1.29798i	0.198731	+	0.980054i	$0.436318\pi$
$313$	−4149.75	+	7187.58i	−0.749386	+	1.29798i	−0.948117	+	0.317921i	$0.897015\pi$
$314$	3132.44			0.562974
$315$		0			0
$316$	5278.23			0.939632
$317$	2139.38	−	3705.52i	0.379053	−	0.656538i	−0.611872	−	0.790957i	$-0.709583\pi$
$317$	2139.38	−	3705.52i	0.379053	−	0.656538i	0.990925	+	0.134418i	$0.0429166\pi$
$318$	−790.764	−	1369.64i	−0.139446	−	0.241528i
$319$	4242.25	+	7347.80i	0.744578	+	1.28965i
$320$	−124.784	+	216.132i	−0.0217988	+	0.0377567i
$321$	1310.86			0.227929
$322$		0			0
$323$	−1791.18			−0.308556
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−2947.88	−	5105.89i	−0.503136	−	0.871457i
$326$	98.7333	+	171.011i	0.0167740	+	0.0290535i
$327$	249.527	−	432.194i	0.0421984	−	0.0730898i
$328$	3419.98			0.575722
$329$		0			0
$330$	1436.50			0.239627
$331$	853.558	−	1478.41i	0.141739	−	0.245500i	−0.786412	−	0.617702i	$-0.788064\pi$
$331$	853.558	−	1478.41i	0.141739	−	0.245500i	0.928152	+	0.372202i	$0.121397\pi$
$332$	2380.66	+	4123.43i	0.393542	+	0.681634i
$333$	−671.427	−	1162.95i	−0.110492	−	0.191379i
$334$	2231.36	−	3864.82i	0.365552	−	0.633155i
$335$	1207.24			0.196891
$336$		0			0
$337$	1710.67			0.276517			0.138259	−	0.990396i	$-0.455849\pi$
$337$	1710.67			0.276517			0.138259	+	0.990396i	$0.455849\pi$
$338$	686.527	−	1189.10i	0.110480	−	0.191357i
$339$	−736.236	−	1275.20i	−0.117955	−	0.204305i
$340$	250.352	+	433.622i	0.0399330	+	0.0691660i
$341$	−4070.71	+	7050.68i	−0.646456	+	1.11969i
$342$	−1004.38			−0.158803
$343$		0			0
$344$	−3500.70			−0.548678
$345$	553.356	−	958.441i	0.0863527	−	0.149567i
$346$	−2100.84	−	3638.77i	−0.326422	−	0.565380i
$347$	−4455.15	−	7716.55i	−0.689236	−	1.19379i	−0.972085	−	0.234628i	$-0.924613\pi$
$347$	−4455.15	−	7716.55i	−0.689236	−	1.19379i	0.282849	−	0.959164i	$-0.408720\pi$
$348$	−829.145	+	1436.12i	−0.127721	+	0.221219i
$349$	−5378.68			−0.824969			−0.412485	−	0.910965i	$-0.635339\pi$
$349$	−5378.68			−0.824969			−0.412485	+	0.910965i	$0.635339\pi$
$350$		0			0
$351$	−1449.86			−0.220478
$352$	−982.352	+	1701.48i	−0.148749	+	0.257640i
$353$	−2126.28	−	3682.83i	−0.320596	−	0.555289i	0.660015	−	0.751253i	$-0.270550\pi$
$353$	−2126.28	−	3682.83i	−0.320596	−	0.555289i	−0.980611	+	0.195963i	$0.937217\pi$
$354$	−1355.40	−	2347.62i	−0.203499	−	0.352470i
$355$	2064.75	−	3576.26i	0.308692	−	0.534670i
$356$	932.341			0.138803
$357$		0			0
$358$	−3445.08			−0.508599
$359$	−2451.94	+	4246.89i	−0.360470	+	0.624352i	−0.988038	−	0.154209i	$-0.950717\pi$
$359$	−2451.94	+	4246.89i	−0.360470	+	0.624352i	0.627568	+	0.778561i	$0.284050\pi$
$360$	140.382	+	243.148i	0.0205521	+	0.0355974i
$361$	1872.74	+	3243.67i	0.273033	+	0.472908i
$362$	−1655.00	+	2866.55i	−0.240290	+	0.416195i
$363$	7315.76			1.05779
$364$		0			0
$365$	−4654.66			−0.667497
$366$	−1737.92	+	3010.17i	−0.248204	+	0.429901i
$367$	−2020.78	−	3500.10i	−0.287423	−	0.497830i	0.685771	−	0.727817i	$-0.259465\pi$
$367$	−2020.78	−	3500.10i	−0.287423	−	0.497830i	−0.973194	+	0.229987i	$0.926132\pi$
$368$	756.824	+	1310.86i	0.107207	+	0.185688i
$369$	1923.74	−	3332.01i	0.271398	−	0.470075i
$370$	−1163.66			−0.163502
$371$		0			0
$372$	−1591.24			−0.221779
$373$	3725.67	−	6453.05i	0.517180	−	0.895781i	−0.482621	−	0.875829i	$-0.660315\pi$
$373$	3725.67	−	6453.05i	0.517180	−	0.895781i	0.999801	−	0.0199523i	$-0.00635144\pi$
$374$	1970.87	+	3413.65i	0.272491	+	0.471967i
$375$	1373.37	+	2378.74i	0.189121	+	0.327567i
$376$	−228.020	+	394.943i	−0.0312746	+	0.0541692i
$377$	−7420.64			−1.01375
$378$		0			0
$379$	−12564.4			−1.70288			−0.851438	−	0.524456i	$-0.824269\pi$
$379$	−12564.4			−1.70288			−0.851438	+	0.524456i	$0.824269\pi$
$380$	−435.176	+	753.747i	−0.0587475	+	0.101754i
$381$	3925.05	+	6798.39i	0.527786	+	0.914153i
$382$	−1007.69	−	1745.37i	−0.134968	−	0.233772i
$383$	−2144.96	+	3715.19i	−0.286169	+	0.495659i	−0.972892	−	0.231260i	$-0.925715\pi$
$383$	−2144.96	+	3715.19i	−0.286169	+	0.495659i	0.686723	+	0.726919i	$0.259048\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	15.2970			0.00201709
$387$	−1969.15	+	3410.66i	−0.258649	+	0.447994i
$388$	−3218.87	−	5575.25i	−0.421169	−	0.729486i
$389$	−2831.39	−	4904.11i	−0.369041	−	0.639198i	0.620375	−	0.784306i	$-0.286981\pi$
$389$	−2831.39	−	4904.11i	−0.369041	−	0.639198i	−0.989416	+	0.145108i	$0.953647\pi$
$390$	−628.191	+	1088.06i	−0.0815633	+	0.141272i
$391$	3036.81			0.392782
$392$		0			0
$393$	−532.764			−0.0683826
$394$	2689.88	−	4659.01i	0.343945	−	0.595729i
$395$	−2572.80	−	4456.23i	−0.327726	−	0.567638i
$396$	1105.15	+	1914.17i	0.140242	+	0.242905i
$397$	7280.69	−	12610.5i	0.920421	−	1.59422i	0.121657	−	0.992572i	$-0.461179\pi$
$397$	7280.69	−	12610.5i	0.920421	−	1.59422i	0.798764	−	0.601644i	$-0.205487\pi$
$398$	1734.99			0.218511
$399$		0			0
$400$	−1756.70			−0.219588
$401$	1871.10	−	3240.83i	0.233013	−	0.403590i	−0.725681	−	0.688032i	$-0.758475\pi$
$401$	1871.10	−	3240.83i	0.233013	−	0.403590i	0.958693	+	0.284442i	$0.0918083\pi$
$402$	928.764	+	1608.67i	0.115230	+	0.199584i
$403$	−3560.29	−	6166.60i	−0.440076	−	0.762234i
$404$	−2958.51	+	5124.29i	−0.364335	+	0.631047i
$405$	315.859			0.0387535
$406$		0			0
$407$	−9160.80			−1.11569
$408$	−385.206	+	667.196i	−0.0467415	+	0.0809587i
$409$	−1758.59	−	3045.96i	−0.212608	−	0.368247i	0.739922	−	0.672692i	$-0.234862\pi$
