LMFDB - Embedded newform 126.9.s.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(53,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.s (of order $6$, degree $2$, 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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 5826111 x^{18} - 52434714 x^{17} + 14609902138197 x^{16} - 116878028586684 x^{15} + \cdots + 46\!\cdots\!67 $ x^20 - 10x^19 + 5826111x^18 - 52434714x^17 + 14609902138197x^16 - 116878028586684x^15 + 20570415019216091666x^14 - 143990859773172188876x^13 + 17778850839861393261577389x^12 - 106671233163309243180965870x^11 + 9680290789684647638481756224861x^10 - 48400476132217676087684309052126x^9 + 3275735646651808421941058995933509711x^8 - 13102652184923818063474053937427650164x^7 + 653502209053902071586784989674537854288110x^6 - 1960460768082339807775059434296031383524340x^5 + 68850375563113059318225998877994832003827914811x^4 - 137697483706898978818817917958243091010522758690x^3 + 3066443413106133675142280126674379287603657139937675x^2 - 3066374564691021503239083252322344289284140820347058*x + 46867859601845955405133191126273914741044351570054374867
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{16}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.6
Root			$0.500000 + 976.270i$ of defining polynomial
Character	$\chi$	$=$	126.53
Dual form			126.9.s.a.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-846.225 + 488.568i) q^{5} +(1031.17 - 2168.29i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-846.225 + 488.568i) q^{5} +(1031.17 - 2168.29i) q^{7} -1448.15i q^{8} +(-5527.52 + 9573.94i) q^{10} +(-8690.52 - 5017.47i) q^{11} +28375.5 q^{13} +(-2162.33 - 27078.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-130881. - 75564.1i) q^{17} +(90118.8 + 156090. i) q^{19} +125073. i q^{20} -113532. q^{22} +(179005. - 103348. i) q^{23} +(282085. - 488586. i) q^{25} +(278022. - 160516. i) q^{26} +(-174363. - 253077. i) q^{28} +1.19213e6i q^{29} +(-882979. + 1.52936e6i) q^{31} +(-160530. - 92681.9i) q^{32} -1.70982e6 q^{34} +(186755. + 2.33866e6i) q^{35} +(1.01152e6 + 1.75200e6i) q^{37} +(1.76596e6 + 1.01958e6i) q^{38} +(707522. + 1.22546e6i) q^{40} +362452. i q^{41} +1.49271e6 q^{43} +(-1.11239e6 + 642237. i) q^{44} +(1.16925e6 - 2.02521e6i) q^{46} +(-2.76190e6 + 1.59458e6i) q^{47} +(-3.63817e6 - 4.47176e6i) q^{49} -6.38286e6i q^{50} +(1.81603e6 - 3.14546e6i) q^{52} +(1.01242e7 + 5.84519e6i) q^{53} +9.80551e6 q^{55} +(-3.14002e6 - 1.49330e6i) q^{56} +(6.74368e6 + 1.16804e7i) q^{58} +(-6.93873e6 - 4.00608e6i) q^{59} +(9.78093e6 + 1.69411e7i) q^{61} +1.99795e7i q^{62} -2.09715e6 q^{64} +(-2.40120e7 + 1.38633e7i) q^{65} +(2.39509e6 - 4.14842e6i) q^{67} +(-1.67528e7 + 9.67221e6i) q^{68} +(1.50593e7 + 2.18576e7i) q^{70} -2.83490e7i q^{71} +(-1.43763e7 + 2.49004e7i) q^{73} +(1.98217e7 + 1.14440e7i) q^{74} +2.30704e7 q^{76} +(-1.98408e7 + 1.36697e7i) q^{77} +(-6.04403e6 - 1.04686e7i) q^{79} +(1.38646e7 + 8.00470e6i) q^{80} +(2.05034e6 + 3.55129e6i) q^{82} +5.87181e7i q^{83} +1.47673e8 q^{85} +(1.46255e7 - 8.44405e6i) q^{86} +(-7.26608e6 + 1.25852e7i) q^{88} +(-8.51910e6 + 4.91851e6i) q^{89} +(2.92600e7 - 6.15263e7i) q^{91} -2.64572e7i q^{92} +(-1.80406e7 + 3.12473e7i) q^{94} +(-1.52522e8 - 8.80584e7i) q^{95} +8.66592e7 q^{97} +(-6.09428e7 - 2.32335e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 - 3710 * q^7	$ 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	9.79796	−	5.65685i	0.612372	−	0.353553i
$2$	9.79796	−	5.65685i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	−	110.851i	0.250000	−	0.433013i
$5$	−846.225	+	488.568i	−1.35396	+	0.781709i	−0.988802	−	0.149236i	$-0.952319\pi$
$5$	−846.225	+	488.568i	−1.35396	+	0.781709i	−0.365158	+	0.930945i	$0.618985\pi$
$6$		0			0
$7$	1031.17	−	2168.29i	0.429476	−	0.903078i
$7$	1031.17	−	2168.29i	0.429476	−	0.903078i
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	−5527.52	+	9573.94i	−0.552752	+	0.957394i
$11$	−8690.52	−	5017.47i	−0.593574	−	0.342700i	0.172935	−	0.984933i	$-0.444675\pi$
$11$	−8690.52	−	5017.47i	−0.593574	−	0.342700i	−0.766509	+	0.642233i	$0.778008\pi$
$12$		0			0
$13$	28375.5			0.993504			0.496752	−	0.867893i	$-0.334526\pi$
$13$	28375.5			0.993504			0.496752	+	0.867893i	$0.334526\pi$
$14$	−2162.33	−	27078.0i	−0.0562873	−	0.704863i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−130881.	−	75564.1i	−1.56704	−	0.904732i	−0.996512	−	0.0834552i	$-0.973404\pi$
$17$	−130881.	−	75564.1i	−1.56704	−	0.904732i	−0.570530	−	0.821277i	$-0.693262\pi$
$18$		0			0
$19$	90118.8	+	156090.i	0.691514	+	1.19774i	0.971342	+	0.237687i	$0.0763894\pi$
$19$	90118.8	+	156090.i	0.691514	+	1.19774i	−0.279827	+	0.960050i	$0.590277\pi$
$20$			125073.i			0.781709i
$21$		0			0
$22$	−113532.			−0.484651
$23$	179005.	−	103348.i	0.639665	−	0.369311i	−0.144820	−	0.989458i	$-0.546260\pi$
$23$	179005.	−	103348.i	0.639665	−	0.369311i	0.784486	+	0.620147i	$0.212927\pi$
$24$		0			0
$25$	282085.	−	488586.i	0.722139	−	1.25078i
$26$	278022.	−	160516.i	0.608394	−	0.351257i
$27$		0			0
$28$	−174363.	−	253077.i	−0.283675	−	0.411738i
$29$			1.19213e6i			1.68551i	0.538301	+	0.842753i	$0.319066\pi$
$29$			1.19213e6i			1.68551i	−0.538301	+	0.842753i	$0.680934\pi$
$30$		0			0
$31$	−882979.	+	1.52936e6i	−0.956101	+	1.65601i	−0.224271	+	0.974527i	$0.572000\pi$
$31$	−882979.	+	1.52936e6i	−0.956101	+	1.65601i	−0.731829	+	0.681488i	$0.761333\pi$
$32$	−160530.	−	92681.9i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−1.70982e6			−1.27948
$35$	186755.	+	2.33866e6i	0.124452	+	1.55846i
$36$		0			0
$37$	1.01152e6	+	1.75200e6i	0.539719	+	0.934820i	0.998919	+	0.0464873i	$0.0148027\pi$
$37$	1.01152e6	+	1.75200e6i	0.539719	+	0.934820i	−0.459200	+	0.888333i	$0.651864\pi$
$38$	1.76596e6	+	1.01958e6i	0.846929	+	0.488974i
$39$		0			0
$40$	707522.	+	1.22546e6i	0.276376	+	0.478697i
