LMFDB - Embedded newform 294.4.e.n.79.2

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

Embedding invariants

Embedding label			79.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.n.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.94975 - 13.7694i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.94975 - 13.7694i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-15.8995 - 27.5387i) q^{10} +(-28.6985 - 49.7072i) q^{11} +(-6.00000 + 10.3923i) q^{12} +5.69848 q^{13} -47.6985 q^{15} +(-8.00000 + 13.8564i) q^{16} +(25.9497 + 44.9463i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-8.10051 + 14.0305i) q^{19} -63.5980 q^{20} -114.794 q^{22} +(106.698 - 184.807i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-63.8970 - 110.673i) q^{25} +(5.69848 - 9.87007i) q^{26} +27.0000 q^{27} -218.191 q^{29} +(-47.6985 + 82.6162i) q^{30} +(125.698 + 217.716i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-86.0955 + 149.122i) q^{33} +103.799 q^{34} +36.0000 q^{36} +(-193.397 + 334.973i) q^{37} +(16.2010 + 28.0610i) q^{38} +(-8.54773 - 14.8051i) q^{39} +(-63.5980 + 110.155i) q^{40} -328.503 q^{41} -37.5879 q^{43} +(-114.794 + 198.829i) q^{44} +(71.5477 + 123.924i) q^{45} +(-213.397 - 369.614i) q^{46} +(127.497 - 220.832i) q^{47} +48.0000 q^{48} -255.588 q^{50} +(77.8492 - 134.839i) q^{51} +(-11.3970 - 19.7401i) q^{52} +(-105.794 - 183.240i) q^{53} +(27.0000 - 46.7654i) q^{54} -912.583 q^{55} +48.6030 q^{57} +(-218.191 + 377.918i) q^{58} +(206.101 + 356.977i) q^{59} +(95.3970 + 165.232i) q^{60} +(418.347 - 724.598i) q^{61} +502.794 q^{62} +64.0000 q^{64} +(45.3015 - 78.4645i) q^{65} +(172.191 + 298.243i) q^{66} +(82.7939 + 143.403i) q^{67} +(103.799 - 179.785i) q^{68} -640.191 q^{69} -465.015 q^{71} +(36.0000 - 62.3538i) q^{72} +(-224.829 - 389.415i) q^{73} +(386.794 + 669.947i) q^{74} +(-191.691 + 332.018i) q^{75} +64.8040 q^{76} -34.1909 q^{78} +(171.779 - 297.530i) q^{79} +(127.196 + 220.310i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-328.503 + 568.983i) q^{82} +1502.33 q^{83} +825.176 q^{85} +(-37.5879 + 65.1041i) q^{86} +(327.286 + 566.877i) q^{87} +(229.588 + 397.658i) q^{88} +(170.543 - 295.389i) q^{89} +286.191 q^{90} -853.588 q^{92} +(377.095 - 653.148i) q^{93} +(-254.995 - 441.664i) q^{94} +(128.794 + 223.078i) q^{95} +(48.0000 - 83.1384i) q^{96} -865.437 q^{97} +516.573 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
$5$	7.94975	−	13.7694i	0.711047	−	1.23157i	−0.253417	−	0.967357i	$-0.581555\pi$
$5$	7.94975	−	13.7694i	0.711047	−	1.23157i	0.964464	−	0.264213i	$-0.0851120\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−15.8995	−	27.5387i	−0.502786	−	0.870851i
$11$	−28.6985	−	49.7072i	−0.786629	−	1.36248i	−0.928021	−	0.372528i	$-0.878491\pi$
$11$	−28.6985	−	49.7072i	−0.786629	−	1.36248i	0.141392	−	0.989954i	$-0.454842\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	5.69848			0.121575			0.0607875	−	0.998151i	$-0.480639\pi$
$13$	5.69848			0.121575			0.0607875	+	0.998151i	$0.480639\pi$
$14$		0			0
$15$	−47.6985			−0.821046
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	25.9497	+	44.9463i	0.370220	+	0.641240i	0.989599	−	0.143852i	$-0.0459490\pi$
$17$	25.9497	+	44.9463i	0.370220	+	0.641240i	−0.619379	+	0.785092i	$0.712616\pi$
$18$	9.00000	+	15.5885i	0.117851	+	0.204124i
$19$	−8.10051	+	14.0305i	−0.0978096	+	0.169411i	−0.910778	−	0.412897i	$-0.864517\pi$
$19$	−8.10051	+	14.0305i	−0.0978096	+	0.169411i	0.812968	+	0.582308i	$0.197850\pi$
$20$	−63.5980			−0.711047
$21$		0			0
$22$	−114.794			−1.11246
$23$	106.698	−	184.807i	0.967312	−	1.67543i	0.264041	−	0.964512i	$-0.414945\pi$
$23$	106.698	−	184.807i	0.967312	−	1.67543i	0.703271	−	0.710922i	$-0.251722\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−63.8970	−	110.673i	−0.511176	−	0.885382i
$26$	5.69848	−	9.87007i	0.0429833	−	0.0744492i
$27$	27.0000			0.192450
$28$		0			0
$29$	−218.191			−1.39714			−0.698570	−	0.715542i	$-0.746180\pi$
$29$	−218.191			−1.39714			−0.698570	+	0.715542i	$0.746180\pi$
$30$	−47.6985	+	82.6162i	−0.290284	+	0.502786i
$31$	125.698	+	217.716i	0.728262	+	1.26139i	0.957617	+	0.288044i	$0.0930048\pi$
$31$	125.698	+	217.716i	0.728262	+	1.26139i	−0.229356	+	0.973343i	$0.573662\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−86.0955	+	149.122i	−0.454160	+	0.786629i
$34$	103.799			0.523570
$35$		0			0
$36$	36.0000			0.166667
$37$	−193.397	+	334.973i	−0.859304	+	1.48836i	0.0132889	+	0.999912i	$0.495770\pi$
$37$	−193.397	+	334.973i	−0.859304	+	1.48836i	−0.872593	+	0.488447i	$0.837563\pi$
$38$	16.2010	+	28.0610i	0.0691619	+	0.119792i
$39$	−8.54773	−	14.8051i	−0.0350957	−	0.0607875i
$40$	−63.5980	+	110.155i	−0.251393	+	0.435426i
$41$	−328.503			−1.25130			−0.625652	−	0.780102i	$-0.715167\pi$
$41$	−328.503			−1.25130			−0.625652	+	0.780102i	$0.715167\pi$
$42$		0			0
$43$	−37.5879			−0.133305			−0.0666523	−	0.997776i	$-0.521232\pi$
$43$	−37.5879			−0.133305			−0.0666523	+	0.997776i	$0.521232\pi$
$44$	−114.794	+	198.829i	−0.393314	+	0.681241i
$45$	71.5477	+	123.924i	0.237016	+	0.410523i
$46$	−213.397	−	369.614i	−0.683993	−	1.18471i
$47$	127.497	−	220.832i	0.395690	−	0.685355i	−0.597499	−	0.801869i	$-0.703839\pi$
$47$	127.497	−	220.832i	0.395690	−	0.685355i	0.993189	+	0.116515i	$0.0371722\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	−255.588			−0.722912
$51$	77.8492	−	134.839i	0.213747	−	0.370220i
$52$	−11.3970	−	19.7401i	−0.0303938	−	0.0526435i
$53$	−105.794	−	183.240i	−0.274187	−	0.474906i	0.695743	−	0.718291i	$-0.255075\pi$
$53$	−105.794	−	183.240i	−0.274187	−	0.474906i	−0.969930	+	0.243385i	$0.921742\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−912.583			−2.23732
$56$		0			0
$57$	48.6030			0.112941
$58$	−218.191	+	377.918i	−0.493963	+	0.855569i
$59$	206.101	+	356.977i	0.454780	+	0.787701i	0.998676	−	0.0514512i	$-0.0163847\pi$
$59$	206.101	+	356.977i	0.454780	+	0.787701i	−0.543896	+	0.839153i	$0.683051\pi$
$60$	95.3970	+	165.232i	0.205262	+	0.355524i
$61$	418.347	−	724.598i	0.878095	−	1.52091i	0.0246666	−	0.999696i	$-0.492148\pi$
$61$	418.347	−	724.598i	0.878095	−	1.52091i	0.853429	−	0.521210i	$-0.174519\pi$
$62$	502.794			1.02992
$63$		0			0
$64$	64.0000			0.125000
$65$	45.3015	−	78.4645i	0.0864456	−	0.149728i
$66$	172.191	+	298.243i	0.321140	+	0.556231i
$67$	82.7939	+	143.403i	0.150969	+	0.261485i	0.931584	−	0.363527i	$-0.118427\pi$
$67$	82.7939	+	143.403i	0.150969	+	0.261485i	−0.780615	+	0.625012i	$0.785094\pi$
$68$	103.799	−	179.785i	0.185110	−	0.320620i
$69$	−640.191			−1.11696
$70$		0			0
$71$	−465.015			−0.777284			−0.388642	−	0.921389i	$-0.627056\pi$
$71$	−465.015			−0.777284			−0.388642	+	0.921389i	$0.627056\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	−224.829	−	389.415i	−0.360469	−	0.624351i	0.627569	−	0.778561i	$-0.284050\pi$
$73$	−224.829	−	389.415i	−0.360469	−	0.624351i	−0.988038	+	0.154210i	$0.950717\pi$
$74$	386.794	+	669.947i	0.607620	+	1.05243i
$75$	−191.691	+	332.018i	−0.295127	+	0.511176i
$76$	64.8040			0.0978096
$77$		0			0
$78$	−34.1909			−0.0496328
$79$	171.779	−	297.530i	0.244641	−	0.423730i	−0.717390	−	0.696672i	$-0.754663\pi$
$79$	171.779	−	297.530i	0.244641	−	0.423730i	0.962031	+	0.272942i	$0.0879966\pi$
$80$	127.196	+	220.310i	0.177762	+	0.307892i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−328.503	+	568.983i	−0.442403	+	0.766264i
$83$	1502.33			1.98677			0.993387	−	0.114812i	$-0.0366265\pi$
$83$	1502.33			1.98677			0.993387	+	0.114812i	$0.0366265\pi$
$84$		0			0
$85$	825.176			1.05298