$409$	−1758.59	−	3045.96i	−0.212608	−	0.368247i	−0.952530	+	0.304445i	$0.901529\pi$
$410$	−1667.02	−	2887.37i	−0.200801	−	0.347798i
$411$	−40.5227	+	70.1874i	−0.00486335	+	0.00842358i
$412$	4581.39			0.547837
$413$		0			0
$414$	1702.85			0.202152
$415$	2320.85	−	4019.82i	0.274520	−	0.475483i
$416$	−859.176	−	1488.14i	−0.101261	−	0.175389i
$417$	−1384.13	−	2397.38i	−0.162545	−	0.281536i
$418$	−3425.89	+	5933.81i	−0.400875	+	0.694336i
$419$	7579.52			0.883732			0.441866	−	0.897081i	$-0.354317\pi$
$419$	7579.52			0.883732			0.441866	+	0.897081i	$0.354317\pi$
$420$		0			0
$421$	−4980.87			−0.576610			−0.288305	−	0.957539i	$-0.593092\pi$
$421$	−4980.87			−0.576610			−0.288305	+	0.957539i	$0.593092\pi$
$422$	162.030	−	280.645i	0.0186908	−	0.0323734i
$423$	256.523	+	444.310i	0.0294860	+	0.0510712i
$424$	−1054.35	−	1826.19i	−0.120764	−	0.209169i
$425$	−1762.22	+	3052.26i	−0.201130	+	0.348367i
$426$	6353.91			0.722648
$427$		0			0
$428$	1747.82			0.197392
$429$	−4945.39	+	8565.66i	−0.556563	+	0.963995i
$430$	1706.37	+	2955.52i	0.191369	+	0.331460i
$431$	−7101.66	−	12300.4i	−0.793678	−	1.37469i	−0.923676	−	0.383176i	$-0.874830\pi$
$431$	−7101.66	−	12300.4i	−0.793678	−	1.37469i	0.129998	−	0.991514i	$-0.458503\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−3874.82			−0.430051			−0.215026	−	0.976608i	$-0.568983\pi$
$433$	−3874.82			−0.430051			−0.215026	+	0.976608i	$0.568983\pi$
$434$		0			0
$435$	1616.62			0.178187
$436$	332.703	−	576.259i	0.0365449	−	0.0632977i
$437$	2639.38	+	4571.53i	0.288921	+	0.500426i
$438$	−3580.97	−	6202.43i	−0.390652	−	0.676629i
$439$	3881.91	−	6723.66i	0.422035	−	0.730986i	−0.574103	−	0.818783i	$-0.694649\pi$
$439$	3881.91	−	6723.66i	0.422035	−	0.730986i	0.996138	+	0.0877966i	$0.0279826\pi$
$440$	1915.34			0.207523
$441$		0			0
$442$	−3447.50			−0.370997
$443$	−4831.12	+	8367.74i	−0.518134	+	0.897435i	0.481644	+	0.876367i	$0.340040\pi$
$443$	−4831.12	+	8367.74i	−0.518134	+	0.897435i	−0.999778	+	0.0210676i	$0.993293\pi$
$444$	−895.236	−	1550.59i	−0.0956893	−	0.165739i
$445$	−454.458	−	787.144i	−0.0484120	−	0.0838521i
$446$	4577.85	−	7929.07i	0.486026	−	0.841821i
$447$	2240.11			0.237032
$448$		0			0
$449$	−10942.6			−1.15014			−0.575069	−	0.818105i	$-0.695025\pi$
$449$	−10942.6			−1.15014			−0.575069	+	0.818105i	$0.695025\pi$
$450$	−988.145	+	1711.52i	−0.103515	+	0.179293i
$451$	−13123.5	−	22730.6i	−1.37021	−	2.37327i
$452$	−981.648	−	1700.27i	−0.102152	−	0.176933i
$453$	−3109.72	+	5386.19i	−0.322533	+	0.558643i
$454$	−4436.38			−0.458612
$455$		0			0
$456$	−1339.18			−0.137528
$457$	−6809.17	+	11793.8i	−0.696979	+	1.20720i	0.272530	+	0.962147i	$0.412140\pi$
$457$	−6809.17	+	11793.8i	−0.696979	+	1.20720i	−0.969509	+	0.245056i	$0.921194\pi$
$458$	−785.217	−	1360.04i	−0.0801108	−	0.138756i
$459$	433.357	+	750.596i	0.0440683	+	0.0763286i
$460$	737.808	−	1277.92i	0.0747836	−	0.129529i
$461$	−11955.8			−1.20789			−0.603947	−	0.797025i	$-0.706406\pi$
$461$	−11955.8			−1.20789			−0.603947	+	0.797025i	$0.706406\pi$
$462$		0			0
$463$	648.503			0.0650939			0.0325470	−	0.999470i	$-0.489638\pi$
$463$	648.503			0.0650939			0.0325470	+	0.999470i	$0.489638\pi$
$464$	−1105.53	+	1914.83i	−0.110610	+	0.191581i
$465$	775.627	+	1343.43i	0.0773524	+	0.133978i
$466$	−5369.12	−	9299.60i	−0.533734	−	0.924454i
$467$	1392.37	−	2411.66i	0.137969	−	0.238969i	−0.788759	−	0.614703i	$-0.789276\pi$
$467$	1392.37	−	2411.66i	0.137969	−	0.238969i	0.926728	+	0.375734i	$0.122609\pi$
$468$	−1933.15			−0.190939
$469$		0			0
$470$	444.582			0.0436320
$471$	2349.33	−	4069.16i	0.229833	−	0.398083i
$472$	−1807.20	−	3130.16i	−0.176235	−	0.305248i
$473$	13433.3	+	23267.1i	1.30584	+	2.26178i
$474$	3958.67	−	6856.62i	0.383603	−	0.664420i
$475$	−6126.39			−0.591785
$476$		0			0
$477$	−2372.29			−0.227714
$478$	3713.28	−	6431.58i	0.355316	−	0.615426i
$479$	5556.70	+	9624.49i	0.530046	+	0.918067i	0.999386	+	0.0350493i	$0.0111588\pi$
$479$	5556.70	+	9624.49i	0.530046	+	0.918067i	−0.469339	+	0.883018i	$0.655508\pi$
$480$	187.176	+	324.198i	0.0177987	+	0.0308282i
$481$	4006.07	−	6938.72i	0.379753	−	0.657751i
$482$	13997.2			1.32273
$483$		0			0
$484$	9754.35			0.916074
$485$	−3138.00	+	5435.17i	−0.293792	+	0.508862i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	1893.14	+	3279.01i	0.176152	+	0.305105i	0.940559	−	0.339629i	$-0.110302\pi$
$487$	1893.14	+	3279.01i	0.176152	+	0.305105i	−0.764407	+	0.644734i	$0.776968\pi$
$488$	−2317.23	+	4013.55i	−0.214951	+	0.372305i
$489$	296.200			0.0273919
$490$		0			0
$491$	−9582.12			−0.880723			−0.440361	−	0.897821i	$-0.645150\pi$
$491$	−9582.12			−0.880723			−0.440361	+	0.897821i	$0.645150\pi$
$492$	2564.98	−	4442.68i	0.235037	−	0.407097i
$493$	2218.00	+	3841.69i	0.202624	+	0.350955i
$494$	−2996.32	−	5189.78i	−0.272896	−	0.472671i
$495$	1077.38	−	1866.07i	0.0978273	−	0.169442i
$496$	−2121.65			−0.192066
$497$		0			0
$498$	7141.99			0.642651
$499$	−2790.77	+	4833.76i	−0.250365	+	0.433645i	−0.963626	−	0.267253i	$-0.913884\pi$
$499$	−2790.77	+	4833.76i	−0.250365	+	0.433645i	0.713261	+	0.700898i	$0.247217\pi$
$500$	1831.16	+	3171.65i	0.163784	+	0.283681i
$501$	−3347.03	−	5797.23i	−0.298472	−	0.516969i
$502$	−3722.75	+	6448.00i	−0.330985	+	0.573283i
$503$	14116.3			1.25132			0.625661	−	0.780095i	$-0.284829\pi$