$41$			362452.i			0.128267i	0.997941	+	0.0641336i	$0.0204284\pi$
$41$			362452.i			0.128267i	−0.997941	+	0.0641336i	$0.979572\pi$
$42$		0			0
$43$	1.49271e6			0.436618			0.218309	−	0.975880i	$-0.429946\pi$
$43$	1.49271e6			0.436618			0.218309	+	0.975880i	$0.429946\pi$
$44$	−1.11239e6	+	642237.i	−0.296787	+	0.171350i
$45$		0			0
$46$	1.16925e6	−	2.02521e6i	0.261142	−	0.452312i
$47$	−2.76190e6	+	1.59458e6i	−0.565999	+	0.326780i	−0.755550	−	0.655091i	$-0.772630\pi$
$47$	−2.76190e6	+	1.59458e6i	−0.565999	+	0.326780i	0.189551	+	0.981871i	$0.439297\pi$
$48$		0			0
$49$	−3.63817e6	−	4.47176e6i	−0.631101	−	0.775701i
$50$		−	6.38286e6i		−	1.02126i
$51$		0			0
$52$	1.81603e6	−	3.14546e6i	0.248376	−	0.430200i
$53$	1.01242e7	+	5.84519e6i	1.28309	+	0.740791i	0.977412	−	0.211345i	$-0.0677844\pi$
$53$	1.01242e7	+	5.84519e6i	1.28309	+	0.740791i	0.305676	+	0.952136i	$0.401118\pi$
$54$		0			0
$55$	9.80551e6			1.07157
$56$	−3.14002e6	−	1.49330e6i	−0.319286	−	0.151843i
$57$		0			0
$58$	6.74368e6	+	1.16804e7i	0.595916	+	1.03216i
$59$	−6.93873e6	−	4.00608e6i	−0.572627	−	0.330606i	0.185571	−	0.982631i	$-0.440587\pi$
$59$	−6.93873e6	−	4.00608e6i	−0.572627	−	0.330606i	−0.758198	+	0.652025i	$0.773920\pi$
$60$		0			0
$61$	9.78093e6	+	1.69411e7i	0.706417	+	1.22355i	0.966178	+	0.257877i	$0.0830229\pi$
$61$	9.78093e6	+	1.69411e7i	0.706417	+	1.22355i	−0.259761	+	0.965673i	$0.583644\pi$
$62$			1.99795e7i			1.35213i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	−2.40120e7	+	1.38633e7i	−1.34516	+	0.776631i
$66$		0			0
$67$	2.39509e6	−	4.14842e6i	0.118857	−	0.205866i	−0.800458	−	0.599388i	$-0.795410\pi$
$67$	2.39509e6	−	4.14842e6i	0.118857	−	0.205866i	0.919315	+	0.393523i	$0.128744\pi$
$68$	−1.67528e7	+	9.67221e6i	−0.783521	+	0.452366i
$69$		0			0
$70$	1.50593e7	+	2.18576e7i	0.627209	+	0.910356i
$71$		−	2.83490e7i		−	1.11559i	−0.829978	−	0.557795i	$-0.811647\pi$
$71$		−	2.83490e7i		−	1.11559i	0.829978	−	0.557795i	$-0.188353\pi$
$72$		0			0
$73$	−1.43763e7	+	2.49004e7i	−0.506238	+	0.876829i	0.493736	+	0.869612i	$0.335631\pi$
$73$	−1.43763e7	+	2.49004e7i	−0.506238	+	0.876829i	−0.999974	+	0.00721750i	$0.997703\pi$
$74$	1.98217e7	+	1.14440e7i	0.661018	+	0.381639i
$75$		0			0
$76$	2.30704e7			0.691514
$77$	−1.98408e7	+	1.36697e7i	−0.564411	+	0.388863i
$78$		0			0
$79$	−6.04403e6	−	1.04686e7i	−0.155174	−	0.268769i	0.777949	−	0.628328i	$-0.216260\pi$
$79$	−6.04403e6	−	1.04686e7i	−0.155174	−	0.268769i	−0.933122	+	0.359559i	$0.882927\pi$
$80$	1.38646e7	+	8.00470e6i	0.338490	+	0.195427i
$81$		0			0
$82$	2.05034e6	+	3.55129e6i	0.0453493	+	0.0785473i
$83$			5.87181e7i			1.23726i	0.785684	+	0.618628i	$0.212311\pi$
$83$			5.87181e7i			1.23726i	−0.785684	+	0.618628i	$0.787689\pi$
$84$		0			0
$85$	1.47673e8			2.82895
$86$	1.46255e7	−	8.44405e6i	0.267373	−	0.154368i
$87$		0			0
$88$	−7.26608e6	+	1.25852e7i	−0.121163	+	0.209860i