$86$	−37.5879	+	65.1041i	−0.0471303	+	0.0816321i
$87$	327.286	+	566.877i	0.403319	+	0.698570i
$88$	229.588	+	397.658i	0.278115	+	0.481710i
$89$	170.543	−	295.389i	0.203118	−	0.351810i	−0.746414	−	0.665482i	$-0.768226\pi$
$89$	170.543	−	295.389i	0.203118	−	0.351810i	0.949531	+	0.313672i	$0.101559\pi$
$90$	286.191			0.335191
$91$		0			0
$92$	−853.588			−0.967312
$93$	377.095	−	653.148i	0.420462	−	0.728262i
$94$	−254.995	−	441.664i	−0.279795	−	0.484619i
$95$	128.794	+	223.078i	0.139095	+	0.240919i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	−865.437			−0.905895			−0.452947	−	0.891537i	$-0.649627\pi$
$97$	−865.437			−0.905895			−0.452947	+	0.891537i	$0.649627\pi$
$98$		0			0
$99$	516.573			0.524419
$100$	−255.588	+	442.691i	−0.255588	+	0.442691i
$101$	121.628	+	210.666i	0.119826	+	0.207545i	0.919699	−	0.392625i	$-0.128433\pi$
$101$	121.628	+	210.666i	0.119826	+	0.207545i	−0.799873	+	0.600170i	$0.795100\pi$
$102$	−155.698	−	269.678i	−0.151142	−	0.261785i
$103$	476.673	−	825.622i	0.456000	−	0.789815i	−0.542745	−	0.839898i	$-0.682615\pi$
$103$	476.673	−	825.622i	0.456000	−	0.789815i	0.998745	+	0.0500822i	$0.0159483\pi$
$104$	−45.5879			−0.0429833
$105$		0			0
$106$	−423.176			−0.387759
$107$	672.477	−	1164.76i	0.607578	−	1.05236i	−0.384061	−	0.923308i	$-0.625475\pi$
$107$	672.477	−	1164.76i	0.607578	−	1.05236i	0.991638	−	0.129048i	$-0.0411921\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	−867.176	−	1501.99i	−0.762022	−	1.31986i	−0.941807	−	0.336155i	$-0.890874\pi$
$109$	−867.176	−	1501.99i	−0.762022	−	1.31986i	0.179785	−	0.983706i	$-0.442460\pi$
$110$	−912.583	+	1580.64i	−0.791012	+	1.37007i
$111$	1160.38			0.992239
$112$		0			0
$113$	1441.18			1.19977			0.599887	−	0.800085i	$-0.295212\pi$
$113$	1441.18			1.19977			0.599887	+	0.800085i	$0.295212\pi$
$114$	48.6030	−	84.1829i	0.0399306	−	0.0691619i
$115$	−1696.45	−	2938.34i	−1.37561	−	2.38262i
$116$	436.382	+	755.835i	0.349285	+	0.604979i
$117$	−25.6432	+	44.4153i	−0.0202625	+	0.0350957i
$118$	824.402			0.643156
$119$		0			0
$120$	381.588			0.290284
$121$	−981.706	+	1700.36i	−0.737570	+	1.27751i
$122$	−836.693	−	1449.20i	−0.620907	−	1.07544i
$123$	492.754	+	853.475i	0.361220	+	0.625652i
$124$	502.794	−	870.865i	0.364131	−	0.630693i
$125$	−44.4222			−0.0317860
$126$		0			0
$127$	1184.70			0.827759			0.413880	−	0.910332i	$-0.364173\pi$
$127$	1184.70			0.827759			0.413880	+	0.910332i	$0.364173\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	56.3818	+	97.6562i	0.0384817	+	0.0666523i
$130$	−90.6030	−	156.929i	−0.0611262	−	0.105874i
$131$	−148.794	+	257.719i	−0.0992381	+	0.171885i	−0.911369	−	0.411589i	$-0.864974\pi$
$131$	−148.794	+	257.719i	−0.0992381	+	0.171885i	0.812131	+	0.583475i	$0.198307\pi$
$132$	688.764			0.454160
$133$		0			0
$134$	331.176			0.213502
$135$	214.643	−	371.773i	0.136841	−	0.237016i
$136$	−207.598	−	359.570i	−0.130892	−	0.226712i
$137$	−310.492	−	537.789i	−0.193629	−	0.335375i	0.752821	−	0.658225i	$-0.228692\pi$
$137$	−310.492	−	537.789i	−0.193629	−	0.335375i	−0.946450	+	0.322850i	$0.895359\pi$
$138$	−640.191	+	1108.84i	−0.394903	+	0.683993i
$139$	−898.754			−0.548426			−0.274213	−	0.961669i	$-0.588417\pi$
$139$	−898.754			−0.548426			−0.274213	+	0.961669i	$0.588417\pi$
$140$		0			0
$141$	−764.985			−0.456903
$142$	−465.015	+	805.430i	−0.274811	+	0.475987i
$143$	−163.538	−	283.256i	−0.0956344	−	0.165644i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−1734.56	+	3004.35i	−0.993432	+	1.72067i
$146$	−899.316			−0.509780
$147$		0			0
$148$	1547.18			0.859304
$149$	1527.35	−	2645.45i	0.839769	−	1.45452i	−0.0503195	−	0.998733i	$-0.516024\pi$
$149$	1527.35	−	2645.45i	0.839769	−	1.45452i	0.890088	−	0.455789i	$-0.150643\pi$
$150$	383.382	+	664.037i	0.208687	+	0.361456i
$151$	32.5727	+	56.4176i	0.0175545	+	0.0304053i	0.874669	−	0.484720i	$-0.161079\pi$
$151$	32.5727	+	56.4176i	0.0175545	+	0.0304053i	−0.857115	+	0.515126i	$0.827745\pi$
$152$	64.8040	−	112.244i	0.0345809	−	0.0598959i
$153$	−467.095			−0.246813
$154$		0			0
$155$	3997.08			2.07131
$156$	−34.1909	+	59.2204i	−0.0175478	+	0.0303938i
$157$	−771.110	−	1335.60i	−0.391983	−	0.678934i	0.600728	−	0.799453i	$-0.294877\pi$
$157$	−771.110	−	1335.60i	−0.391983	−	0.678934i	−0.992711	+	0.120519i	$0.961544\pi$
$158$	−343.558	−	595.059i	−0.172987	−	0.299623i
$159$	−317.382	+	549.721i	−0.158302	+	0.274187i
$160$	508.784			0.251393
$161$		0			0
$162$	−162.000			−0.0785674
$163$	1257.37	−	2177.82i	0.604200	−	1.04650i	−0.387978	−	0.921669i	$-0.626826\pi$
$163$	1257.37	−	2177.82i	0.604200	−	1.04650i	0.992177	−	0.124836i	$-0.0398404\pi$
$164$	657.005	+	1137.97i	0.312826	+	0.541831i
$165$	1368.87	+	2370.96i	0.645859	+	1.11866i
$166$	1502.33	−	2602.11i	0.702431	−	1.21665i
$167$	528.643			0.244956			0.122478	−	0.992471i	$-0.460916\pi$
$167$	528.643			0.244956			0.122478	+	0.992471i	$0.460916\pi$
$168$		0			0
$169$	−2164.53			−0.985220
$170$	825.176	−	1429.25i	0.372283	−	0.644813i
$171$	−72.9045	−	126.274i	−0.0326032	−	0.0564704i
$172$	75.1758	+	130.208i	0.0333261	+	0.0577226i
$173$	−48.4220	+	83.8693i	−0.0212801	+	0.0368582i	−0.876469	−	0.481458i	$-0.840108\pi$
$173$	−48.4220	+	83.8693i	−0.0212801	+	0.0368582i	0.855189	+	0.518316i	$0.173441\pi$
$174$	1309.15			0.570380
$175$		0			0
$176$	918.352			0.393314
$177$	618.302	−	1070.93i	0.262567	−	0.454780i
$178$	−341.085	−	590.777i	−0.143626	−	0.248768i
$179$	267.271	+	462.927i	0.111602	+	0.193301i	0.916416	−	0.400226i	$-0.131068\pi$
$179$	267.271	+	462.927i	0.111602	+	0.193301i	−0.804814	+	0.593527i	$0.797735\pi$
$180$	286.191	−	495.697i	0.118508	−	0.205262i
$181$	2087.00			0.857049			0.428524	−	0.903530i	$-0.359034\pi$
$181$	2087.00			0.857049			0.428524	+	0.903530i	$0.359034\pi$
$182$		0			0
$183$	−2510.08			−1.01394
$184$	−853.588	+	1478.46i	−0.341996	+	0.592355i
$185$	3074.91	+	5325.91i	1.22201	+	2.11659i
$186$	−754.191	−	1306.30i	−0.297312	−	0.514959i
$187$	1489.44	−	2579.78i	0.582451	−	1.00884i
$188$	−1019.98			−0.395690
$189$		0			0
$190$	515.176			0.196709
$191$	−1693.84	+	2933.82i	−0.641687	+	1.11143i	0.343369	+	0.939201i	$0.388432\pi$
$191$	−1693.84	+	2933.82i	−0.641687	+	1.11143i	−0.985056	+	0.172234i	$0.944901\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	954.176	+	1652.68i	0.355871	+	0.616386i	0.987267	−	0.159074i	$-0.0508510\pi$
$193$	954.176	+	1652.68i	0.355871	+	0.616386i	−0.631396	+	0.775461i	$0.717518\pi$
$194$	−865.437	+	1498.98i	−0.320282	+	0.554745i
$195$	−271.809			−0.0998187
$196$		0			0
$197$	−2061.88			−0.745699			−0.372850	−	0.927892i	$-0.621619\pi$
$197$	−2061.88			−0.745699			−0.372850	+	0.927892i	$0.621619\pi$
$198$	516.573	−	894.730i	0.185410	−	0.321140i
$199$	−1585.75	−	2746.60i	−0.564878	−	0.978397i	−0.997061	−	0.0766115i	$-0.975590\pi$
$199$	−1585.75	−	2746.60i	−0.564878	−	0.978397i	0.432183	−	0.901786i	$-0.357743\pi$
$200$	511.176	+	885.382i	0.180728	+	0.313030i
$201$	248.382	−	430.210i	0.0871617	−	0.150969i
$202$	486.512			0.169460
$203$		0			0
$204$	−622.794			−0.213747
$205$	−2611.51	+	4523.27i	−0.889736	+	1.54107i
$206$	−953.346	−	1651.24i	−0.322441	−	0.558484i
$207$	960.286	+	1663.26i	0.322437	+	0.558478i
$208$	−45.5879	+	78.9605i	−0.0151969	+	0.0263218i
$209$	929.889			0.307760
$210$		0			0
$211$	1349.97			0.440454			0.220227	−	0.975449i	$-0.429320\pi$
$211$	1349.97			0.440454			0.220227	+	0.975449i	$0.429320\pi$
$212$	−423.176	+	732.962i	−0.137094	+	0.237453i
$213$	697.523	+	1208.14i	0.224382	+	0.388642i
$214$	−1344.95	−	2329.53i	−0.429622	−	0.744128i