$503$	14116.3			1.25132			0.625661	+	0.780095i	$0.284829\pi$
$504$		0			0
$505$	5768.35			0.508294
$506$	5808.34	−	10060.3i	0.510301	−	0.883867i
$507$	−1029.79	−	1783.65i	−0.0902064	−	0.156242i
$508$	5233.41	+	9064.53i	0.457076	+	0.791680i
$509$	8393.81	−	14538.5i	0.730941	−	1.26603i	−0.225540	−	0.974234i	$-0.572415\pi$
$509$	8393.81	−	14538.5i	0.730941	−	1.26603i	0.956481	−	0.291793i	$-0.0942519\pi$
$510$	751.055			0.0652103
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−753.286	+	1304.73i	−0.0648312	+	0.112291i
$514$	−1230.15	−	2130.68i	−0.105563	−	0.182841i
$515$	−2233.14	−	3867.91i	−0.191075	−	0.330952i
$516$	−2625.53	+	4547.55i	−0.223997	+	0.387974i
$517$	3499.94			0.297731
$518$		0			0
$519$	−6302.53			−0.533045
$520$	−837.588	+	1450.74i	−0.0706359	+	0.122345i
$521$	−2799.31	−	4848.54i	−0.235393	−	0.407713i	0.723994	−	0.689807i	$-0.242304\pi$
$521$	−2799.31	−	4848.54i	−0.235393	−	0.407713i	−0.959387	+	0.282094i	$0.908971\pi$
$522$	1243.72	+	2154.18i	0.104284	+	0.180625i
$523$	−6635.37	+	11492.8i	−0.554769	+	0.960889i	0.443152	+	0.896446i	$0.353860\pi$
$523$	−6635.37	+	11492.8i	−0.554769	+	0.960889i	−0.997921	+	0.0644422i	$0.979473\pi$
$524$	−710.352			−0.0592211
$525$		0			0
$526$	−4777.27			−0.396005
$527$	−2128.31	+	3686.34i	−0.175922	+	0.304705i
$528$	1473.53	+	2552.22i	0.121453	+	0.210362i
$529$	1608.63	+	2786.23i	0.132213	+	0.228999i
$530$	−1027.86	+	1780.31i	−0.0842403	+	0.145909i
$531$	−4066.19			−0.332312
$532$		0			0
$533$	22956.0			1.86554
$534$	699.256	−	1211.15i	0.0566662	−	0.0981488i
$535$	−851.951	−	1475.62i	−0.0688468	−	0.119246i
$536$	1238.35	+	2144.89i	0.0997922	+	0.172845i
$537$	−2583.81	+	4475.30i	−0.207635	+	0.359634i
$538$	13404.6			1.07419
$539$		0			0
$540$	421.145			0.0335615
$541$	11508.8	−	19933.8i	0.914603	−	1.58414i	0.107121	−	0.994246i	$-0.465837\pi$
$541$	11508.8	−	19933.8i	0.914603	−	1.58414i	0.807482	−	0.589893i	$-0.200830\pi$
$542$	−4950.37	−	8574.29i	−0.392319	−	0.679516i
$543$	2482.51	+	4299.83i	0.196196	+	0.339822i
$544$	−513.608	+	889.595i	−0.0404793	+	0.0701123i
$545$	−648.687			−0.0509848
$546$		0			0
$547$	4475.84			0.349859			0.174930	−	0.984581i	$-0.444030\pi$
$547$	4475.84			0.349859			0.174930	+	0.984581i	$0.444030\pi$
$548$	−54.0303	+	93.5832i	−0.00421179	+	0.00729503i
$549$	2606.88	+	4515.25i	0.202657	+	0.351013i
$550$	6741.02	+	11675.8i	0.522614	+	0.905194i
$551$	−3855.46	+	6677.85i	−0.298091	+	0.516308i
$552$	2270.47			0.175068
$553$		0			0
$554$	7410.35			0.568295
$555$	−872.742	+	1511.63i	−0.0667493	+	0.115613i
$556$	−1845.51	−	3196.51i	−0.140768	−	0.243817i
$557$	−770.848	−	1335.15i	−0.0586390	−	0.101566i	0.835216	−	0.549922i	$-0.185343\pi$
$557$	−770.848	−	1335.15i	−0.0586390	−	0.101566i	−0.893855	+	0.448357i	$0.852009\pi$
$558$	−1193.43	+	2067.08i	−0.0905409	+	0.156821i
$559$	−23497.8			−1.77791
$560$		0			0
$561$	5912.62			0.444975
$562$	9324.74	−	16150.9i	0.699894	−	1.21225i
$563$	6539.83	+	11327.3i	0.489557	+	0.847938i	0.999928	−	0.0120164i	$-0.00382502\pi$
$563$	6539.83	+	11327.3i	0.489557	+	0.847938i	−0.510370	+	0.859955i	$0.670492\pi$
$564$	342.030	+	592.414i	0.0255356	+	0.0442289i
$565$	−956.983	+	1657.54i	−0.0712577	+	0.123422i
$566$	−11139.0			−0.827219
$567$		0			0
$568$	8471.88			0.625831
$569$	−5705.59	+	9882.37i	−0.420370	+	0.728102i	−0.995976	−	0.0896251i	$-0.971433\pi$
$569$	−5705.59	+	9882.37i	−0.420370	+	0.728102i	0.575605	+	0.817728i	$0.304766\pi$
$570$	652.764	+	1130.62i	0.0479671	+	0.0830815i
$571$	−1155.87	−	2002.03i	−0.0847139	−	0.146729i	0.820555	−	0.571567i	$-0.193664\pi$
$571$	−1155.87	−	2002.03i	−0.0847139	−	0.146729i	−0.905269	+	0.424838i	$0.860331\pi$
$572$	−6593.85	+	11420.9i	−0.481998	+	0.834844i
$573$	−3023.06			−0.220402
$574$		0			0
$575$	10386.8			0.753324
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	12548.5	+	21734.6i	0.905373	+	1.56815i	0.820415	+	0.571768i	$0.193742\pi$
$577$	12548.5	+	21734.6i	0.905373	+	1.56815i	0.0849578	+	0.996385i	$0.472924\pi$
$578$	−3882.56	−	6724.79i	−0.279400	−	0.483935i
$579$	11.4727	−	19.8713i	0.000823472	−	0.00142630i
$580$	2155.50			0.154314
$581$		0			0
$582$	−9656.62			−0.687766
$583$	−8091.75	+	14015.3i	−0.574830	+	0.995635i
$584$	−4774.63	−	8269.91i	−0.338315	−	0.585978i
$585$	942.286	+	1632.09i	0.0665961	+	0.115348i
$586$	1665.31	−	2884.40i	0.117395	−	0.203333i
$587$	−19789.1			−1.39145			−0.695726	−	0.718307i	$-0.744917\pi$
$587$	−19789.1			−1.39145			−0.695726	+	0.718307i	$0.744917\pi$
$588$		0			0
$589$	−7399.12			−0.517615
$590$	−1761.79	+	3051.51i	−0.122935	+	0.212930i
$591$	−4034.82	−	6988.51i	−0.280830	−	0.486411i
$592$	−1193.65	−	2067.46i	−0.0828693	−	0.143534i
$593$	−1387.07	+	2402.47i	−0.0960540	+	0.166370i	−0.910048	−	0.414503i	$-0.863955\pi$
$593$	−1387.07	+	2402.47i	−0.0960540	+	0.166370i	0.813994	+	0.580873i	$0.197289\pi$
$594$	3315.44			0.229013
$595$		0			0
$596$	2986.81			0.205276
$597$	1301.25	−	2253.82i	0.0892068	−	0.154511i
$598$	5080.04	+	8798.89i	0.347388	+	0.601694i
$599$	13095.2	+	22681.5i	0.893245	+	1.54715i	0.835962	+	0.548788i	$0.184910\pi$
$599$	13095.2	+	22681.5i	0.893245	+	1.54715i	0.0572831	+	0.998358i	$0.481756\pi$
$600$	−1317.53	+	2282.02i	−0.0896464	+	0.155272i
$601$	11038.6			0.749211			0.374605	−	0.927184i	$-0.377778\pi$
$601$	11038.6			0.749211			0.374605	+	0.927184i	$0.377778\pi$