$89$	−8.51910e6	+	4.91851e6i	−0.135779	+	0.0783922i	−0.566351	−	0.824164i	$-0.691645\pi$
$89$	−8.51910e6	+	4.91851e6i	−0.135779	+	0.0783922i	0.430572	+	0.902556i	$0.358312\pi$
$90$		0			0
$91$	2.92600e7	−	6.15263e7i	0.426686	−	0.897212i
$92$		−	2.64572e7i		−	0.369311i
$93$		0			0
$94$	−1.80406e7	+	3.12473e7i	−0.231068	+	0.400222i
$95$	−1.52522e8	−	8.80584e7i	−1.87257	−	1.08113i
$96$		0			0
$97$	8.66592e7			0.978877			0.489438	−	0.872038i	$-0.337202\pi$
$97$	8.66592e7			0.978877			0.489438	+	0.872038i	$0.337202\pi$
$98$	−6.09428e7	−	2.32335e7i	−0.660721	−	0.251890i
$99$		0			0
$100$	−3.61069e7	−	6.25390e7i	−0.361069	−	0.625390i
$101$	1.24686e8	+	7.19877e7i	1.19821	+	0.691788i	0.960156	−	0.279464i	$-0.0901568\pi$
$101$	1.24686e8	+	7.19877e7i	1.19821	+	0.691788i	0.238055	+	0.971252i	$0.423490\pi$
$102$		0			0
$103$	6.45470e7	+	1.11799e8i	0.573491	+	0.993316i	0.996204	+	0.0870524i	$0.0277447\pi$
$103$	6.45470e7	+	1.11799e8i	0.573491	+	0.993316i	−0.422712	+	0.906264i	$0.638922\pi$
$104$		−	4.10921e7i		−	0.351257i
$105$		0			0
$106$	1.32262e8			1.04764
$107$	−1.61359e8	+	9.31609e7i	−1.23100	+	0.710720i	−0.967239	−	0.253867i	$-0.918297\pi$
$107$	−1.61359e8	+	9.31609e7i	−1.23100	+	0.710720i	−0.263764	+	0.964587i	$0.584964\pi$
$108$		0			0
$109$	2.32458e7	−	4.02628e7i	0.164679	−	0.285232i	−0.771862	−	0.635790i	$-0.780675\pi$
$109$	2.32458e7	−	4.02628e7i	0.164679	−	0.285232i	0.936541	+	0.350558i	$0.114008\pi$
$110$	9.60740e7	−	5.54684e7i	0.656198	−	0.378856i
$111$		0			0
$112$	−3.92132e7	+	3.13139e6i	−0.249207	+	0.0199006i
$113$		−	3.30915e7i		−	0.202956i	−0.994838	−	0.101478i	$-0.967643\pi$
$113$		−	3.30915e7i		−	0.202956i	0.994838	−	0.101478i	$-0.0323572\pi$
$114$		0			0
$115$	−1.00985e8	+	1.74912e8i	−0.577387	+	1.00006i
$116$	1.32149e8	+	7.62961e7i	0.729845	+	0.421376i
$117$		0			0
$118$	−9.06472e7			−0.467548
$119$	−2.98806e8	+	2.05868e8i	−1.49005	+	1.02660i
$120$		0			0
$121$	−5.68294e7	−	9.84313e7i	−0.265113	−	0.459189i
$122$	1.91666e8	+	1.10659e8i	0.865180	+	0.499512i
$123$		0			0
$124$	1.13021e8	+	1.95759e8i	0.478050	+	0.828007i
$125$			1.69578e8i			0.694591i
$126$		0			0
$127$	−3.28049e8			−1.26103			−0.630514	−	0.776178i	$-0.717156\pi$
$127$	−3.28049e8			−1.26103			−0.630514	+	0.776178i	$0.717156\pi$
$128$	−2.05478e7	+	1.18633e7i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.56846e8	+	2.71665e8i	−0.549161	+	0.951175i
$131$	3.43511e8	−	1.98326e8i	1.16642	−	0.673433i	0.213586	−	0.976924i	$-0.431486\pi$
$131$	3.43511e8	−	1.98326e8i	1.16642	−	0.673433i	0.952834	+	0.303491i	$0.0981524\pi$
$132$		0			0
$133$	4.31377e8	−	3.44480e7i	1.37864	−	0.110092i
$134$		−	5.41948e7i		−	0.168089i
$135$		0			0
$136$	−1.09429e8	+	1.89536e8i	−0.319871	+	0.554033i
$137$	2.57146e8	+	1.48463e8i	0.729956	+	0.421441i	0.818406	−	0.574640i	$-0.194858\pi$
$137$	2.57146e8	+	1.48463e8i	0.729956	+	0.421441i	−0.0884498	+	0.996081i	$0.528191\pi$
$138$		0			0