$215$	−298.814	+	517.561i	−0.0947858	+	0.164174i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	−3468.70			−1.07766
$219$	−674.487	+	1168.25i	−0.208117	+	0.360469i
$220$	1825.17	+	3161.28i	0.559330	+	0.968788i
$221$	147.874	+	256.126i	0.0450095	+	0.0779587i
$222$	1160.38	−	2009.84i	0.350810	−	0.607620i
$223$	−1361.85			−0.408951			−0.204476	−	0.978872i	$-0.565549\pi$
$223$	−1361.85			−0.408951			−0.204476	+	0.978872i	$0.565549\pi$
$224$		0			0
$225$	1150.15			0.340784
$226$	1441.18	−	2496.19i	0.424184	−	0.734708i
$227$	−930.905	−	1612.37i	−0.272186	−	0.471441i	0.697235	−	0.716843i	$-0.254413\pi$
$227$	−930.905	−	1612.37i	−0.272186	−	0.471441i	−0.969421	+	0.245402i	$0.921080\pi$
$228$	−97.2061	−	168.366i	−0.0282352	−	0.0489048i
$229$	2679.39	−	4640.84i	0.773184	−	1.33919i	−0.162625	−	0.986688i	$-0.551996\pi$
$229$	2679.39	−	4640.84i	0.773184	−	1.33919i	0.935809	−	0.352506i	$-0.114671\pi$
$230$	−6785.81			−1.94540
$231$		0			0
$232$	1745.53			0.493963
$233$	−2720.56	+	4712.15i	−0.764935	+	1.32491i	0.175345	+	0.984507i	$0.443896\pi$
$233$	−2720.56	+	4712.15i	−0.764935	+	1.32491i	−0.940281	+	0.340400i	$0.889438\pi$
$234$	51.2864	+	88.8306i	0.0143278	+	0.0248164i
$235$	−2027.15	−	3511.12i	−0.562708	−	0.974639i
$236$	824.402	−	1427.91i	0.227390	−	0.393851i
$237$	−1030.67			−0.282487
$238$		0			0
$239$	−1157.28			−0.313213			−0.156607	−	0.987661i	$-0.550055\pi$
$239$	−1157.28			−0.313213			−0.156607	+	0.987661i	$0.550055\pi$
$240$	381.588	−	660.930i	0.102631	−	0.177762i
$241$	1984.69	+	3437.58i	0.530477	+	0.918814i	0.999368	+	0.0355573i	$0.0113206\pi$
$241$	1984.69	+	3437.58i	0.530477	+	0.918814i	−0.468890	+	0.883256i	$0.655346\pi$
$242$	1963.41	+	3400.73i	0.521541	+	0.903335i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−3346.77			−0.878095
$245$		0			0
$246$	1971.02			0.510843
$247$	−46.1606	+	79.9525i	−0.0118912	+	0.0205962i
$248$	−1005.59	−	1741.73i	−0.257479	−	0.445967i
$249$	−2253.50	−	3903.17i	−0.573532	−	0.993387i
$250$	−44.4222	+	76.9415i	−0.0112380	+	0.0194648i
$251$	5978.75			1.50349			0.751744	−	0.659455i	$-0.229213\pi$
$251$	5978.75			1.50349			0.751744	+	0.659455i	$0.229213\pi$
$252$		0			0
$253$	−12248.3			−3.04366
$254$	1184.70	−	2051.97i	0.292657	−	0.506897i
$255$	−1237.76	−	2143.87i	−0.303968	−	0.526488i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2325.07	+	4027.15i	−0.564335	+	0.977458i	0.432776	+	0.901502i	$0.357534\pi$
$257$	−2325.07	+	4027.15i	−0.564335	+	0.977458i	−0.997111	+	0.0759560i	$0.975799\pi$
$258$	225.527			0.0544214
$259$		0			0
$260$	−362.412			−0.0864456
$261$	981.859	−	1700.63i	0.232857	−	0.403319i
$262$	297.588	+	515.437i	0.0701719	+	0.121541i
$263$	−1847.68	−	3200.28i	−0.433205	−	0.750334i	0.563942	−	0.825815i	$-0.309284\pi$
$263$	−1847.68	−	3200.28i	−0.433205	−	0.750334i	−0.997147	+	0.0754807i	$0.975951\pi$
$264$	688.764	−	1192.97i	0.160570	−	0.278115i
$265$	−3364.14			−0.779840
$266$		0			0
$267$	−1023.26			−0.234540
$268$	331.176	−	573.613i	0.0754843	−	0.130743i
$269$	3578.84	+	6198.74i	0.811175	+	1.40500i	0.912042	+	0.410096i	$0.134505\pi$
$269$	3578.84	+	6198.74i	0.811175	+	1.40500i	−0.100868	+	0.994900i	$0.532162\pi$
$270$	−429.286	−	743.546i	−0.0967612	−	0.167595i
$271$	−2019.19	+	3497.33i	−0.452608	+	0.783940i	−0.998547	−	0.0538847i	$-0.982840\pi$
$271$	−2019.19	+	3497.33i	−0.452608	+	0.783940i	0.545939	+	0.837825i	$0.316173\pi$
$272$	−830.392			−0.185110
$273$		0			0
$274$	−1241.97			−0.273833
$275$	−3667.49	+	6352.28i	−0.804211	+	1.39293i
$276$	1280.38	+	2217.69i	0.279239	+	0.483656i
$277$	1377.41	+	2385.75i	0.298775	+	0.517493i	0.975856	−	0.218415i	$-0.0700887\pi$
$277$	1377.41	+	2385.75i	0.298775	+	0.517493i	−0.677081	+	0.735909i	$0.736755\pi$
$278$	−898.754	+	1556.69i	−0.193898	+	0.335841i
$279$	−2262.57			−0.485508
$280$		0			0
$281$	−772.742			−0.164050			−0.0820248	−	0.996630i	$-0.526139\pi$
$281$	−772.742			−0.164050			−0.0820248	+	0.996630i	$0.526139\pi$
$282$	−764.985	+	1324.99i	−0.161540	+	0.279795i
$283$	3372.74	+	5841.76i	0.708441	+	1.22706i	0.965435	+	0.260643i	$0.0839344\pi$
$283$	3372.74	+	5841.76i	0.708441	+	1.22706i	−0.256995	+	0.966413i	$0.582732\pi$
$284$	930.030	+	1610.86i	0.194321	+	0.336574i
$285$	386.382	−	669.233i	0.0803063	−	0.139095i
$286$	−654.152			−0.135248
$287$		0			0
$288$	−288.000			−0.0589256
$289$	1109.72	−	1922.09i	0.225874	−	0.391226i
$290$	3469.13	+	6008.70i	0.702462	+	1.21670i
$291$	1298.16	+	2248.47i	0.261509	+	0.452947i
$292$	−899.316	+	1557.66i	−0.180235	+	0.312175i
$293$	1922.69			0.383362			0.191681	−	0.981457i	$-0.438606\pi$
$293$	1922.69			0.383362			0.191681	+	0.981457i	$0.438606\pi$
$294$		0			0
$295$	6553.79			1.29348
$296$	1547.18	−	2679.79i	0.303810	−	0.526214i
$297$	−774.859	−	1342.10i	−0.151387	−	0.262210i
$298$	−3054.70	−	5290.90i	−0.593806	−	1.02850i
$299$	608.020	−	1053.12i	0.117601	−	0.203691i
$300$	1533.53			0.295127
$301$		0			0
$302$	130.291			0.0248258
$303$	364.884	−	631.998i	0.0691817	−	0.119826i
$304$	−129.608	−	224.488i	−0.0244524	−	0.0423528i
$305$	−6651.50	−	11520.7i	−1.24873	−	2.16287i
$306$	−467.095	+	809.033i	−0.0872617	+	0.151142i
$307$	2016.68			0.374913			0.187456	−	0.982273i	$-0.439976\pi$
$307$	2016.68			0.374913			0.187456	+	0.982273i	$0.439976\pi$
$308$		0			0
$309$	−2860.04			−0.526544
$310$	3997.08	−	6923.15i	0.732320	−	1.26842i
$311$	−3574.99	−	6192.07i	−0.651831	−	1.12900i	−0.982678	−	0.185320i	$-0.940668\pi$
$311$	−3574.99	−	6192.07i	−0.651831	−	1.12900i	0.330848	−	0.943684i	$-0.392665\pi$
$312$	68.3818	+	118.441i	0.0124082	+	0.0214916i
$313$	−4298.25	+	7444.78i	−0.776202	+	1.34442i	0.157914	+	0.987453i	$0.449523\pi$
$313$	−4298.25	+	7444.78i	−0.776202	+	1.34442i	−0.934116	+	0.356969i	$0.883810\pi$
$314$	−3084.44			−0.554347
$315$		0			0
$316$	−1374.23			−0.244641
$317$	1426.62	−	2470.98i	0.252766	−	0.437804i	−0.711520	−	0.702666i	$-0.751993\pi$
$317$	1426.62	−	2470.98i	0.252766	−	0.437804i	0.964286	+	0.264862i	$0.0853263\pi$
$318$	634.764	+	1099.44i	0.111936	+	0.193880i
$319$	6261.75	+	10845.7i	1.09903	+	1.90358i
$320$	508.784	−	881.239i	0.0888809	−	0.153946i
$321$	−4034.86			−0.701570
$322$		0			0
$323$	−840.824			−0.144844
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−364.116	−	630.667i	−0.0621462	−	0.107640i
$326$	−2514.73	−	4355.65i	−0.427234	−	0.739991i
$327$	−2601.53	+	4505.98i	−0.439953	+	0.762022i
$328$	2628.02			0.442403
$329$		0			0
$330$	5475.50			0.913382
$331$	−809.558	+	1402.19i	−0.134433	+	0.232845i	−0.925381	−	0.379039i	$-0.876255\pi$
$331$	−809.558	+	1402.19i	−0.134433	+	0.232845i	0.790948	+	0.611884i	$0.209588\pi$
$332$	−3004.66	−	5204.23i	−0.496694	−	0.860299i
$333$	−1740.57	−	3014.76i	−0.286435	−	0.496120i
$334$	528.643	−	915.637i	0.0866050	−	0.150004i
$335$	2632.76			0.429383
$336$		0			0
$337$	−3278.67			−0.529972			−0.264986	−	0.964252i	$-0.585367\pi$
$337$	−3278.67			−0.529972			−0.264986	+	0.964252i	$0.585367\pi$
$338$	−2164.53	+	3749.07i	−0.348328	+	0.603321i
$339$	−2161.76	−	3744.28i	−0.346345	−	0.599887i
$340$	−1650.35	−	2858.49i	−0.263244	−	0.455952i
$341$	7214.71	−	12496.2i	1.14574	−	1.98449i
$342$	−291.618			−0.0461079
$343$		0			0
$344$	300.703			0.0471303
$345$	−5089.36	+	8815.02i	−0.794208	+	1.37561i
$346$	96.8439	+	167.739i	0.0150473	+	0.0260627i
$347$	1425.15	+	2468.43i	0.220479	+	0.381880i	0.954953	−	0.296756i	$-0.0959048\pi$
$347$	1425.15	+	2468.43i	0.220479	+	0.381880i	−0.734475	+	0.678636i	$0.762571\pi$
$348$	1309.15	−	2267.51i	0.201660	−	0.349285i
$349$	−4725.32			−0.724758			−0.362379	−	0.932031i	$-0.618035\pi$