$602$		0			0
$603$	2786.29			0.188170
$604$	−4146.29	+	7181.59i	−0.279321	+	0.483799i
$605$	−4754.63	−	8235.26i	−0.319509	−	0.553407i
$606$	4437.77	+	7686.44i	0.297479	+	0.515248i
$607$	−927.197	+	1605.95i	−0.0619996	+	0.107386i	−0.895359	−	0.445345i	$-0.853081\pi$
$607$	−927.197	+	1605.95i	−0.0619996	+	0.107386i	0.833360	+	0.552731i	$0.186414\pi$
$608$	−1785.57			−0.119103
$609$		0			0
$610$	4518.01			0.299883
$611$	−1530.54	+	2650.98i	−0.101341	+	0.175527i
$612$	577.809	+	1000.79i	0.0381643	+	0.0661025i
$613$	7428.42	+	12866.4i	0.489447	+	0.847747i	0.999926	−	0.0121428i	$-0.00386527\pi$
$613$	7428.42	+	12866.4i	0.489447	+	0.847747i	−0.510479	+	0.859890i	$0.670532\pi$
$614$	5303.32	−	9185.61i	0.348574	−	0.603748i
$615$	−5001.07			−0.327907
$616$		0			0
$617$	7600.00			0.495890			0.247945	−	0.968774i	$-0.420245\pi$
$617$	7600.00			0.495890			0.247945	+	0.968774i	$0.420245\pi$
$618$	3436.04	−	5951.39i	0.223653	−	0.387379i
$619$	11342.6	+	19646.0i	0.736509	+	1.27567i	0.954058	+	0.299622i	$0.0968606\pi$
$619$	11342.6	+	19646.0i	0.736509	+	1.27567i	−0.217549	+	0.976049i	$0.569806\pi$
$620$	1034.17	+	1791.23i	0.0669891	+	0.116029i
$621$	1277.14	−	2212.07i	0.0825280	−	0.142943i
$622$	2251.98			0.145171
$623$		0			0
$624$	−2577.53			−0.165358
$625$	−5076.98	+	8793.58i	−0.324926	+	0.562789i
$626$	8299.51	+	14375.2i	0.529896	+	0.917807i
$627$	5138.83	+	8900.72i	0.327313	+	0.566923i
$628$	3132.44	−	5425.55i	0.199041	−	0.344750i
$629$	−4789.59			−0.303614
$630$		0			0
$631$	−12024.1			−0.758595			−0.379297	−	0.925275i	$-0.623834\pi$
$631$	−12024.1			−0.758595			−0.379297	+	0.925275i	$0.623834\pi$
$632$	5278.23	−	9142.16i	0.332210	−	0.575405i
$633$	−243.045	−	420.967i	−0.0152610	−	0.0264328i
$634$	−4278.76	−	7411.04i	−0.268031	−	0.464243i
$635$	5101.91	−	8836.77i	0.318840	−	0.552246i
$636$	−3163.05			−0.197206
$637$		0			0
$638$	16969.0			1.05299
$639$	4765.43	−	8253.97i	0.295020	−	0.510989i
$640$	249.568	+	432.264i	0.0154141	+	0.0266980i
$641$	−5660.28	−	9803.89i	−0.348779	−	0.604104i	0.637253	−	0.770654i	$-0.280070\pi$
$641$	−5660.28	−	9803.89i	−0.348779	−	0.604104i	−0.986033	+	0.166551i	$0.946737\pi$
$642$	1310.86	−	2270.48i	0.0805851	−	0.139578i
$643$	−16843.6			−1.03304			−0.516521	−	0.856275i	$-0.672773\pi$
$643$	−16843.6			−1.03304			−0.516521	+	0.856275i	$0.672773\pi$
$644$		0			0
$645$	5119.12			0.312504
$646$	−1791.18	+	3102.41i	−0.109091	+	0.188951i
$647$	3859.66	+	6685.13i	0.234527	+	0.406212i	0.959135	−	0.282949i	$-0.0913126\pi$
$647$	3859.66	+	6685.13i	0.234527	+	0.406212i	−0.724608	+	0.689161i	$0.757979\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	−13869.5	+	24022.8i	−0.838871	+	1.45297i
$650$	−11791.5			−0.711542
$651$		0			0
$652$	394.933			0.0237221
$653$	15401.6	−	26676.3i	0.922987	−	1.59866i	0.128219	−	0.991746i	$-0.459074\pi$
$653$	15401.6	−	26676.3i	0.922987	−	1.59866i	0.794768	−	0.606914i	$-0.207593\pi$
$654$	−499.055	−	864.388i	−0.0298388	−	0.0516823i
$655$	346.252	+	599.725i	0.0206552	+	0.0357759i
$656$	3419.98	−	5923.58i	0.203548	−	0.352556i
$657$	−10742.9			−0.637932
$658$		0			0
$659$	9760.68			0.576968			0.288484	−	0.957485i	$-0.406849\pi$
$659$	9760.68			0.576968			0.288484	+	0.957485i	$0.406849\pi$
$660$	1436.50	−	2488.10i	0.0847209	−	0.146741i
$661$	9035.53	+	15650.0i	0.531682	+	0.920899i	0.999316	+	0.0369775i	$0.0117730\pi$
$661$	9035.53	+	15650.0i	0.531682	+	0.920899i	−0.467635	+	0.883922i	$0.654894\pi$
$662$	−1707.12	−	2956.81i	−0.100225	−	0.173595i
$663$	−2585.62	+	4478.43i	−0.151459	+	0.262335i
$664$	9522.65			0.556552
$665$		0			0
$666$	−2685.71			−0.156260
$667$	6536.64	−	11321.8i	0.379460	−	0.657244i
$668$	−4462.71	−	7729.65i	−0.258484	−	0.447708i
$669$	−6866.77	−	11893.6i	−0.396838	−	0.687344i
$670$	1207.24	−	2090.99i	0.0696114	−	0.120570i
$671$	35567.7			2.04631
$672$		0			0
$673$	26591.1			1.52305			0.761524	−	0.648137i	$-0.224451\pi$
$673$	26591.1			1.52305			0.761524	+	0.648137i	$0.224451\pi$
$674$	1710.67	−	2962.97i	0.0977636	−	0.169331i
$675$	1482.22	+	2567.28i	0.0845194	+	0.146392i
$676$	−1373.05	−	2378.20i	−0.0781210	−	0.135310i
$677$	16540.1	−	28648.3i	0.938979	−	1.62636i	0.171599	−	0.985167i	$-0.445107\pi$
$677$	16540.1	−	28648.3i	0.938979	−	1.62636i	0.767380	−	0.641192i	$-0.221560\pi$
$678$	−2944.95			−0.166814
$679$		0			0
$680$	1001.41			0.0564738
$681$	−3327.29	+	5763.03i	−0.187227	+	0.324287i
$682$	8141.42	+	14101.4i	0.457113	+	0.791743i
$683$	5233.04	+	9063.89i	0.293172	+	0.507789i	0.974558	−	0.224135i	$-0.0719557\pi$
$683$	5233.04	+	9063.89i	0.293172	+	0.507789i	−0.681386	+	0.731924i	$0.738622\pi$
$684$	−1004.38	+	1739.64i	−0.0561455	+	0.0972468i
$685$	105.345			0.00587597
$686$		0			0
$687$	−2355.65			−0.130820
$688$	−3500.70	+	6063.40i	−0.193987	+	0.335995i
$689$	−7077.13	−	12258.0i	−0.391317	−	0.677781i
$690$	−1106.71	−	1916.88i	−0.0610606	−	0.105760i
$691$	6634.95	−	11492.1i	0.365275	−	0.632675i	−0.623545	−	0.781787i	$-0.714308\pi$
$691$	6634.95	−	11492.1i	0.365275	−	0.632675i	0.988820	+	0.149112i	$0.0476415\pi$
$692$	−8403.38			−0.461631
$693$		0			0
$694$	−17820.6			−0.974727
$695$	−1799.14	+	3116.20i	−0.0981944	+	0.170078i
$696$	1658.29	+	2872.24i	0.0903123	+	0.156425i
$697$	−6861.44	−	11884.4i	−0.372878	−	0.645843i
$698$	−5378.68	+	9316.15i	−0.291671	+	0.505189i