$139$	−5.40402e8			−1.44763			−0.723815	−	0.689994i	$-0.757613\pi$
$139$	−5.40402e8			−1.44763			−0.723815	+	0.689994i	$0.757613\pi$
$140$	2.71196e8	+	1.28972e8i	0.705945	+	0.335725i
$141$		0			0
$142$	−1.60366e8	−	2.77763e8i	−0.394421	−	0.683157i
$143$	−2.46597e8	−	1.42373e8i	−0.589718	−	0.340474i
$144$		0			0
$145$	−5.82435e8	−	1.00881e9i	−1.31758	−	2.28211i
$146$			3.25298e8i			0.715928i
$147$		0			0
$148$	2.58949e8			0.539719
$149$	−4.17224e8	+	2.40884e8i	−0.846494	+	0.488724i	−0.859466	−	0.511192i	$-0.829204\pi$
$149$	−4.17224e8	+	2.40884e8i	−0.846494	+	0.488724i	0.0129722	+	0.999916i	$0.495871\pi$
$150$		0			0
$151$	1.72625e8	−	2.98996e8i	0.332045	−	0.575119i	−0.650868	−	0.759191i	$-0.725595\pi$
$151$	1.72625e8	−	2.98996e8i	0.332045	−	0.575119i	0.982913	+	0.184072i	$0.0589281\pi$
$152$	2.26043e8	−	1.30506e8i	0.423464	−	0.244487i
$153$		0			0
$154$	−1.17071e8	+	2.46171e8i	−0.208146	+	0.437678i
$155$		−	1.72558e9i		−	2.98957i
$156$		0			0
$157$	4.87309e7	−	8.44044e7i	0.0802058	−	0.138921i	−0.823132	−	0.567849i	$-0.807776\pi$
$157$	4.87309e7	−	8.44044e7i	0.0802058	−	0.138921i	0.903338	+	0.428929i	$0.141109\pi$
$158$	−1.18438e8	−	6.83804e7i	−0.190048	−	0.109724i
$159$		0			0
$160$	1.81126e8			0.276376
$161$	−3.95049e7	−	4.94704e8i	−0.0587960	−	0.736278i
$162$		0			0
$163$	−2.81849e8	−	4.88177e8i	−0.399270	−	0.691556i	0.594366	−	0.804195i	$-0.297403\pi$
$163$	−2.81849e8	−	4.88177e8i	−0.399270	−	0.691556i	−0.993636	+	0.112639i	$0.964070\pi$
$164$	4.01783e7	+	2.31969e7i	0.0555413	+	0.0320668i
$165$		0			0
$166$	3.32160e8	+	5.75317e8i	0.437436	+	0.757661i
$167$			6.25112e7i			0.0803696i	0.999192	+	0.0401848i	$0.0127947\pi$
$167$			6.25112e7i			0.0803696i	−0.999192	+	0.0401848i	$0.987205\pi$
$168$		0			0
$169$	−1.05639e7			−0.0129502
$170$	1.44689e9	−	8.35364e8i	1.73237	−	1.00018i
$171$		0			0
$172$	9.55335e7	−	1.65469e8i	0.109155	−	0.189061i
$173$	−2.70300e8	+	1.56058e8i	−0.301760	+	0.174221i	−0.643233	−	0.765670i	$-0.722408\pi$
$173$	−2.70300e8	+	1.56058e8i	−0.301760	+	0.174221i	0.341473	+	0.939892i	$0.389074\pi$
$174$		0			0
$175$	−7.68519e8	−	1.11546e9i	−0.819412	−	1.18933i
$176$			1.64413e8i			0.171350i
$177$		0			0
$178$	−5.56465e7	+	9.63826e7i	−0.0554317	+	0.0960105i
$179$	−3.94988e6	−	2.28046e6i	−0.00384744	−	0.00222132i	0.498075	−	0.867134i	$-0.334040\pi$
$179$	−3.94988e6	−	2.28046e6i	−0.00384744	−	0.00222132i	−0.501922	+	0.864913i	$0.667374\pi$
$180$		0			0
$181$	−1.31105e9			−1.22153			−0.610765	−	0.791812i	$-0.709138\pi$
$181$	−1.31105e9			−1.22153			−0.610765	+	0.791812i	$0.709138\pi$
$182$	−6.13572e7	−	7.68351e8i	−0.0559217	−	0.700284i
$183$		0			0
$184$	−1.49664e8	−	2.59226e8i	−0.130571	−	0.226156i
$185$	−1.71195e9	−	9.88393e8i	−1.46152	−	0.843806i
$186$		0			0
$187$	7.58282e8	+	1.31338e9i	0.620104	+	1.07405i
$188$			4.08213e8i			0.326780i
$189$		0			0
$190$	−1.99253e9			−1.52894
$191$	−3.47113e8	+	2.00406e8i	−0.260818	+	0.150583i	−0.624708	−	0.780859i	$-0.714782\pi$