$349$	−4725.32			−0.724758			−0.362379	+	0.932031i	$0.618035\pi$
$350$		0			0
$351$	153.859			0.0233971
$352$	918.352	−	1590.63i	0.139058	−	0.240855i
$353$	−3363.72	−	5826.13i	−0.507175	−	0.878452i	−0.999966	−	0.00830453i	$-0.997357\pi$
$353$	−3363.72	−	5826.13i	−0.507175	−	0.878452i	0.492791	−	0.870148i	$-0.335977\pi$
$354$	−1236.60	−	2141.86i	−0.185663	−	0.321578i
$355$	−3696.75	+	6402.96i	−0.552685	+	0.957279i
$356$	−1364.34			−0.203118
$357$		0			0
$358$	1069.08			0.157829
$359$	3665.94	−	6349.60i	0.538945	−	0.933479i	−0.460017	−	0.887910i	$-0.652157\pi$
$359$	3665.94	−	6349.60i	0.538945	−	0.933479i	0.998961	−	0.0455691i	$-0.0145101\pi$
$360$	−572.382	−	991.394i	−0.0837977	−	0.145142i
$361$	3298.26	+	5712.76i	0.480867	+	0.832885i
$362$	2087.00	−	3614.80i	0.303012	−	0.524833i
$363$	5890.24			0.851673
$364$		0			0
$365$	−7149.34			−1.02524
$366$	−2510.08	+	4347.59i	−0.358481	+	0.620907i
$367$	−1387.22	−	2402.73i	−0.197308	−	0.341748i	0.750347	−	0.661045i	$-0.229887\pi$
$367$	−1387.22	−	2402.73i	−0.197308	−	0.341748i	−0.947655	+	0.319297i	$0.896553\pi$
$368$	1707.18	+	2956.92i	0.241828	+	0.418858i
$369$	1478.26	−	2560.42i	0.208551	−	0.361220i
$370$	12299.7			1.72819
$371$		0			0
$372$	−3016.76			−0.420462
$373$	−1263.67	+	2188.75i	−0.175417	+	0.303831i	−0.940305	−	0.340332i	$-0.889461\pi$
$373$	−1263.67	+	2188.75i	−0.175417	+	0.303831i	0.764889	+	0.644163i	$0.222794\pi$
$374$	−2978.87	−	5159.56i	−0.411855	−	0.713354i
$375$	66.6333	+	115.412i	0.00917581	+	0.0158930i
$376$	−1019.98	+	1766.66i	−0.139897	+	0.242309i
$377$	−1243.36			−0.169857
$378$		0			0
$379$	3116.40			0.422371			0.211186	−	0.977446i	$-0.432268\pi$
$379$	3116.40			0.422371			0.211186	+	0.977446i	$0.432268\pi$
$380$	515.176	−	892.311i	0.0695473	−	0.120459i
$381$	−1777.05	−	3077.95i	−0.238953	−	0.413880i
$382$	3387.69	+	5867.65i	0.453741	+	0.785903i
$383$	−759.035	+	1314.69i	−0.101266	+	0.175398i	−0.912207	−	0.409731i	$-0.865623\pi$
$383$	−759.035	+	1314.69i	−0.101266	+	0.175398i	0.810940	+	0.585129i	$0.198956\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	3816.70			0.503277
$387$	169.145	−	292.969i	0.0222174	−	0.0384817i
$388$	1730.87	+	2997.96i	0.226474	+	0.392264i
$389$	1623.39	+	2811.79i	0.211591	+	0.366487i	0.952213	−	0.305436i	$-0.0988021\pi$
$389$	1623.39	+	2811.79i	0.211591	+	0.366487i	−0.740622	+	0.671922i	$0.765469\pi$
$390$	−271.809	+	470.787i	−0.0352913	+	0.0611262i
$391$	11075.2			1.43247
$392$		0			0
$393$	892.764			0.114590
$394$	−2061.88	+	3571.28i	−0.263645	+	0.456646i
$395$	−2731.20	−	4730.57i	−0.347902	−	0.602584i
$396$	−1033.15	−	1789.46i	−0.131105	−	0.227080i
$397$	915.312	−	1585.37i	0.115713	−	0.200421i	−0.802351	−	0.596852i	$-0.796418\pi$
$397$	915.312	−	1585.37i	0.115713	−	0.200421i	0.918065	+	0.396431i	$0.129751\pi$
$398$	−6342.99			−0.798858
$399$		0			0
$400$	2044.70			0.255588
$401$	1692.90	−	2932.20i	0.210822	−	0.365154i	−0.741150	−	0.671339i	$-0.765719\pi$
$401$	1692.90	−	2932.20i	0.210822	−	0.365154i	0.951972	+	0.306185i	$0.0990526\pi$
$402$	−496.764	−	860.420i	−0.0616326	−	0.106751i
$403$	716.291	+	1240.65i	0.0885384	+	0.153353i
$404$	486.512	−	842.664i	0.0599131	−	0.103772i
$405$	−1287.86			−0.158010
$406$		0			0
$407$	22200.8			2.70382
$408$	−622.794	+	1078.71i	−0.0755708	+	0.130892i
$409$	4626.59	+	8013.48i	0.559340	+	0.968805i	0.997552	+	0.0699333i	$0.0222787\pi$
$409$	4626.59	+	8013.48i	0.559340	+	0.968805i	−0.438212	+	0.898872i	$0.644388\pi$
$410$	5223.02	+	9046.54i	0.629138	+	1.08970i
$411$	−931.477	+	1613.37i	−0.111792	+	0.193629i
$412$	−3813.39			−0.456000
$413$		0			0
$414$	3841.15			0.455995
$415$	11943.2	−	20686.2i	1.41269	−	2.44685i
$416$	91.1758	+	157.921i	0.0107458	+	0.0186123i
$417$	1348.13	+	2335.03i	0.158317	+	0.274213i
$418$	929.889	−	1610.61i	0.108809	−	0.188464i
$419$	−3547.52			−0.413622			−0.206811	−	0.978381i	$-0.566308\pi$
$419$	−3547.52			−0.413622			−0.206811	+	0.978381i	$0.566308\pi$
$420$		0			0
$421$	7848.87			0.908624			0.454312	−	0.890843i	$-0.349885\pi$
$421$	7848.87			0.908624			0.454312	+	0.890843i	$0.349885\pi$
$422$	1349.97	−	2338.22i	0.155724	−	0.269722i
$423$	1147.48	+	1987.49i	0.131897	+	0.228452i
$424$	846.352	+	1465.92i	0.0969398	+	0.167905i
$425$	3316.22	−	5743.86i	0.378495	−	0.655572i
$426$	2790.09			0.317325
$427$		0			0
$428$	−5379.82			−0.607578
$429$	−490.614	+	849.768i	−0.0552146	+	0.0956344i
$430$	597.628	+	1035.12i	0.0670237	+	0.116088i
$431$	2223.66	+	3851.50i	0.248515	+	0.430441i	0.963114	−	0.269094i	$-0.0867241\pi$
$431$	2223.66	+	3851.50i	0.248515	+	0.430441i	−0.714599	+	0.699534i	$0.753391\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	6994.82			0.776327			0.388164	−	0.921590i	$-0.373110\pi$
$433$	6994.82			0.776327			0.388164	+	0.921590i	$0.373110\pi$
$434$		0			0
$435$	10407.4			1.14712
$436$	−3468.70	+	6007.97i	−0.381011	+	0.659930i
$437$	1728.62	+	2994.06i	0.189225	+	0.327747i
$438$	1348.97	+	2336.49i	0.147161	+	0.254890i
$439$	318.091	−	550.950i	0.0345823	−	0.0598984i	−0.848216	−	0.529650i	$-0.822323\pi$
$439$	318.091	−	550.950i	0.0345823	−	0.0598984i	0.882799	+	0.469752i	$0.155657\pi$
$440$	7300.66			0.791012
$441$		0			0
$442$	591.497			0.0636530
$443$	2237.12	−	3874.80i	0.239929	−	0.415570i	−0.720764	−	0.693180i	$-0.756209\pi$
$443$	2237.12	−	3874.80i	0.239929	−	0.415570i	0.960694	+	0.277610i	$0.0895423\pi$
$444$	−2320.76	−	4019.68i	−0.248060	−	0.429652i
$445$	−2711.54	−	4696.53i	−0.288853	−	0.500308i
$446$	−1361.85	+	2358.79i	−0.144586	+	0.250430i
$447$	−9164.11			−0.969681
$448$		0			0
$449$	−2389.42			−0.251144			−0.125572	−	0.992085i	$-0.540077\pi$
$449$	−2389.42			−0.251144			−0.125572	+	0.992085i	$0.540077\pi$
$450$	1150.15	−	1992.11i	0.120485	−	0.208687i
$451$	9427.52	+	16329.0i	0.984312	+	1.70488i
$452$	−2882.35	−	4992.38i	−0.299943	−	0.519517i
$453$	97.7182	−	169.253i	0.0101351	−	0.0175545i
$454$	−3723.62			−0.384930
$455$		0			0
$456$	−388.824			−0.0399306
$457$	2219.17	−	3843.71i	0.227152	−	0.393438i	−0.729811	−	0.683649i	$-0.760392\pi$
$457$	2219.17	−	3843.71i	0.227152	−	0.393438i	0.956963	+	0.290210i	$0.0937253\pi$
$458$	−5358.78	−	9281.68i	−0.546724	−	0.946953i
$459$	700.643	+	1213.55i	0.0712489	+	0.123407i
$460$	−6785.81	+	11753.4i	−0.687804	+	1.19131i
$461$	14079.8			1.42248			0.711240	−	0.702949i	$-0.248134\pi$
$461$	14079.8			1.42248			0.711240	+	0.702949i	$0.248134\pi$
$462$		0			0
$463$	4687.50			0.470511			0.235255	−	0.971934i	$-0.424407\pi$
$463$	4687.50			0.470511			0.235255	+	0.971934i	$0.424407\pi$
$464$	1745.53	−	3023.34i	0.174642	−	0.302489i
$465$	−5995.63	−	10384.7i	−0.597937	−	1.03566i
$466$	5441.12	+	9424.30i	0.540891	+	0.936851i
$467$	4223.63	−	7315.54i	0.418514	−	0.724888i	−0.577276	−	0.816549i	$-0.695884\pi$
$467$	4223.63	−	7315.54i	0.418514	−	0.724888i	0.995790	+	0.0916611i	$0.0292176\pi$
$468$	205.145			0.0202625
$469$		0			0
$470$	−8108.58			−0.795789
$471$	−2313.33	+	4006.81i	−0.226311	+	0.391983i
$472$	−1648.80	−	2855.81i	−0.160789	−	0.278495i
$473$	1078.72	+	1868.39i	0.104861	+	0.181625i
$474$	−1030.67	+	1785.18i	−0.0998742	+	0.172987i
$475$	2070.39			0.199992
$476$		0			0
$477$	1904.29			0.182791
$478$	−1157.28	+	2004.46i	−0.110738	+	0.191803i
$479$	−2184.70	−	3784.02i	−0.208396	−	0.360952i	0.742814	−	0.669498i	$-0.233491\pi$
$479$	−2184.70	−	3784.02i	−0.208396	−	0.360952i	−0.951209	+	0.308546i	$0.900158\pi$
$480$	−763.176	−	1321.86i	−0.0725709	−	0.125697i
$481$	−1102.07	+	1908.84i	−0.104470	+	0.180947i
$482$	7938.75			0.750208
$483$		0			0