$699$	−16107.4			−0.871583
$700$		0			0
$701$	−15169.9			−0.817344			−0.408672	−	0.912681i	$-0.634008\pi$
$701$	−15169.9			−0.817344			−0.408672	+	0.912681i	$0.634008\pi$
$702$	−1449.86	+	2511.23i	−0.0779507	+	0.135015i
$703$	−4162.77	−	7210.14i	−0.223331	−	0.386821i
$704$	1964.70	+	3402.97i	0.105181	+	0.182179i
$705$	333.436	−	577.529i	0.0178127	−	0.0308525i
$706$	−8505.13			−0.453392
$707$		0			0
$708$	−5421.59			−0.287791
$709$	−13158.9	+	22791.8i	−0.697026	+	1.20728i	0.272467	+	0.962165i	$0.412160\pi$
$709$	−13158.9	+	22791.8i	−0.697026	+	1.20728i	−0.969493	+	0.245119i	$0.921173\pi$
$710$	−4129.51	−	7152.51i	−0.218278	−	0.378069i
$711$	−5938.01	−	10284.9i	−0.313211	−	0.542497i
$712$	932.341	−	1614.86i	0.0490744	−	0.0849994i
$713$	12544.6			0.658907
$714$		0			0
$715$	12856.3			0.672447
$716$	−3445.08	+	5967.06i	−0.179817	+	0.311452i
$717$	−5569.91	−	9647.37i	−0.290115	−	0.502493i
$718$	4903.89	+	8493.78i	0.254891	+	0.441484i
$719$	11506.5	−	19929.9i	0.596831	−	1.03374i	−0.396455	−	0.918054i	$-0.629760\pi$
$719$	11506.5	−	19929.9i	0.596831	−	1.03374i	0.993286	−	0.115687i	$-0.0369069\pi$
$720$	561.527			0.0290651
$721$		0			0
$722$	7490.95			0.386128
$723$	10497.9	−	18183.0i	0.540003	−	0.935313i
$724$	3310.01	+	5733.10i	0.169911	+	0.294294i
$725$	7586.26	+	13139.8i	0.388616	+	0.673103i
$726$	7315.76	−	12671.3i	0.373985	−	0.647762i
$727$	16265.4			0.829780			0.414890	−	0.909872i	$-0.363820\pi$
$727$	16265.4			0.829780			0.414890	+	0.909872i	$0.363820\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−4654.66	+	8062.11i	−0.235996	+	0.408756i
$731$	7023.40	+	12164.9i	0.355362	+	0.615505i
$732$	3475.84	+	6020.33i	0.175506	+	0.303986i
$733$	−433.222	+	750.362i	−0.0218300	+	0.0378107i	−0.876734	−	0.480975i	$-0.840283\pi$
$733$	−433.222	+	750.362i	−0.0218300	+	0.0378107i	0.854904	+	0.518786i	$0.173616\pi$
$734$	−8083.14			−0.406477
$735$		0			0
$736$	3027.30			0.151614
$737$	9503.88	−	16461.2i	0.475007	−	0.822736i
$738$	−3847.48	−	6664.03i	−0.191907	−	0.332393i
$739$	−5495.03	−	9517.68i	−0.273529	−	0.473766i	0.696234	−	0.717815i	$-0.254858\pi$
$739$	−5495.03	−	9517.68i	−0.273529	−	0.473766i	−0.969763	+	0.244049i	$0.921524\pi$
$740$	−1163.66	+	2015.51i	−0.0578066	+	0.100124i
$741$	−8988.96			−0.445638
$742$		0			0
$743$	−22416.4			−1.10683			−0.553417	−	0.832905i	$-0.686676\pi$
$743$	−22416.4			−1.10683			−0.553417	+	0.832905i	$0.686676\pi$
$744$	−1591.24	+	2756.10i	−0.0784107	+	0.135811i
$745$	−1455.88	−	2521.66i	−0.0715965	−	0.124009i
$746$	−7451.35	−	12906.1i	−0.365701	−	0.633413i
$747$	5356.49	−	9277.71i	0.262361	−	0.454423i
$748$	7883.49			0.385360
$749$		0			0
$750$	5493.47			0.267457
$751$	9858.97	−	17076.2i	0.479040	−	0.829722i	−0.520671	−	0.853757i	$-0.674318\pi$
$751$	9858.97	−	17076.2i	0.479040	−	0.829722i	0.999711	+	0.0240358i	$0.00765155\pi$
$752$	456.040	+	789.885i	0.0221145	+	0.0383034i
$753$	5584.13	+	9671.99i	0.270248	+	0.468084i
$754$	−7420.64	+	12852.9i	−0.358414	+	0.620791i
$755$	8084.22			0.389689
$756$		0			0
$757$	839.321			0.0402981			0.0201490	−	0.999797i	$-0.493586\pi$
$757$	839.321			0.0402981			0.0201490	+	0.999797i	$0.493586\pi$
$758$	−12564.4	+	21762.2i	−0.602057	+	1.04279i
$759$	−8712.51	−	15090.5i	−0.416659	−	0.721674i
$760$	870.352	+	1507.49i	0.0415407	+	0.0719507i
$761$	9182.25	−	15904.1i	0.437393	−	0.757587i	−0.560094	−	0.828429i	$-0.689235\pi$
$761$	9182.25	−	15904.1i	0.437393	−	0.757587i	0.997488	+	0.0708415i	$0.0225685\pi$
$762$	15700.2			0.746403
$763$		0			0
$764$	−4030.75			−0.190874
$765$	563.291	−	975.648i	0.0266220	−	0.0461106i
$766$	4289.93	+	7430.38i	0.202352	+	0.350484i
$767$	−12130.5	−	21010.6i	−0.571063	−	0.989111i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	14890.8			0.698277			0.349138	−	0.937071i	$-0.386474\pi$
$769$	14890.8			0.698277			0.349138	+	0.937071i	$0.386474\pi$
$770$		0			0
$771$	−3690.45			−0.172384
$772$	15.2970	−	26.4951i	0.000713148	−	0.00123521i
$773$	−8303.10	−	14381.4i	−0.386341	−	0.669163i	0.605613	−	0.795759i	$-0.292928\pi$
$773$	−8303.10	−	14381.4i	−0.386341	−	0.669163i	−0.991954	+	0.126597i	$0.959595\pi$
$774$	3938.29	+	6821.32i	0.182893	+	0.316779i
$775$	−7279.50	+	12608.5i	−0.337403	+	0.584400i
$776$	−12875.5			−0.595623
$777$		0			0
$778$	−11325.5			−0.521903
$779$	11927.0	−	20658.1i	0.548559	−	0.950133i
$780$	1256.38	+	2176.12i	0.0576740	+	0.0998942i
$781$	−32509.2	−	56307.6i	−1.48946	−	2.57983i
$782$	3036.81	−	5259.90i	0.138869	−	0.240529i
$783$	3731.15			0.170294
$784$		0			0
$785$	−6107.47			−0.277688
$786$	−532.764	+	922.774i	−0.0241769	+	0.0418756i
$787$	1578.10	+	2733.35i	0.0714781	+	0.123804i	0.899549	−	0.436819i	$-0.143895\pi$
$787$	1578.10	+	2733.35i	0.0714781	+	0.123804i	−0.828071	+	0.560623i	$0.810562\pi$
$788$	−5379.76	−	9318.01i	−0.243205	−	0.421244i
$789$	−3582.95	+	6205.85i	−0.161668	+	0.280018i
$790$	−10291.2			−0.463475
$791$		0			0
$792$	4420.58			0.198331
$793$	−15553.9	+	26940.2i	−0.696515	+	1.20640i
$794$	−14561.4	−	25221.0i	−0.650836	−	1.12728i
$795$	1541.79	+	2670.46i	0.0687819	+	0.119134i
$796$	1734.99	−	3005.10i	0.0772553	−	0.133810i
$797$	13514.8			0.600652			0.300326	−	0.953837i	$-0.402904\pi$
$797$	13514.8			0.600652			0.300326	+	0.953837i	$0.402904\pi$
$798$		0			0
$799$	1829.89			0.0810224
$800$	−1756.70	+	3042.70i	−0.0776360	+	0.134470i