$191$	−3.47113e8	+	2.00406e8i	−0.260818	+	0.150583i	0.363890	+	0.931442i	$0.381448\pi$
$192$		0			0
$193$	1.04486e9	−	1.80975e9i	0.753059	−	1.30434i	−0.193275	−	0.981145i	$-0.561911\pi$
$193$	1.04486e9	−	1.80975e9i	0.753059	−	1.30434i	0.946334	−	0.323191i	$-0.104756\pi$
$194$	8.49084e8	−	4.90219e8i	0.599437	−	0.346085i
$195$		0			0
$196$	−7.28543e8	+	1.17103e8i	−0.493663	+	0.0793497i
$197$			1.96116e9i			1.30211i	0.759029	+	0.651057i	$0.225674\pi$
$197$			1.96116e9i			1.30211i	−0.759029	+	0.651057i	$0.774326\pi$
$198$		0			0
$199$	2.23641e8	−	3.87357e8i	0.142606	−	0.247001i	−0.785871	−	0.618390i	$-0.787785\pi$
$199$	2.23641e8	−	3.87357e8i	0.142606	−	0.247001i	0.928477	+	0.371389i	$0.121118\pi$
$200$	−7.07548e8	−	4.08503e8i	−0.442218	−	0.255315i
$201$		0			0
$202$	1.62890e9			0.978335
$203$	2.58488e9	+	1.22929e9i	1.52214	+	0.723884i
$204$		0			0
$205$	−1.77083e8	−	3.06716e8i	−0.100268	−	0.173669i
$206$	1.26486e9	+	7.30266e8i	0.702381	+	0.405520i
$207$		0			0
$208$	−2.32452e8	−	4.02618e8i	−0.124188	−	0.215100i
$209$		−	1.80868e9i		−	0.947928i
$210$		0			0
$211$	−1.03716e9			−0.523257			−0.261629	−	0.965169i	$-0.584260\pi$
$211$	−1.03716e9			−0.523257			−0.261629	+	0.965169i	$0.584260\pi$
$212$	1.29589e9	−	7.48185e8i	0.641544	−	0.370395i
$213$		0			0
$214$	−1.05400e9	+	1.82557e9i	−0.502555	+	0.870451i
$215$	−1.26317e9	+	7.29291e8i	−0.591163	+	0.341308i
$216$		0			0
$217$	2.40561e9	+	3.49159e9i	1.08489	+	1.57465i
$218$		−	5.25992e8i		−	0.232891i
$219$		0			0
$220$	6.27553e8	−	1.08695e9i	0.267892	−	0.464002i
$221$	−3.71381e9	−	2.14417e9i	−1.55686	−	0.898855i
$222$		0			0
$223$	4.33625e8			0.175346			0.0876728	−	0.996149i	$-0.472057\pi$
$223$	4.33625e8			0.175346			0.0876728	+	0.996149i	$0.472057\pi$
$224$	−3.66495e8	+	2.52504e8i	−0.145571	+	0.100294i
$225$		0			0
$226$	−1.87194e8	−	3.24229e8i	−0.0717559	−	0.124285i
$227$	−2.53853e9	−	1.46562e9i	−0.956047	−	0.551974i	−0.0610931	−	0.998132i	$-0.519459\pi$
$227$	−2.53853e9	−	1.46562e9i	−0.956047	−	0.551974i	−0.894954	+	0.446158i	$0.852792\pi$
$228$		0			0
$229$	−5.29423e8	−	9.16987e8i	−0.192513	−	0.333443i	0.753569	−	0.657369i	$-0.228330\pi$
$229$	−5.29423e8	−	9.16987e8i	−0.192513	−	0.333443i	−0.946082	+	0.323926i	$0.894997\pi$
$230$			2.28504e9i			0.816549i
$231$		0			0
$232$	1.72638e9			0.595916
$233$	−3.71347e8	+	2.14397e8i	−0.125996	+	0.0727437i	−0.561673	−	0.827359i	$-0.689842\pi$
$233$	−3.71347e8	+	2.14397e8i	−0.125996	+	0.0727437i	0.435677	+	0.900103i	$0.356509\pi$
$234$		0			0
$235$	1.55812e9	−	2.69875e9i	0.510894	−	0.884894i
$236$	−8.88157e8	+	5.12778e8i	−0.286313	+	0.165303i
$237$		0			0
$238$	−1.76312e9	+	3.70739e9i	−0.549507	+	1.15547i
$239$			1.48225e9i			0.454286i	0.973861	+	0.227143i	$0.0729384\pi$
$239$			1.48225e9i			0.454286i	−0.973861	+	0.227143i	$0.927062\pi$
$240$		0			0
$241$	1.05313e9	−	1.82407e9i	0.312185	−	0.540720i	−0.666650	−	0.745371i	$-0.732273\pi$