$484$	7853.65			0.737570
$485$	−6880.00	+	11916.5i	−0.644134	+	1.11567i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	7238.86	+	12538.1i	0.673561	+	1.16664i	0.976887	+	0.213755i	$0.0685695\pi$
$487$	7238.86	+	12538.1i	0.673561	+	1.16664i	−0.303326	+	0.952887i	$0.598097\pi$
$488$	−3346.77	+	5796.78i	−0.310454	+	0.537721i
$489$	−7544.20			−0.697670
$490$		0			0
$491$	9306.12			0.855355			0.427677	−	0.903931i	$-0.359332\pi$
$491$	9306.12			0.855355			0.427677	+	0.903931i	$0.359332\pi$
$492$	1971.02	−	3413.90i	0.180610	−	0.312826i
$493$	−5662.00	−	9806.87i	−0.517249	−	0.895901i
$494$	92.3212	+	159.905i	0.00840836	+	0.0145637i
$495$	4106.62	−	7112.88i	0.372887	−	0.645859i
$496$	−4022.35			−0.364131
$497$		0			0
$498$	−9013.99			−0.811097
$499$	6118.77	−	10598.0i	0.548926	−	0.950767i	−0.449423	−	0.893319i	$-0.648370\pi$
$499$	6118.77	−	10598.0i	0.548926	−	0.950767i	0.998349	−	0.0574479i	$-0.0182963\pi$
$500$	88.8444	+	153.883i	0.00794649	+	0.0137637i
$501$	−792.965	−	1373.46i	−0.0707127	−	0.122478i
$502$	5978.75	−	10355.5i	0.531563	−	0.920695i
$503$	−5524.30			−0.489694			−0.244847	−	0.969562i	$-0.578738\pi$
$503$	−5524.30			−0.489694			−0.244847	+	0.969562i	$0.578738\pi$
$504$		0			0
$505$	3867.65			0.340808
$506$	−12248.3	+	21214.7i	−1.07610	+	1.86385i
$507$	3246.79	+	5623.61i	0.284408	+	0.492610i
$508$	−2369.41	−	4103.93i	−0.206940	−	0.358430i
$509$	−5039.81	+	8729.20i	−0.438871	+	0.760148i	−0.997603	−	0.0692012i	$-0.977955\pi$
$509$	−5039.81	+	8729.20i	−0.438871	+	0.760148i	0.558731	+	0.829349i	$0.311288\pi$
$510$	−4951.05			−0.429875
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−218.714	+	378.823i	−0.0188235	+	0.0326032i
$514$	4650.15	+	8054.30i	0.399045	+	0.691167i
$515$	−7578.86	−	13127.0i	−0.648475	−	1.12319i
$516$	225.527	−	390.625i	0.0192409	−	0.0333261i
$517$	−14635.9			−1.24504
$518$		0			0
$519$	290.532			0.0245721
$520$	−362.412	+	627.716i	−0.0305631	+	0.0529369i
$521$	2853.31	+	4942.07i	0.239934	+	0.415578i	0.960695	−	0.277606i	$-0.0895409\pi$
$521$	2853.31	+	4942.07i	0.239934	+	0.415578i	−0.720761	+	0.693184i	$0.756208\pi$
$522$	−1963.72	−	3401.26i	−0.164654	−	0.285190i
$523$	−5328.63	+	9229.46i	−0.445516	+	0.771656i	−0.998088	−	0.0618088i	$-0.980313\pi$
$523$	−5328.63	+	9229.46i	−0.445516	+	0.771656i	0.552572	+	0.833465i	$0.313646\pi$
$524$	1190.35			0.0992381
$525$		0			0
$526$	−7390.73			−0.612645
$527$	−6523.69	+	11299.4i	−0.539234	+	0.933981i
$528$	−1377.53	−	2385.95i	−0.113540	−	0.196657i
$529$	−16685.6	−	28900.4i	−1.37138	−	2.37531i
$530$	−3364.14	+	5826.86i	−0.275715	+	0.477552i
$531$	−3709.81			−0.303186
$532$		0			0
$533$	−1871.97			−0.152127
$534$	−1023.26	+	1772.33i	−0.0829225	+	0.143626i
$535$	−10692.0	−	18519.2i	−0.864033	−	1.49655i
$536$	−662.352	−	1147.23i	−0.0533754	−	0.0924489i
$537$	801.814	−	1388.78i	0.0644335	−	0.111602i
$538$	14315.4			1.14717
$539$		0			0
$540$	−1717.15			−0.136841
$541$	2005.24	−	3473.18i	0.159357	−	0.276014i	−0.775280	−	0.631618i	$-0.782391\pi$
$541$	2005.24	−	3473.18i	0.159357	−	0.276014i	0.934637	+	0.355603i	$0.115725\pi$
$542$	4038.37	+	6994.66i	0.320042	+	0.554329i
$543$	−3130.51	−	5422.20i	−0.247409	−	0.428524i
$544$	−830.392	+	1438.28i	−0.0654462	+	0.113356i
$545$	−27575.3			−2.16733
$546$		0			0
$547$	−17619.8			−1.37728			−0.688638	−	0.725105i	$-0.741791\pi$
$547$	−17619.8			−1.37728			−0.688638	+	0.725105i	$0.741791\pi$
$548$	−1241.97	+	2151.15i	−0.0968144	+	0.167688i
$549$	3765.12	+	6521.38i	0.292698	+	0.506969i
$550$	7334.98	+	12704.6i	0.568663	+	0.984954i
$551$	1767.46	−	3061.32i	0.136654	−	0.236691i
$552$	5121.53			0.394903
$553$		0			0
$554$	5509.65			0.422532
$555$	9224.74	−	15977.7i	0.705529	−	1.22201i
$556$	1797.51	+	3113.37i	0.137107	+	0.237476i
$557$	5168.85	+	8952.71i	0.393198	+	0.681038i	0.992869	−	0.119208i	$-0.0380355\pi$
$557$	5168.85	+	8952.71i	0.393198	+	0.681038i	−0.599672	+	0.800246i	$0.704702\pi$
$558$	−2262.57	+	3918.89i	−0.171653	+	0.297312i
$559$	−214.194			−0.0162065
$560$		0			0
$561$	−8936.62			−0.672557
$562$	−772.742	+	1338.43i	−0.0580003	+	0.100459i
$563$	−12011.8	−	20805.1i	−0.899180	−	1.55742i	−0.828545	−	0.559923i	$-0.810831\pi$
$563$	−12011.8	−	20805.1i	−0.899180	−	1.55742i	−0.0706347	−	0.997502i	$-0.522502\pi$
$564$	1529.97	+	2649.99i	0.114226	+	0.197845i
$565$	11457.0	−	19844.1i	0.853095	−	1.47760i
$566$	13491.0			1.00189
$567$		0			0
$568$	3720.12			0.274811
$569$	6589.59	−	11413.5i	0.485501	−	0.840912i	−0.514361	−	0.857574i	$-0.671971\pi$
$569$	6589.59	−	11413.5i	0.485501	−	0.840912i	0.999861	+	0.0166623i	$0.00530403\pi$
$570$	−772.764	−	1338.47i	−0.0567851	−	0.0983547i
$571$	−3888.13	−	6734.44i	−0.284962	−	0.493568i	0.687638	−	0.726054i	$-0.258648\pi$
$571$	−3888.13	−	6734.44i	−0.284962	−	0.493568i	−0.972600	+	0.232485i	$0.925314\pi$
$572$	−654.152	+	1133.02i	−0.0478172	+	0.0828219i
$573$	10163.1			0.740956
$574$		0			0
$575$	−27270.8			−1.97787
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	10083.5	+	17465.2i	0.727525	+	1.26011i	0.957926	+	0.287015i	$0.0926630\pi$
$577$	10083.5	+	17465.2i	0.727525	+	1.26011i	−0.230401	+	0.973096i	$0.574004\pi$
$578$	−2219.44	−	3844.19i	−0.159717	−	0.276639i
$579$	2862.53	−	4958.04i	0.205462	−	0.355871i
$580$	13876.5			0.993432
$581$		0			0
$582$	5192.62			0.369830
$583$	−6072.25	+	10517.4i	−0.431367	+	0.747150i
$584$	1798.63	+	3115.32i	0.127445	+	0.220741i
$585$	407.714	+	706.181i	0.0288152	+	0.0499094i
$586$	1922.69	−	3330.20i	0.135539	−	0.234760i
$587$	8365.08			0.588184			0.294092	−	0.955777i	$-0.404983\pi$
$587$	8365.08			0.588184			0.294092	+	0.955777i	$0.404983\pi$
$588$		0			0
$589$	−4072.88			−0.284924
$590$	6553.79	−	11351.5i	0.457314	−	0.792091i
$591$	3092.82	+	5356.92i	0.215265	+	0.372850i
$592$	−3094.35	−	5359.57i	−0.214826	−	0.372090i
$593$	−13810.9	+	23921.2i	−0.956403	+	1.65654i	−0.225279	+	0.974294i	$0.572329\pi$
$593$	−13810.9	+	23921.2i	−0.956403	+	1.65654i	−0.731124	+	0.682244i	$0.761004\pi$
$594$	−3099.44			−0.214093
$595$		0			0
$596$	−12218.8			−0.839769
$597$	−4757.25	+	8239.79i	−0.326132	+	0.564878i
$598$	−1216.04	−	2106.24i	−0.0831564	−	0.144031i
$599$	−269.159	−	466.197i	−0.0183598	−	0.0318002i	0.856700	−	0.515816i	$-0.172511\pi$
$599$	−269.159	−	466.197i	−0.0183598	−	0.0318002i	−0.875059	+	0.484016i	$0.839178\pi$
$600$	1533.53	−	2656.15i	0.104343	−	0.180728i
$601$	−6958.64			−0.472294			−0.236147	−	0.971717i	$-0.575885\pi$
$601$	−6958.64			−0.472294			−0.236147	+	0.971717i	$0.575885\pi$
$602$		0			0
$603$	−1490.29			−0.100646
$604$	130.291	−	225.670i	0.00877725	−	0.0152027i
$605$	15608.6	+	27034.9i	1.04889	+	1.81674i
$606$	−729.768	−	1264.00i	−0.0489188	−	0.0847299i
$607$	−8648.80	+	14980.2i	−0.578326	+	1.00169i	0.417345	+	0.908748i	$0.362961\pi$
$607$	−8648.80	+	14980.2i	−0.578326	+	1.00169i	−0.995671	+	0.0929425i	$0.970373\pi$
$608$	−518.432			−0.0345809
$609$		0			0
$610$	−26606.0			−1.76598
$611$	726.542	−	1258.41i	0.0481060	−	0.0833220i
$612$	934.191	+	1618.07i	0.0617033	+	0.106873i
$613$	419.579	+	726.732i	0.0276454	+	0.0478832i	0.879517	−	0.475867i	$-0.157866\pi$
$613$	419.579	+	726.732i	0.0276454	+	0.0478832i	−0.851872	+	0.523751i	$0.824532\pi$
$614$	2016.68	−	3493.00i	0.132552	−	0.229586i
$615$	15669.1			1.02738
$616$		0			0
$617$	−16040.0			−1.04659			−0.523295	−	0.852152i	$-0.675297\pi$
$617$	−16040.0			−1.04659			−0.523295	+	0.852152i	$0.675297\pi$
$618$	−2860.04	+	4953.73i	−0.186161	+	0.322441i
$619$	−2714.64	−	4701.90i	−0.176269	−	0.305307i	0.764331	−	0.644825i	$-0.223070\pi$