$801$	−1048.88	−	1816.72i	−0.0462678	−	0.0801382i
$802$	−3742.19	−	6481.66i	−0.164765	−	0.285381i
$803$	−36643.5	+	63468.4i	−1.61036	+	2.78923i
$804$	3715.05			0.162960
$805$		0			0
$806$	−14241.2			−0.622362
$807$	10053.5	−	17413.1i	0.438536	−	0.759567i
$808$	5917.02	+	10248.6i	0.257624	+	0.446218i
$809$	13379.1	+	23173.2i	0.581437	+	1.00708i	0.995309	+	0.0967438i	$0.0308427\pi$
$809$	13379.1	+	23173.2i	0.581437	+	1.00708i	−0.413872	+	0.910335i	$0.635824\pi$
$810$	315.859	−	547.084i	0.0137014	−	0.0237316i
$811$	15920.7			0.689338			0.344669	−	0.938724i	$-0.387991\pi$
$811$	15920.7			0.689338			0.344669	+	0.938724i	$0.387991\pi$
$812$		0			0
$813$	−14851.1			−0.640653
$814$	−9160.80	+	15867.0i	−0.394454	+	0.683215i
$815$	−192.505	−	333.429i	−0.00827381	−	0.0143307i
$816$	770.412	+	1334.39i	0.0330512	+	0.0572464i
$817$	−12208.5	+	21145.7i	−0.522792	+	0.905501i
$818$	−7034.35			−0.300673
$819$		0			0
$820$	−6668.10			−0.283976
$821$	9653.11	−	16719.7i	0.410348	−	0.710744i	−0.584580	−	0.811336i	$-0.698741\pi$
$821$	9653.11	−	16719.7i	0.410348	−	0.710744i	0.994928	+	0.100593i	$0.0320739\pi$
$822$	81.0455	+	140.375i	0.00343891	+	0.00595637i
$823$	−395.500	−	685.026i	−0.0167512	−	0.0290140i	0.857528	−	0.514437i	$-0.171999\pi$
$823$	−395.500	−	685.026i	−0.0167512	−	0.0290140i	−0.874280	+	0.485423i	$0.838666\pi$
$824$	4581.39	−	7935.19i	0.193689	−	0.335480i
$825$	20223.0			0.853426
$826$		0			0
$827$	29537.6			1.24199			0.620993	−	0.783816i	$-0.286730\pi$
$827$	29537.6			1.24199			0.620993	+	0.783816i	$0.286730\pi$
$828$	1702.85	−	2949.43i	0.0714714	−	0.123792i
$829$	−2883.26	−	4993.96i	−0.120796	−	0.209225i	0.799286	−	0.600951i	$-0.205211\pi$
$829$	−2883.26	−	4993.96i	−0.120796	−	0.209225i	−0.920082	+	0.391726i	$0.871878\pi$
$830$	−4641.69	−	8039.64i	−0.194115	−	0.336217i
$831$	5557.76	−	9626.33i	0.232006	−	0.401846i
$832$	−3436.70			−0.143205
$833$		0			0
$834$	−5536.52			−0.229873
$835$	−4350.58	+	7535.43i	−0.180309	+	0.312305i
$836$	6851.78	+	11867.6i	0.283461	+	0.490969i
$837$	1790.14	+	3100.62i	0.0739263	+	0.128044i
$838$	7579.52	−	13128.1i	0.312446	−	0.541173i
$839$	−29726.4			−1.22321			−0.611603	−	0.791165i	$-0.709475\pi$
$839$	−29726.4			−1.22321			−0.611603	+	0.791165i	$0.709475\pi$
$840$		0			0
$841$	−5292.27			−0.216994
$842$	−4980.87	+	8627.12i	−0.203862	+	0.353100i
$843$	−13987.1	−	24226.4i	−0.571461	−	0.989800i
$844$	−324.061	−	561.289i	−0.0132164	−	0.0228914i
$845$	−1338.55	+	2318.44i	−0.0544943	+	0.0943869i
$846$	1026.09			0.0416994
$847$		0			0
$848$	−4217.41			−0.170786
$849$	−8354.23	+	14469.9i	−0.337711	+	0.584932i
$850$	3524.44	+	6104.51i	0.142220	+	0.246333i
$851$	7057.67	+	12224.2i	0.284294	+	0.492411i
$852$	6353.91	−	11005.3i	0.255495	−	0.442530i
$853$	17829.6			0.715677			0.357838	−	0.933784i	$-0.383514\pi$
$853$	17829.6			0.715677			0.357838	+	0.933784i	$0.383514\pi$
$854$		0			0
$855$	1958.29			0.0783300
$856$	1747.82	−	3027.31i	0.0697888	−	0.120878i
$857$	−19841.2	−	34366.0i	−0.790856	−	1.36980i	−0.925438	−	0.378900i	$-0.876303\pi$
$857$	−19841.2	−	34366.0i	−0.790856	−	1.36980i	0.134582	−	0.990902i	$-0.457031\pi$
$858$	9890.77	+	17131.3i	0.393549	+	0.681648i
$859$	−1097.57	+	1901.04i	−0.0435955	+	0.0755096i	−0.887000	−	0.461770i	$-0.847215\pi$
$859$	−1097.57	+	1901.04i	−0.0435955	+	0.0755096i	0.843404	+	0.537279i	$0.180548\pi$
$860$	6825.49			0.270636
$861$		0			0
$862$	−28406.6			−1.12243
$863$	−15958.5	+	27641.0i	−0.629472	+	1.09028i	0.358186	+	0.933650i	$0.383396\pi$
$863$	−15958.5	+	27641.0i	−0.629472	+	1.09028i	−0.987658	+	0.156627i	$0.949938\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	4096.12	+	7094.68i	0.161008	+	0.278874i
$866$	−3874.82	+	6711.39i	−0.152046	+	0.263351i
$867$	−11647.7			−0.456258
$868$		0			0
$869$	−81016.8			−3.16261
$870$	1616.62	−	2800.08i	0.0629985	−	0.109117i
$871$	8312.20	+	14397.2i	0.323362	+	0.560079i
$872$	−665.406	−	1152.52i	−0.0258412	−	0.0447582i
$873$	−7242.47	+	12544.3i	−0.280779	+	0.486324i
$874$	10557.5			0.408596
$875$		0			0
$876$	−14323.9			−0.552465
$877$	−14421.4	+	24978.6i	−0.555276	+	0.961766i	0.442606	+	0.896716i	$0.354054\pi$
$877$	−14421.4	+	24978.6i	−0.555276	+	0.961766i	−0.997882	+	0.0650500i	$0.979279\pi$
$878$	−7763.82	−	13447.3i	−0.298424	−	0.516885i
$879$	−2497.96	−	4326.59i	−0.0958522	−	0.166021i
$880$	1915.34	−	3317.46i	0.0733705	−	0.127081i
$881$	15350.2			0.587015			0.293508	−	0.955957i	$-0.405177\pi$
$881$	15350.2			0.587015			0.293508	+	0.955957i	$0.405177\pi$
$882$		0			0
$883$	6089.64			0.232087			0.116043	−	0.993244i	$-0.462979\pi$
$883$	6089.64			0.232087			0.116043	+	0.993244i	$0.462979\pi$
$884$	−3447.50	+	5971.24i	−0.131167	+	0.227188i
$885$	2642.68	+	4577.26i	0.100376	+	0.173856i
$886$	9662.24	+	16735.5i	0.366376	+	0.634582i
$887$	−192.221	+	332.936i	−0.00727637	+	0.0126030i	−0.869641	−	0.493685i	$-0.835649\pi$
$887$	−192.221	+	332.936i	−0.00727637	+	0.0126030i	0.862364	+	0.506288i	$0.168983\pi$
$888$	−3580.95			−0.135325
$889$		0			0
$890$	−1817.83			−0.0684650
$891$	2486.58	−	4306.88i	0.0934944	−	0.161937i
$892$	−9155.70	−	15858.1i	−0.343672	−	0.595257i
$893$	1590.41	+	2754.67i	0.0595981	+	0.103227i
$894$	2240.11	−	3879.98i	0.0838036	−	0.145152i
$895$	6717.05			0.250867
$896$		0			0
$897$	15240.1			0.567283
$898$	−10942.6	+	18953.1i	−0.406636	+	0.704313i