$241$	1.05313e9	−	1.82407e9i	0.312185	−	0.540720i	0.978835	+	0.204651i	$0.0656058\pi$
$242$	−1.11362e9	−	6.42951e8i	−0.324696	−	0.187463i
$243$		0			0
$244$	2.50392e9			0.706417
$245$	5.26347e9	+	2.00662e9i	1.46086	+	0.556930i
$246$		0			0
$247$	2.55716e9	+	4.42914e9i	0.687022	+	1.18996i
$248$	2.21476e9	+	1.27869e9i	0.585490	+	0.338033i
$249$		0			0
$250$	9.59277e8	+	1.66152e9i	0.245575	+	0.425348i
$251$			3.30015e9i			0.831456i	0.909489	+	0.415728i	$0.136473\pi$
$251$			3.30015e9i			0.831456i	−0.909489	+	0.415728i	$0.863527\pi$
$252$		0			0
$253$	−2.07419e9			−0.506252
$254$	−3.21422e9	+	1.85573e9i	−0.772218	+	0.445840i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−3.36074e8	+	1.94033e8i	−0.0770376	+	0.0444777i	−0.538024	−	0.842930i	$-0.680829\pi$
$257$	−3.36074e8	+	1.94033e8i	−0.0770376	+	0.0444777i	0.460986	+	0.887407i	$0.347496\pi$
$258$		0			0
$259$	4.84190e9	−	3.86654e8i	1.07601	−	0.0859257i
$260$			3.54902e9i			0.776631i
$261$		0			0
$262$	2.24380e9	−	3.88638e9i	0.476189	−	0.824783i
$263$	4.35358e9	+	2.51354e9i	0.909964	+	0.525368i	0.880419	−	0.474196i	$-0.157261\pi$
$263$	4.35358e9	+	2.51354e9i	0.909964	+	0.525368i	0.0295442	+	0.999563i	$0.490594\pi$
$264$		0			0
$265$	−1.14231e10			−2.31633
$266$	4.03175e9	−	2.77776e9i	0.805317	−	0.554840i
$267$		0			0
$268$	−3.06572e8	−	5.30998e8i	−0.0594283	−	0.102933i
$269$	3.97594e9	+	2.29551e9i	0.759330	+	0.438399i	0.829055	−	0.559167i	$-0.188879\pi$
$269$	3.97594e9	+	2.29551e9i	0.759330	+	0.438399i	−0.0697250	+	0.997566i	$0.522212\pi$
$270$		0			0
$271$	1.49901e9	+	2.59636e9i	0.277925	+	0.481380i	0.970869	−	0.239611i	$-0.0770200\pi$
$271$	1.49901e9	+	2.59636e9i	0.277925	+	0.481380i	−0.692944	+	0.720991i	$0.743687\pi$
$272$			2.47608e9i			0.452366i
$273$		0			0
$274$	3.35934e9			0.596007
$275$	−4.90294e9	+	2.83071e9i	−0.857286	+	0.494954i
$276$		0			0
$277$	−2.71235e9	+	4.69793e9i	−0.460709	+	0.797972i	−0.998996	−	0.0447896i	$-0.985738\pi$
$277$	−2.71235e9	+	4.69793e9i	−0.460709	+	0.797972i	0.538287	+	0.842761i	$0.319072\pi$
$278$	−5.29483e9	+	3.05697e9i	−0.886488	+	0.511814i
$279$		0			0
$280$	3.38674e9	−	2.70451e8i	0.550998	−	0.0440003i
$281$			6.41122e9i			1.02829i	0.857703	+	0.514145i	$0.171891\pi$
$281$			6.41122e9i			1.02829i	−0.857703	+	0.514145i	$0.828109\pi$
$282$		0			0
$283$	−6.56150e8	+	1.13648e9i	−0.102296	+	0.177181i	−0.912630	−	0.408786i	$-0.865952\pi$
$283$	−6.56150e8	+	1.13648e9i	−0.102296	+	0.177181i	0.810334	+	0.585968i	$0.199285\pi$
$284$	−3.14253e9	−	1.81434e9i	−0.483065	−	0.278898i
$285$		0			0
$286$	−3.22154e9			−0.481503
$287$	7.85902e8	+	3.73750e8i	0.115835	+	0.0550876i
$288$		0			0
$289$	7.93199e9	+	1.37386e10i	1.13708	+	1.96948i
$290$	−1.14133e10	−	6.58950e9i	−1.61369	−	0.931666i
$291$		0			0
$292$	1.84016e9	+	3.18725e9i	0.253119	+	0.438415i
$293$			1.27727e9i			0.173305i	0.996239	+	0.0866525i	$0.0276170\pi$