$619$	−2714.64	−	4701.90i	−0.176269	−	0.305307i	−0.940600	+	0.339517i	$0.889736\pi$
$620$	−7994.17	−	13846.3i	−0.517828	−	0.896905i
$621$	2880.86	−	4989.79i	0.186159	−	0.322437i
$622$	−14300.0			−0.921828
$623$		0			0
$624$	273.527			0.0175478
$625$	7633.98	−	13222.4i	0.488574	−	0.846236i
$626$	8596.49	+	14889.6i	0.548858	+	0.950649i
$627$	−1394.83	−	2415.92i	−0.0888425	−	0.153880i
$628$	−3084.44	+	5342.41i	−0.195991	+	0.339467i
$629$	−20074.4			−1.27253
$630$		0			0
$631$	−1807.86			−0.114057			−0.0570284	−	0.998373i	$-0.518163\pi$
$631$	−1807.86			−0.114057			−0.0570284	+	0.998373i	$0.518163\pi$
$632$	−1374.23	+	2380.24i	−0.0864936	+	0.149811i
$633$	−2024.95	−	3507.32i	−0.127148	−	0.220227i
$634$	−2853.24	−	4941.95i	−0.178733	−	0.309574i
$635$	9418.09	−	16312.6i	0.588576	−	1.01944i
$636$	2539.05			0.158302
$637$		0			0
$638$	25047.0			1.55426
$639$	2092.57	−	3624.43i	0.129547	−	0.224382i
$640$	−1017.57	−	1762.48i	−0.0628483	−	0.108856i
$641$	2952.28	+	5113.50i	0.181916	+	0.315087i	0.942533	−	0.334113i	$-0.108437\pi$
$641$	2952.28	+	5113.50i	0.181916	+	0.315087i	−0.760617	+	0.649201i	$0.775103\pi$
$642$	−4034.86	+	6988.59i	−0.248043	+	0.429622i
$643$	−8092.42			−0.496320			−0.248160	−	0.968719i	$-0.579826\pi$
$643$	−8092.42			−0.496320			−0.248160	+	0.968719i	$0.579826\pi$
$644$		0			0
$645$	1792.88			0.109449
$646$	−840.824	+	1456.35i	−0.0512102	+	0.0886987i
$647$	10096.3	+	17487.4i	0.613490	+	1.06260i	0.990647	+	0.136447i	$0.0435683\pi$
$647$	10096.3	+	17487.4i	0.613490	+	1.06260i	−0.377157	+	0.926149i	$0.623098\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	11829.5	−	20489.4i	0.715486	−	1.23926i
$650$	−1456.46			−0.0878880
$651$		0			0
$652$	−10058.9			−0.604200
$653$	10590.4	−	18343.2i	0.634664	−	1.09927i	−0.351923	−	0.936029i	$-0.614472\pi$
$653$	10590.4	−	18343.2i	0.634664	−	1.09927i	0.986586	−	0.163240i	$-0.0521946\pi$
$654$	5203.05	+	9011.95i	0.311094	+	0.538831i
$655$	2365.75	+	4097.60i	0.141126	+	0.244437i
$656$	2628.02	−	4551.86i	0.156413	−	0.270915i
$657$	4046.92			0.240313
$658$		0			0
$659$	28411.3			1.67944			0.839718	−	0.543023i	$-0.182720\pi$
$659$	28411.3			1.67944			0.839718	+	0.543023i	$0.182720\pi$
$660$	5475.50	−	9483.84i	0.322929	−	0.559330i
$661$	8352.47	+	14466.9i	0.491488	+	0.851282i	0.999952	−	0.00980149i	$-0.00311996\pi$
$661$	8352.47	+	14466.9i	0.491488	+	0.851282i	−0.508464	+	0.861083i	$0.669787\pi$
$662$	1619.12	+	2804.39i	0.0950585	+	0.164646i
$663$	443.623	−	768.377i	0.0259862	−	0.0450095i
$664$	−12018.7			−0.702431
$665$		0			0
$666$	−6962.29			−0.405080
$667$	−23280.6	+	40323.3i	−1.35147	+	2.34081i
$668$	−1057.29	−	1831.27i	−0.0612390	−	0.106069i
$669$	2042.77	+	3538.19i	0.118054	+	0.204476i
$670$	2632.76	−	4560.08i	0.151810	−	0.262942i
$671$	−48023.7			−2.76294
$672$		0			0
$673$	−9047.09			−0.518187			−0.259093	−	0.965852i	$-0.583424\pi$
$673$	−9047.09			−0.518187			−0.259093	+	0.965852i	$0.583424\pi$
$674$	−3278.67	+	5678.83i	−0.187374	+	0.324540i
$675$	−1725.22	−	2988.17i	−0.0983758	−	0.170392i
$676$	4329.05	+	7498.14i	0.246305	+	0.426613i
$677$	−3922.13	+	6793.32i	−0.222658	+	0.385655i	−0.955614	−	0.294621i	$-0.904807\pi$
$677$	−3922.13	+	6793.32i	−0.222658	+	0.385655i	0.732956	+	0.680276i	$0.238140\pi$
$678$	−8647.05			−0.489806
$679$		0			0
$680$	−6601.41			−0.372283
$681$	−2792.71	+	4837.12i	−0.157147	+	0.272186i
$682$	−14429.4	−	24992.5i	−0.810163	−	1.40324i
$683$	−12883.0	−	22314.1i	−0.721751	−	1.25011i	−0.960298	−	0.278978i	$-0.910004\pi$
$683$	−12883.0	−	22314.1i	−0.721751	−	1.25011i	0.238547	−	0.971131i	$-0.423329\pi$
$684$	−291.618	+	505.098i	−0.0163016	+	0.0282352i
$685$	−9873.35			−0.550717
$686$		0			0
$687$	−16076.3			−0.892796
$688$	300.703	−	520.833i	0.0166631	−	0.0288613i
$689$	−602.865	−	1044.19i	−0.0333343	−	0.0577367i
$690$	10178.7	+	17630.0i	0.561590	+	0.972702i
$691$	12337.1	−	21368.4i	0.679195	−	1.17640i	−0.296029	−	0.955179i	$-0.595662\pi$
$691$	12337.1	−	21368.4i	0.679195	−	1.17640i	0.975224	−	0.221221i	$-0.0710042\pi$
$692$	387.376			0.0212801
$693$		0			0
$694$	5700.60			0.311804
$695$	−7144.86	+	12375.3i	−0.389957	+	0.675425i
$696$	−2618.29	−	4535.01i	−0.142595	−	0.246982i
$697$	−8524.56	−	14765.0i	−0.463258	−	0.802386i
$698$	−4725.32	+	8184.49i	−0.256241	+	0.443822i
$699$	16323.4			0.883271
$700$		0			0
$701$	29377.9			1.58286			0.791431	−	0.611258i	$-0.209336\pi$
$701$	29377.9			1.58286			0.791431	+	0.611258i	$0.209336\pi$
$702$	153.859	−	266.492i	0.00827213	−	0.0143278i
$703$	−3133.23	−	5426.91i	−0.168097	−	0.291152i
$704$	−1836.70	−	3181.26i	−0.0983286	−	0.170310i
$705$	−6081.44	+	10533.4i	−0.324880	+	0.562708i
$706$	−13454.9			−0.717253
$707$		0			0
$708$	−4946.41			−0.262567
$709$	−15297.1	+	26495.4i	−0.810291	+	1.40347i	0.102369	+	0.994746i	$0.467358\pi$
$709$	−15297.1	+	26495.4i	−0.810291	+	1.40347i	−0.912660	+	0.408719i	$0.865976\pi$
$710$	7393.51	+	12805.9i	0.390808	+	0.676898i
$711$	1546.01	+	2677.77i	0.0815469	+	0.141243i
$712$	−1364.34	+	2363.11i	−0.0718130	+	0.124384i
$713$	53647.4			2.81782
$714$		0			0
$715$	−5200.34			−0.272002
$716$	1069.08	−	1851.71i	0.0558011	−	0.0966503i
$717$	1735.91	+	3006.69i	0.0904169	+	0.156607i
$718$	−7331.89	−	12699.2i	−0.381091	−	0.660070i
$719$	973.469	−	1686.10i	0.0504927	−	0.0874559i	−0.839674	−	0.543090i	$-0.817254\pi$
$719$	973.469	−	1686.10i	0.0504927	−	0.0874559i	0.890167	+	0.455634i	$0.150588\pi$
$720$	−2289.53			−0.118508
$721$		0			0
$722$	13193.1			0.680048
$723$	5954.07	−	10312.7i	0.306271	−	0.530477i
$724$	−4174.01	−	7229.60i	−0.214262	−	0.371113i
$725$	13941.7	+	24147.8i	0.714184	+	1.23700i
$726$	5890.24	−	10202.2i	0.301112	−	0.521541i
$727$	15750.6			0.803518			0.401759	−	0.915745i	$-0.368399\pi$
$727$	15750.6			0.803518			0.401759	+	0.915745i	$0.368399\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−7149.34	+	12383.0i	−0.362478	+	0.627830i
$731$	−975.396	−	1689.44i	−0.0493520	−	0.0854802i
$732$	5020.16	+	8695.17i	0.253484	+	0.439048i
$733$	−7174.78	+	12427.1i	−0.361537	+	0.626200i	−0.988214	−	0.153079i	$-0.951081\pi$
$733$	−7174.78	+	12427.1i	−0.361537	+	0.626200i	0.626677	+	0.779279i	$0.284414\pi$
$734$	−5548.86			−0.279036
$735$		0			0
$736$	6828.70			0.341996
$737$	4752.12	−	8230.92i	0.237512	−	0.411384i
$738$	−2956.52	−	5120.85i	−0.147468	−	0.255421i
$739$	8879.03	+	15378.9i	0.441976	+	0.765525i	0.997836	−	0.0657506i	$-0.0209442\pi$
$739$	8879.03	+	15378.9i	0.441976	+	0.765525i	−0.555860	+	0.831276i	$0.687611\pi$
$740$	12299.7	−	21303.6i	0.611006	−	1.05829i
$741$	276.964			0.0137308
$742$		0			0
$743$	−29187.6			−1.44117			−0.720586	−	0.693366i	$-0.756127\pi$
$743$	−29187.6			−1.44117			−0.720586	+	0.693366i	$0.756127\pi$
$744$	−3016.76	+	5225.19i	−0.148656	+	0.257479i
$745$	−24284.1	−	42061.3i	−1.19423	−	2.06847i
$746$	2527.35	+	4377.49i	0.124038	+	0.214841i
$747$	−6760.49	+	11709.5i	−0.331129	+	0.573532i
$748$	−11915.5			−0.582451
$749$		0			0
$750$	266.533			0.0129766
$751$	−6890.97	+	11935.5i	−0.334827	+	0.579938i	−0.983452	−	0.181171i	$-0.942011\pi$
$751$	−6890.97	+	11935.5i	−0.334827	+	0.579938i	0.648624	+	0.761109i	$0.275345\pi$
$752$	2039.96	+	3533.31i	0.0989224	+	0.171339i
$753$	−8968.13	−	15533.3i	−0.434020	−	0.751744i
$754$	−1243.36	+	2153.56i	−0.0600536	+	0.104016i
$755$	1035.78			0.0499283
$756$		0			0
$757$	36952.7			1.77420			0.887099	−	0.461579i	$-0.152717\pi$
$757$	36952.7			1.77420			0.887099	+	0.461579i	$0.152717\pi$
$758$	3116.40	−	5397.76i	0.149331	−	0.258649i
$759$	18372.5	+	31822.1i	0.878630	+	1.52183i