$899$	9162.27	+	15869.5i	0.339910	+	0.588741i
$900$	1976.29	+	3423.04i	0.0731960	+	0.126779i
$901$	−4230.65	+	7327.70i	−0.156430	+	0.270945i
$902$	−52494.1			−1.93776
$903$		0			0
$904$	−3926.59			−0.144465
$905$	3226.84	−	5589.05i	0.118524	−	0.205289i
$906$	6219.44	+	10772.4i	0.228065	+	0.395020i
$907$	3633.97	+	6294.21i	0.133036	+	0.230426i	0.924846	−	0.380343i	$-0.124194\pi$
$907$	3633.97	+	6294.21i	0.133036	+	0.230426i	−0.791809	+	0.610768i	$0.790861\pi$
$908$	−4436.38	+	7684.04i	−0.162144	+	0.280841i
$909$	13313.3			0.485780
$910$		0			0
$911$	−8535.12			−0.310408			−0.155204	−	0.987882i	$-0.549603\pi$
$911$	−8535.12			−0.310408			−0.155204	+	0.987882i	$0.549603\pi$
$912$	−1339.18	+	2319.52i	−0.0486234	+	0.0842182i
$913$	−36541.4	−	63291.5i	−1.32458	−	2.29424i
$914$	13618.3	+	23587.7i	0.492839	+	0.853622i
$915$	3388.50	−	5869.06i	0.122427	−	0.212049i
$916$	−3140.87			−0.113294
$917$		0			0
$918$	1733.43			0.0623220
$919$	5425.86	−	9397.87i	0.194758	−	0.337331i	−0.752063	−	0.659091i	$-0.770941\pi$
$919$	5425.86	−	9397.87i	0.194758	−	0.337331i	0.946821	+	0.321760i	$0.104275\pi$
$920$	−1475.62	−	2555.84i	−0.0528800	−	0.0915909i
$921$	−7954.97	−	13778.4i	−0.284609	−	0.492958i
$922$	−11955.8	+	20708.1i	−0.427055	+	0.739681i
$923$	56865.9			2.02791
$924$		0			0
$925$	−16381.9			−0.582307
$926$	648.503	−	1123.24i	0.0230142	−	0.0398617i
$927$	−5154.06	−	8927.09i	−0.182612	−	0.316294i
$928$	2211.05	+	3829.66i	0.0782127	+	0.135468i
$929$	−780.319	+	1351.55i	−0.0275581	+	0.0477320i	−0.879476	−	0.475944i	$-0.842106\pi$
$929$	−780.319	+	1351.55i	−0.0275581	+	0.0477320i	0.851917	+	0.523676i	$0.175440\pi$
$930$	3102.51			0.109393
$931$		0			0
$932$	−21476.5			−0.754813
$933$	1688.98	−	2925.40i	0.0592656	−	0.102651i
$934$	−2784.74	−	4823.32i	−0.0975585	−	0.168976i
$935$	−3842.71	−	6655.76i	−0.134406	−	0.232799i
$936$	−1933.15	+	3348.31i	−0.0675073	+	0.116926i
$937$	−11978.4			−0.417627			−0.208813	−	0.977956i	$-0.566960\pi$
$937$	−11978.4			−0.417627			−0.208813	+	0.977956i	$0.566960\pi$
$938$		0			0
$939$	24898.5			0.865317
$940$	444.582	−	770.038i	0.0154262	−	0.0267190i
$941$	12298.8	+	21302.2i	0.426068	+	0.737972i	0.996520	−	0.0833594i	$-0.0265649\pi$
$941$	12298.8	+	21302.2i	0.426068	+	0.737972i	−0.570451	+	0.821332i	$0.693232\pi$
$942$	−4698.66	−	8138.32i	−0.162517	−	0.281487i
$943$	−20221.3	+	35024.3i	−0.698298	+	1.20949i
$944$	−7228.78			−0.249234
$945$		0			0
$946$	53733.1			1.84674
$947$	5417.32	−	9383.07i	0.185891	−	0.321973i	−0.757985	−	0.652272i	$-0.773816\pi$
$947$	5417.32	−	9383.07i	0.185891	−	0.321973i	0.943877	+	0.330298i	$0.107149\pi$
$948$	−7917.35	−	13713.2i	−0.271248	−	0.469816i
$949$	−32048.8	−	55510.2i	−1.09626	−	1.89877i
$950$	−6126.39	+	10611.2i	−0.209228	+	0.362393i
$951$	−12836.3			−0.437692
$952$		0			0
$953$	701.418			0.0238417			0.0119209	−	0.999929i	$-0.496205\pi$
$953$	701.418			0.0238417			0.0119209	+	0.999929i	$0.496205\pi$
$954$	−2372.29	+	4108.93i	−0.0805092	+	0.139446i
$955$	1964.74	+	3403.02i	0.0665732	+	0.115308i
$956$	−7426.55	−	12863.2i	−0.251247	−	0.435172i
$957$	12726.8	−	22043.4i	0.429882	−	0.744578i
$958$	22226.8			0.749599
$959$		0			0
$960$	748.703			0.0251711
$961$	6103.72	−	10571.9i	0.204885	−	0.354871i
$962$	−8012.14	−	13877.4i	−0.268526	−	0.465100i
$963$	−1966.30	−	3405.72i	−0.0657975	−	0.113965i
$964$	13997.2	−	24243.9i	0.467657	−	0.810005i
$965$	−29.8252			−0.000994931
$966$		0			0
$967$	42402.5			1.41011			0.705053	−	0.709154i	$-0.250923\pi$
$967$	42402.5			1.41011			0.705053	+	0.709154i	$0.250923\pi$
$968$	9754.35	−	16895.0i	0.323881	−	0.560978i
$969$	2686.76	+	4653.61i	0.0890725	+	0.154278i
$970$	6275.99	+	10870.3i	0.207742	+	0.359820i
$971$	7731.69	−	13391.7i	0.255532	−	0.442595i	−0.709508	−	0.704698i	$-0.751083\pi$
$971$	7731.69	−	13391.7i	0.255532	−	0.442595i	0.965040	+	0.262103i	$0.0844160\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	7572.55			0.249117
$975$	−8843.65	+	15317.7i	−0.290486	+	0.503136i
$976$	4634.45	+	8027.11i	0.151993	+	0.263260i
$977$	17242.1	+	29864.1i	0.564609	+	0.977931i	0.997086	+	0.0762860i	$0.0243062\pi$
$977$	17242.1	+	29864.1i	0.564609	+	0.977931i	−0.432477	+	0.901645i	$0.642360\pi$
$978$	296.200	−	513.033i	0.00968449	−	0.0167740i
$979$	−14310.7			−0.467184
$980$		0			0
$981$	−1497.16			−0.0487266
$982$	−9582.12	+	16596.7i	−0.311383	+	0.539330i
$983$	3667.68	+	6352.61i	0.119004	+	0.206121i	0.919373	−	0.393386i	$-0.128697\pi$
$983$	3667.68	+	6352.61i	0.119004	+	0.206121i	−0.800369	+	0.599507i	$0.795363\pi$
$984$	−5129.97	−	8885.37i	−0.166197	−	0.287861i
$985$	−5244.58	+	9083.89i	−0.169651	+	0.293844i
$986$	8872.00			0.286554
$987$		0			0
$988$	−11985.3			−0.385934
$989$	20698.6	−	35851.0i	0.665497	−	1.15267i
$990$	−2154.75	−	3732.14i	−0.0691743	−	0.119813i
$991$	5061.48	+	8766.74i	0.162243	+	0.281014i	0.935673	−	0.352869i	$-0.114794\pi$
$991$	5061.48	+	8766.74i	0.162243	+	0.281014i	−0.773430	+	0.633882i	$0.781460\pi$
$992$	−2121.65	+	3674.80i	−0.0679057	+	0.117616i
$993$	−5121.35			−0.163667
$994$		0			0
$995$	−3382.80			−0.107781
$996$	7141.99	−	12370.3i	0.227211	−	0.393542i
$997$	28334.6	+	49076.9i	0.900066	+	1.55896i	0.827407	+	0.561602i	$0.189815\pi$
$997$	28334.6	+	49076.9i	0.900066	+	1.55896i	0.0726582	+	0.997357i	$0.476852\pi$
$998$	5581.55	+	9667.52i	0.177035	+	0.306633i
$999$	−2014.28	+	3488.84i	−0.0637928	+	0.110492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.n.79.1		4
3.2	odd	2		882.4.g.y.667.2		4
7.2	even	3		294.4.a.k.1.2	yes	2
7.3	odd	6		294.4.e.o.67.2		4
7.4	even	3	inner	294.4.e.n.67.1		4
7.5	odd	6		294.4.a.j.1.1	✓	2
7.6	odd	2		294.4.e.o.79.2		4
21.2	odd	6		882.4.a.bi.1.1		2
21.5	even	6		882.4.a.bc.1.2		2
21.11	odd	6		882.4.g.y.361.2		4
21.17	even	6		882.4.g.bd.361.1		4
21.20	even	2		882.4.g.bd.667.1		4
28.19	even	6		2352.4.a.cd.1.1		2
28.23	odd	6		2352.4.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.j.1.1	✓	2	7.5	odd	6
294.4.a.k.1.2	yes	2	7.2	even	3
294.4.e.n.67.1		4	7.4	even	3	inner
294.4.e.n.79.1		4	1.1	even	1	trivial
294.4.e.o.67.2		4	7.3	odd	6
294.4.e.o.79.2		4	7.6	odd	2
882.4.a.bc.1.2		2	21.5	even	6
882.4.a.bi.1.1		2	21.2	odd	6
882.4.g.y.361.2		4	21.11	odd	6
882.4.g.y.667.2		4	3.2	odd	2
882.4.g.bd.361.1		4	21.17	even	6
882.4.g.bd.667.1		4	21.20	even	2
2352.4.a.bn.1.2		2	28.23	odd	6
2352.4.a.cd.1.1		2	28.19	even	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.94975 + 3.37706i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(3.89949 + 6.75412i) q^{10} +(30.6985 + 53.1713i) q^{11} +(-6.00000 + 10.3923i) q^{12} -53.6985 q^{13} +11.6985 q^{15} +(-8.00000 + 13.8564i) q^{16} +(16.0503 + 27.7999i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-27.8995 + 48.3233i) q^{19} +15.5980 q^{20} +122.794 q^{22} +(47.3015 - 81.9286i) q^{23} +(12.0000 + 20.7846i) q^{24} +(54.8970 + 95.0843i) q^{25} +(-53.6985 + 93.0085i) q^{26} +27.0000 q^{27} +138.191 q^{29} +(11.6985 - 20.2624i) q^{30} +(66.3015 + 114.838i) q^{31} +(16.0000 + 27.7128i) q^{32} +(92.0955 - 159.514i) q^{33} +64.2010 q^{34} +36.0000 q^{36} +(-74.6030 + 129.216i) q^{37} +(55.7990 + 96.6467i) q^{38} +(80.5477 + 139.513i) q^{39} +(15.5980 - 27.0165i) q^{40} -427.497 q^{41} +437.588 q^{43} +(122.794 - 212.685i) q^{44} +(-17.5477 - 30.3936i) q^{45} +(-94.6030 - 163.857i) q^{46} +(28.5025 - 49.3678i) q^{47} +48.0000 q^{48} +219.588 q^{50} +(48.1508 - 83.3996i) q^{51} +(107.397 + 186.017i) q^{52} +(131.794 + 228.274i) q^{53} +(27.0000 - 46.7654i) q^{54} -239.417 q^{55} +167.397 q^{57} +(138.191 - 239.354i) q^{58} +(225.899 + 391.269i) q^{59} +(-23.3970 - 40.5247i) q^{60} +(289.653 - 501.694i) q^{61} +265.206 q^{62} +64.0000 q^{64} +(104.698 - 181.343i) q^{65} +(-184.191 - 319.028i) q^{66} +(-154.794 - 268.111i) q^{67} +(64.2010 - 111.199i) q^{68} -283.809 q^{69} -1058.98 q^{71} +(36.0000 - 62.3538i) q^{72} +(596.829 + 1033.74i) q^{73} +(149.206 + 258.432i) q^{74} +(164.691 - 285.253i) q^{75} +223.196 q^{76} +322.191 q^{78} +(-659.779 + 1142.77i) q^{79} +(-31.1960 - 54.0330i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-427.497 + 740.447i) q^{82} -1190.33 q^{83} -125.176 q^{85} +(437.588 - 757.924i) q^{86} +(-207.286 - 359.031i) q^{87} +(-245.588 - 425.371i) q^{88} +(-116.543 + 201.858i) q^{89} -70.1909 q^{90} -378.412 q^{92} +(198.905 - 344.513i) q^{93} +(-57.0051 - 98.7356i) q^{94} +(-108.794 - 188.437i) q^{95} +(48.0000 - 83.1384i) q^{96} +1609.44 q^{97} -552.573 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	\( 4 q + 4 q^{2} - 6 q^{3} - 8 q^{4} + 12 q^{5} - 24 q^{6} - 32 q^{8} - 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 96 q^{13} - 72 q^{15} - 32 q^{16} + 84 q^{17} + 36 q^{18} - 72 q^{19} - 96 q^{20} + 16 q^{22} + 308 q^{23} + 48 q^{24} - 18 q^{25} - 96 q^{26} + 108 q^{27} - 160 q^{29} - 72 q^{30} + 384 q^{31} + 64 q^{32} + 12 q^{33} + 336 q^{34} + 144 q^{36} - 536 q^{37} + 144 q^{38} + 144 q^{39} - 96 q^{40} - 1512 q^{41} + 800 q^{43} + 16 q^{44} + 108 q^{45} - 616 q^{46} + 312 q^{47} + 192 q^{48} - 72 q^{50} + 252 q^{51} + 192 q^{52} + 52 q^{53} + 108 q^{54} - 2304 q^{55} + 432 q^{57} - 160 q^{58} + 864 q^{59} + 144 q^{60} + 1416 q^{61} + 1536 q^{62} + 256 q^{64} + 300 q^{65} - 24 q^{66} - 144 q^{67} + 336 q^{68} - 1848 q^{69} - 3048 q^{71} + 144 q^{72} + 744 q^{73} + 1072 q^{74} - 54 q^{75} + 576 q^{76} + 576 q^{78} - 976 q^{79} + 192 q^{80} - 162 q^{81} - 1512 q^{82} + 624 q^{83} + 1400 q^{85} + 800 q^{86} + 240 q^{87} - 32 q^{88} + 108 q^{89} + 432 q^{90} - 2464 q^{92} + 1152 q^{93} - 624 q^{94} + 40 q^{95} + 192 q^{96} + 1488 q^{97} - 72 q^{99}+O(q^{100}) \) 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 + 84 * q^17 + 36 * q^18 - 72 * q^19 - 96 * q^20 + 16 * q^22 + 308 * q^23 + 48 * q^24 - 18 * q^25 - 96 * q^26 + 108 * q^27 - 160 * q^29 - 72 * q^30 + 384 * q^31 + 64 * q^32 + 12 * q^33 + 336 * q^34 + 144 * q^36 - 536 * q^37 + 144 * q^38 + 144 * q^39 - 96 * q^40 - 1512 * q^41 + 800 * q^43 + 16 * q^44 + 108 * q^45 - 616 * q^46 + 312 * q^47 + 192 * q^48 - 72 * q^50 + 252 * q^51 + 192 * q^52 + 52 * q^53 + 108 * q^54 - 2304 * q^55 + 432 * q^57 - 160 * q^58 + 864 * q^59 + 144 * q^60 + 1416 * q^61 + 1536 * q^62 + 256 * q^64 + 300 * q^65 - 24 * q^66 - 144 * q^67 + 336 * q^68 - 1848 * q^69 - 3048 * q^71 + 144 * q^72 + 744 * q^73 + 1072 * q^74 - 54 * q^75 + 576 * q^76 + 576 * q^78 - 976 * q^79 + 192 * q^80 - 162 * q^81 - 1512 * q^82 + 624 * q^83 + 1400 * q^85 + 800 * q^86 + 240 * q^87 - 32 * q^88 + 108 * q^89 + 432 * q^90 - 2464 * q^92 + 1152 * q^93 - 624 * q^94 + 40 * q^95 + 192 * q^96 + 1488 * q^97 - 72 * q^99

Introduction

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