$760$	−1030.35	−	1784.62i	−0.0491773	−	0.0851776i
$761$	−14408.2	+	24955.8i	−0.686332	+	1.18876i	0.286684	+	0.958025i	$0.407447\pi$
$761$	−14408.2	+	24955.8i	−0.686332	+	1.18876i	−0.973016	+	0.230737i	$0.925886\pi$
$762$	−7108.22			−0.337931
$763$		0			0
$764$	13550.8			0.641687
$765$	−3713.29	+	6431.61i	−0.175496	+	0.303968i
$766$	1518.07	+	2629.38i	0.0716059	+	0.124025i
$767$	1174.46	+	2034.23i	0.0552898	+	0.0957648i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	25285.2			1.18571			0.592854	−	0.805310i	$-0.298001\pi$
$769$	25285.2			1.18571			0.592854	+	0.805310i	$0.298001\pi$
$770$		0			0
$771$	13950.4			0.651638
$772$	3816.70	−	6610.72i	0.177935	−	0.308193i
$773$	9209.10	+	15950.6i	0.428497	+	0.742179i	0.996740	−	0.0806820i	$-0.0257098\pi$
$773$	9209.10	+	15950.6i	0.428497	+	0.742179i	−0.568243	+	0.822861i	$0.692376\pi$
$774$	−338.291	−	585.937i	−0.0157101	−	0.0272107i
$775$	16063.5	−	27822.8i	0.744540	−	1.28958i
$776$	6923.49			0.320282
$777$		0			0
$778$	6493.55			0.299235
$779$	2661.04	−	4609.05i	0.122390	−	0.211985i
$780$	543.618	+	941.574i	0.0249547	+	0.0432228i
$781$	13345.2	+	23114.6i	0.611434	+	1.05903i
$782$	11075.2	−	19182.8i	0.506455	−	0.877207i
$783$	−5891.15			−0.268880
$784$		0			0
$785$	−24520.5			−1.11487
$786$	892.764	−	1546.31i	0.0405138	−	0.0701719i
$787$	5537.90	+	9591.92i	0.250832	+	0.434454i	0.963755	−	0.266788i	$-0.0859625\pi$
$787$	5537.90	+	9591.92i	0.250832	+	0.434454i	−0.712923	+	0.701242i	$0.752629\pi$
$788$	4123.76	+	7142.56i	0.186425	+	0.322897i
$789$	−5543.05	+	9600.84i	−0.250111	+	0.433205i
$790$	−10924.8			−0.492008
$791$		0			0
$792$	−4132.58			−0.185410
$793$	2383.94	−	4129.11i	0.106754	−	0.184904i
$794$	−1830.62	−	3170.74i	−0.0818217	−	0.141719i
$795$	5046.21	+	8740.29i	0.225120	+	0.389920i
$796$	−6342.99	+	10986.4i	−0.282439	+	0.489199i
$797$	−4838.83			−0.215057			−0.107528	−	0.994202i	$-0.534294\pi$
$797$	−4838.83			−0.215057			−0.107528	+	0.994202i	$0.534294\pi$
$798$		0			0
$799$	13234.1			0.585969
$800$	2044.70	−	3541.53i	0.0903640	−	0.156515i
$801$	1534.88	+	2658.50i	0.0677059	+	0.117270i
$802$	−3385.81	−	5864.39i	−0.149074	−	0.258203i
$803$	−12904.5	+	22351.3i	−0.567111	+	0.982265i
$804$	−1987.05			−0.0871617
$805$		0			0
$806$	2865.16			0.125212
$807$	10736.5	−	18596.2i	0.468332	−	0.811175i
$808$	−973.024	−	1685.33i	−0.0423649	−	0.0733782i
$809$	15754.9	+	27288.4i	0.684690	+	1.18592i	0.973534	+	0.228542i	$0.0733957\pi$
$809$	15754.9	+	27288.4i	0.684690	+	1.18592i	−0.288844	+	0.957376i	$0.593271\pi$
$810$	−1287.86	+	2230.64i	−0.0558651	+	0.0967612i
$811$	29463.3			1.27570			0.637851	−	0.770160i	$-0.279823\pi$
$811$	29463.3			1.27570			0.637851	+	0.770160i	$0.279823\pi$
$812$		0			0
$813$	12115.1			0.522627
$814$	22200.8	−	38452.9i	0.955943	−	1.65574i
$815$	−19991.5	−	34626.3i	−0.859229	−	1.48823i
$816$	1245.59	+	2157.42i	0.0534366	+	0.0925550i
$817$	304.481	−	527.376i	0.0130385	−	0.0225833i
$818$	18506.3			0.791026
$819$		0			0
$820$	20892.1			0.889736
$821$	−1751.11	+	3033.01i	−0.0744386	+	0.128932i	−0.900842	−	0.434147i	$-0.857050\pi$
$821$	−1751.11	+	3033.01i	−0.0744386	+	0.128932i	0.826403	+	0.563079i	$0.190383\pi$
$822$	1862.95	+	3226.73i	0.0790487	+	0.136916i
$823$	−19996.5	−	34635.0i	−0.846943	−	1.46695i	−0.883923	−	0.467632i	$-0.845107\pi$
$823$	−19996.5	−	34635.0i	−0.846943	−	1.46695i	0.0369799	−	0.999316i	$-0.488226\pi$
$824$	−3813.39	+	6604.98i	−0.161220	+	0.279242i
$825$	22005.0			0.928623
$826$		0			0
$827$	−10733.6			−0.451322			−0.225661	−	0.974206i	$-0.572454\pi$
$827$	−10733.6			−0.451322			−0.225661	+	0.974206i	$0.572454\pi$
$828$	3841.15	−	6653.06i	0.161219	−	0.279239i
$829$	−7268.74	−	12589.8i	−0.304528	−	0.527458i	0.672628	−	0.739981i	$-0.265165\pi$
$829$	−7268.74	−	12589.8i	−0.304528	−	0.527458i	−0.977156	+	0.212523i	$0.931832\pi$
$830$	−23886.3	−	41372.3i	−0.998923	−	1.73018i
$831$	4132.24	−	7157.24i	0.172498	−	0.298775i
$832$	364.703			0.0151969
$833$		0			0
$834$	5392.52			0.223894
$835$	4202.58	−	7279.09i	0.174175	−	0.301680i
$836$	−1859.78	−	3221.23i	−0.0769399	−	0.133264i
$837$	3393.86	+	5878.34i	0.140154	+	0.242754i
$838$	−3547.52	+	6144.48i	−0.146237	+	0.253291i
$839$	−7353.57			−0.302591			−0.151295	−	0.988489i	$-0.548344\pi$
$839$	−7353.57			−0.302591			−0.151295	+	0.988489i	$0.548344\pi$
$840$		0			0
$841$	23218.3			0.951998
$842$	7848.87	−	13594.6i	0.321247	−	0.556416i
$843$	1159.11	+	2007.64i	0.0473571	+	0.0820248i
$844$	−2699.94	−	4676.43i	−0.110113	−	0.190722i
$845$	−17207.4	+	29804.2i	−0.700537	+	1.21337i
$846$	4589.91			0.186530
$847$		0			0
$848$	3385.41			0.137094
$849$	10118.2	−	17525.3i	0.409019	−	0.708441i
$850$	−6632.44	−	11487.7i	−0.267636	−	0.463560i
$851$	41270.3	+	71482.3i	1.66243	+	2.87941i
$852$	2790.09	−	4832.58i	0.112191	−	0.194321i
$853$	−19293.6			−0.774442			−0.387221	−	0.921987i	$-0.626565\pi$
$853$	−19293.6			−0.774442			−0.387221	+	0.921987i	$0.626565\pi$
$854$		0			0
$855$	−2318.29			−0.0927297
$856$	−5379.82	+	9318.12i	−0.214811	+	0.372064i
$857$	−7080.78	−	12264.3i	−0.282234	−	0.488844i	0.689701	−	0.724095i	$-0.257742\pi$
$857$	−7080.78	−	12264.3i	−0.282234	−	0.488844i	−0.971935	+	0.235251i	$0.924409\pi$
$858$	981.227	+	1699.54i	0.0390426	+	0.0676238i
$859$	4109.57	−	7117.98i	0.163232	−	0.282727i	−0.772794	−	0.634657i	$-0.781141\pi$
$859$	4109.57	−	7117.98i	0.163232	−	0.282727i	0.936026	+	0.351930i	$0.114475\pi$
$860$	2390.51			0.0947858
$861$		0			0
$862$	8894.65			0.351454
$863$	−1287.47	+	2229.97i	−0.0507835	+	0.0879595i	−0.890300	−	0.455375i	$-0.849505\pi$
$863$	−1287.47	+	2229.97i	−0.0507835	+	0.0879595i	0.839516	+	0.543335i	$0.182839\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	769.885	+	1333.48i	0.0302623	+	0.0524158i
$866$	6994.82	−	12115.4i	0.274473	−	0.475401i
$867$	−6658.33			−0.260817
$868$		0			0
$869$	−19719.2			−0.769766
$870$	10407.4	−	18026.1i	0.405567	−	0.702462i
$871$	471.800	+	817.182i	0.0183540	+	0.0317901i
$872$	6937.41	+	12015.9i	0.269415	+	0.466641i
$873$	3894.47	−	6745.41i	0.150982	−	0.261509i
$874$	6914.49			0.267604
$875$		0			0
$876$	5395.90			0.208117
$877$	−15490.6	+	26830.5i	−0.596442	+	1.03307i	0.396900	+	0.917862i	$0.370086\pi$
$877$	−15490.6	+	26830.5i	−0.596442	+	1.03307i	−0.993342	+	0.115206i	$0.963247\pi$
$878$	−636.182	−	1101.90i	−0.0244534	−	0.0423546i
$879$	−2884.04	−	4995.30i	−0.110667	−	0.191681i
$880$	7300.66	−	12645.1i	0.279665	−	0.484394i
$881$	41781.8			1.59780			0.798902	−	0.601461i	$-0.205415\pi$
$881$	41781.8			1.59780			0.798902	+	0.601461i	$0.205415\pi$
$882$		0			0
$883$	−39289.6			−1.49740			−0.748699	−	0.662911i	$-0.769321\pi$
$883$	−39289.6			−1.49740			−0.748699	+	0.662911i	$0.769321\pi$
$884$	591.497	−	1024.50i	0.0225047	−	0.0389794i
$885$	−9830.68	−	17027.2i	−0.373395	−	0.646739i
$886$	−4474.24	−	7749.61i	−0.169656	−	0.293852i
$887$	2916.22	−	5051.04i	0.110391	−	0.191203i	−0.805537	−	0.592546i	$-0.798123\pi$
$887$	2916.22	−	5051.04i	0.110391	−	0.191203i	0.915928	+	0.401342i	$0.131456\pi$
$888$	−9283.05			−0.350810
$889$		0			0
$890$	−10846.2			−0.408499
$891$	−2324.58	+	4026.29i	−0.0874032	+	0.151387i
$892$	2723.70	+	4717.58i	0.102238	+	0.177081i
$893$	2065.59	+	3577.70i	0.0774045	+	0.134069i
$894$	−9164.11	+	15872.7i	−0.342834	+	0.593806i
$895$	8498.95			0.317418
$896$		0			0
$897$	−3648.12			−0.135794
$898$	−2389.42	+	4138.59i	−0.0887928	+	0.153794i
$899$	−27426.3	−	47503.7i	−1.01748	−	1.76233i
$900$	−2300.29	−	3984.22i	−0.0851960	−	0.147564i
$901$	5490.65	−	9510.09i	0.203019	−	0.351639i
$902$	37710.1			1.39203
$903$		0			0
$904$	−11529.4			−0.424184
$905$	16591.2	−	28736.7i	0.609402	−	1.05552i
$906$	−195.436	−	338.506i	−0.00716660	−	0.0124129i
$907$	−21194.0	−	36709.0i	−0.775892	−	1.34388i	−0.934292	−	0.356509i	$-0.883967\pi$
$907$	−21194.0	−	36709.0i	−0.775892	−	1.34388i	0.158400	−	0.987375i	$-0.449367\pi$
$908$	−3723.62	+	6449.50i	−0.136093	+	0.235720i
$909$	−2189.30			−0.0798841
$910$		0			0
$911$	2275.12			0.0827423			0.0413711	−	0.999144i	$-0.486827\pi$
$911$	2275.12			0.0827423			0.0413711	+	0.999144i	$0.486827\pi$
$912$	−388.824	+	673.463i	−0.0141176	+	0.0244524i
$913$	−43114.6	−	74676.7i	−1.56285	−	2.70694i
$914$	−4438.34	−	7687.43i	−0.160621	−	0.278203i
$915$	−19954.5	+	34562.2i	−0.720957	+	1.24873i
$916$	−21435.1			−0.773184
$917$		0			0
$918$	2802.57			0.100761
$919$	15642.1	−	27093.0i	0.561465	−	0.972486i	−0.435904	−	0.899993i	$-0.643571\pi$
$919$	15642.1	−	27093.0i	0.561465	−	0.972486i	0.997369	−	0.0724930i	$-0.0230955\pi$
$920$	13571.6	+	23506.7i	0.486351	+	0.842385i
$921$	−3025.03	−	5239.50i	−0.108228	−	0.187456i
$922$	14079.8	−	24387.0i	0.502923	−	0.871088i
$923$	−2649.88			−0.0944983
$924$		0			0
$925$	49429.9			1.75702
$926$	4687.50	−	8118.98i	0.166351	−	0.288128i
$927$	4290.06	+	7430.60i	0.152000	+	0.263272i
$928$	−3491.05	−	6046.68i	−0.123491	−	0.213892i
$929$	16098.3	−	27883.1i	0.568535	−	0.984731i	−0.428176	−	0.903695i	$-0.640844\pi$
$929$	16098.3	−	27883.1i	0.568535	−	0.984731i	0.996711	−	0.0810358i	$-0.0258228\pi$
$930$	−23982.5			−0.845610
$931$		0			0
$932$	21764.5			0.764935
$933$	−10725.0	+	18576.2i	−0.376335	+	0.651831i
$934$	−8447.26	−	14631.1i	−0.295934	−	0.512573i
$935$	−23681.3	−	41017.2i	−0.828301	−	1.43466i
$936$	205.145	−	355.322i	0.00716388	−	0.0124082i
$937$	−22293.6			−0.777269			−0.388635	−	0.921392i	$-0.627053\pi$
$937$	−22293.6			−0.777269			−0.388635	+	0.921392i	$0.627053\pi$
$938$		0			0
$939$	25789.5			0.896281
$940$	−8108.58	+	14044.5i	−0.281354	+	0.487319i
$941$	−15904.8	−	27548.0i	−0.550991	−	0.954345i	−0.998203	−	0.0599168i	$-0.980916\pi$
$941$	−15904.8	−	27548.0i	−0.550991	−	0.954345i	0.447212	−	0.894428i	$-0.352417\pi$
$942$	4626.66	+	8013.61i	0.160026	+	0.277174i
$943$	−35050.7	+	60709.6i	−1.21040	+	2.09648i
$944$	−6595.22			−0.227390
$945$		0			0
$946$	4314.86			0.148296
$947$	−9491.32	+	16439.4i	−0.325688	+	0.564108i	−0.981651	−	0.190685i	$-0.938929\pi$
$947$	−9491.32	+	16439.4i	−0.325688	+	0.564108i	0.655963	+	0.754793i	$0.272263\pi$
$948$	2061.35	+	3570.36i	0.0706217	+	0.122320i
$949$	−1281.18	−	2219.08i	−0.0438240	−	0.0759055i
$950$	2070.39	−	3586.02i	0.0707077	−	0.122469i
$951$	−8559.71			−0.291869
$952$		0			0
$953$	9254.58			0.314570			0.157285	−	0.987553i	$-0.449726\pi$
$953$	9254.58			0.314570			0.157285	+	0.987553i	$0.449726\pi$
$954$	1904.29	−	3298.33i	0.0646265	−	0.111936i
$955$	26931.3	+	46646.3i	0.912539	+	1.58056i
$956$	2314.55	+	4008.92i	0.0783033	+	0.135625i
$957$	18785.2	−	32537.0i	0.634525	−	1.09903i
$958$	−8738.81			−0.294716
$959$		0			0
$960$	−3052.70			−0.102631
$961$	−16704.7	+	28933.4i	−0.560730	+	0.971213i
$962$	2204.14	+	3817.68i	0.0738714	+	0.127949i
$963$	6052.30	+	10482.9i	0.202526	+	0.350785i
$964$	7938.75	−	13750.3i	0.265239	−	0.459407i
$965$	30341.8			1.01216
$966$		0			0
$967$	15317.5			0.509387			0.254694	−	0.967022i	$-0.418025\pi$
$967$	15317.5			0.509387			0.254694	+	0.967022i	$0.418025\pi$
$968$	7853.65	−	13602.9i	0.260770	−	0.451668i
$969$	1261.24	+	2184.53i	0.0418130	+	0.0724222i
$970$	13760.0	+	23833.0i	0.455471	+	0.788900i
$971$	11216.3	−	19427.2i	0.370699	−	0.642069i	−0.618974	−	0.785411i	$-0.712452\pi$
$971$	11216.3	−	19427.2i	0.370699	−	0.642069i	0.989673	+	0.143342i	$0.0457849\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	28955.5			0.952559
$975$	−1092.35	+	1892.00i	−0.0358801	+	0.0621462i
$976$	6693.55	+	11593.6i	0.219524	+	0.380226i
$977$	313.932	+	543.746i	0.0102800	+	0.0178055i	0.871120	−	0.491071i	$-0.163394\pi$
$977$	313.932	+	543.746i	0.0102800	+	0.0178055i	−0.860840	+	0.508876i	$0.830061\pi$
$978$	−7544.20	+	13066.9i	−0.246664	+	0.427234i
$979$	−19577.3			−0.639114
$980$		0			0
$981$	15609.2			0.508015
$982$	9306.12	−	16118.7i	0.302414	−	0.523796i
$983$	22516.3	+	38999.4i	0.730579	+	1.26540i	0.956636	+	0.291286i	$0.0940830\pi$
$983$	22516.3	+	38999.4i	0.730579	+	1.26540i	−0.226057	+	0.974114i	$0.572584\pi$
$984$	−3942.03	−	6827.80i	−0.127711	−	0.221201i
$985$	−16391.4	+	28390.8i	−0.530227	+	0.918381i
$986$	−22648.0			−0.731500
$987$		0			0
$988$	369.285			0.0118912
$989$	−4010.57	+	6946.51i	−0.128947	+	0.223343i
$990$	−8213.25	−	14225.8i	−0.263671	−	0.456691i
$991$	15990.5	+	27696.4i	0.512569	+	0.887795i	0.999894	+	0.0145745i	$0.00463937\pi$
$991$	15990.5	+	27696.4i	0.512569	+	0.887795i	−0.487325	+	0.873221i	$0.662027\pi$
$992$	−4022.35	+	6966.92i	−0.128740	+	0.222984i
$993$	4857.35			0.155230
$994$		0			0
$995$	−50425.2			−1.60662
$996$	−9013.99	+	15612.7i	−0.286766	+	0.496694i
$997$	6189.41	+	10720.4i	0.196611	+	0.340539i	0.947427	−	0.319971i	$-0.103673\pi$
$997$	6189.41	+	10720.4i	0.196611	+	0.340539i	−0.750817	+	0.660511i	$0.770340\pi$
$998$	−12237.5	−	21196.1i	−0.388149	−	0.672294i
$999$	−5221.72	+	9044.28i	−0.165373	+	0.286435i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.94975 - 13.7694i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(7.94975 - 13.7694i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-15.8995 - 27.5387i) q^{10} +(-28.6985 - 49.7072i) q^{11} +(-6.00000 + 10.3923i) q^{12} +5.69848 q^{13} -47.6985 q^{15} +(-8.00000 + 13.8564i) q^{16} +(25.9497 + 44.9463i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-8.10051 + 14.0305i) q^{19} -63.5980 q^{20} -114.794 q^{22} +(106.698 - 184.807i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-63.8970 - 110.673i) q^{25} +(5.69848 - 9.87007i) q^{26} +27.0000 q^{27} -218.191 q^{29} +(-47.6985 + 82.6162i) q^{30} +(125.698 + 217.716i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-86.0955 + 149.122i) q^{33} +103.799 q^{34} +36.0000 q^{36} +(-193.397 + 334.973i) q^{37} +(16.2010 + 28.0610i) q^{38} +(-8.54773 - 14.8051i) q^{39} +(-63.5980 + 110.155i) q^{40} -328.503 q^{41} -37.5879 q^{43} +(-114.794 + 198.829i) q^{44} +(71.5477 + 123.924i) q^{45} +(-213.397 - 369.614i) q^{46} +(127.497 - 220.832i) q^{47} +48.0000 q^{48} -255.588 q^{50} +(77.8492 - 134.839i) q^{51} +(-11.3970 - 19.7401i) q^{52} +(-105.794 - 183.240i) q^{53} +(27.0000 - 46.7654i) q^{54} -912.583 q^{55} +48.6030 q^{57} +(-218.191 + 377.918i) q^{58} +(206.101 + 356.977i) q^{59} +(95.3970 + 165.232i) q^{60} +(418.347 - 724.598i) q^{61} +502.794 q^{62} +64.0000 q^{64} +(45.3015 - 78.4645i) q^{65} +(172.191 + 298.243i) q^{66} +(82.7939 + 143.403i) q^{67} +(103.799 - 179.785i) q^{68} -640.191 q^{69} -465.015 q^{71} +(36.0000 - 62.3538i) q^{72} +(-224.829 - 389.415i) q^{73} +(386.794 + 669.947i) q^{74} +(-191.691 + 332.018i) q^{75} +64.8040 q^{76} -34.1909 q^{78} +(171.779 - 297.530i) q^{79} +(127.196 + 220.310i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-328.503 + 568.983i) q^{82} +1502.33 q^{83} +825.176 q^{85} +(-37.5879 + 65.1041i) q^{86} +(327.286 + 566.877i) q^{87} +(229.588 + 397.658i) q^{88} +(170.543 - 295.389i) q^{89} +286.191 q^{90} -853.588 q^{92} +(377.095 - 653.148i) q^{93} +(-254.995 - 441.664i) q^{94} +(128.794 + 223.078i) q^{95} +(48.0000 - 83.1384i) q^{96} -865.437 q^{97} +516.573 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

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