$293$			1.27727e9i			0.173305i	−0.996239	+	0.0866525i	$0.972383\pi$
$294$		0			0
$295$	7.82897e9			1.03375
$296$	2.53717e9	−	1.46484e9i	0.330509	−	0.190819i
$297$		0			0
$298$	−2.72529e9	+	4.72035e9i	−0.345580	+	0.598562i
$299$	5.07934e9	−	2.93256e9i	0.635510	−	0.366912i
$300$		0			0
$301$	1.53924e9	−	3.23663e9i	0.187517	−	0.394300i
$302$		−	3.90607e9i		−	0.469582i
$303$		0			0
$304$	1.47651e9	−	2.55738e9i	0.172879	−	0.299434i
$305$	−1.65537e10	−	9.55731e9i	−1.91292	−	1.10443i
$306$		0			0
$307$	6.91746e9			0.778742			0.389371	−	0.921081i	$-0.372692\pi$
$307$	6.91746e9			0.778742			0.389371	+	0.921081i	$0.372692\pi$
$308$	2.45495e8	+	3.07423e9i	0.0272797	+	0.341613i
$309$		0			0
$310$	−9.76137e9	−	1.69072e10i	−1.05697	−	1.83073i
$311$	3.56553e9	+	2.05856e9i	0.381138	+	0.220050i	0.678313	−	0.734773i	$-0.262711\pi$
$311$	3.56553e9	+	2.05856e9i	0.381138	+	0.220050i	−0.297175	+	0.954823i	$0.596045\pi$
$312$		0			0
$313$	7.56998e9	+	1.31116e10i	0.788710	+	1.36609i	0.926758	+	0.375660i	$0.122584\pi$
$313$	7.56998e9	+	1.31116e10i	0.788710	+	1.36609i	−0.138048	+	0.990426i	$0.544083\pi$
$314$		−	1.10265e9i		−	0.113428i
$315$		0			0
$316$	−1.54727e9			−0.155174
$317$	3.50865e9	−	2.02572e9i	0.347458	−	0.200605i	−0.316107	−	0.948724i	$-0.602376\pi$
$317$	3.50865e9	−	2.02572e9i	0.347458	−	0.200605i	0.663565	+	0.748118i	$0.269043\pi$
$318$		0			0
$319$	5.98146e9	−	1.03602e10i	0.577623	−	1.00047i
$320$	1.77466e9	−	1.02460e9i	0.169245	−	0.0977136i
$321$		0			0
$322$	−3.18554e9	−	4.62361e9i	−0.296319	−	0.430089i
$323$		−	2.72390e10i		−	2.50254i
$324$		0			0
$325$	8.00430e9	−	1.38639e10i	0.717447	−	1.24266i
$326$	−5.52309e9	−	3.18876e9i	−0.489004	−	0.282326i
$327$		0			0
$328$	5.24887e8			0.0453493
$329$	6.09529e8	+	7.63288e9i	0.0520249	+	0.651486i
$330$		0			0
$331$	−7.70818e9	−	1.33510e10i	−0.642155	−	1.11224i	−0.984951	−	0.172835i	$-0.944707\pi$
$331$	−7.70818e9	−	1.33510e10i	−0.642155	−	1.11224i	0.342796	−	0.939410i	$-0.388626\pi$
$332$	6.50897e9	+	3.75796e9i	0.535747	+	0.309314i
$333$		0			0
$334$	3.53617e8	+	6.12482e8i	0.0284149	+	0.0492161i
$335$			4.68066e9i			0.371645i
$336$		0			0
$337$	−1.67594e10			−1.29939			−0.649693	−	0.760197i	$-0.725103\pi$
$337$	−1.67594e10			−1.29939			−0.649693	+	0.760197i	$0.725103\pi$
$338$	−1.03505e8	+	5.97585e7i	−0.00793037	+	0.00457860i
$339$		0			0
$340$	9.45107e9	−	1.63697e10i	0.707237	−	1.22497i
$341$	1.53471e10	−	8.86065e9i	1.13503	−	0.655312i
$342$		0			0
$343$	−1.34477e10	+	3.27747e9i	−0.971561	+	0.236789i
$344$		−	2.16168e9i		−	0.154368i
$345$		0			0
$346$	−1.76560e9	+	3.05810e9i	−0.123193	+	0.213377i
$347$	1.35565e10	+	7.82686e9i	0.935040	+	0.539846i	0.888402	−	0.459066i	$-0.151816\pi$
$347$	1.35565e10	+	7.82686e9i	0.935040	+	0.539846i	0.0466379	+	0.998912i	$0.485149\pi$
$348$		0			0
$349$	−1.37539e10			−0.927097			−0.463548	−	0.886072i	$-0.653424\pi$
$349$	−1.37539e10			−0.927097			−0.463548	+	0.886072i	$0.653424\pi$
$350$	−1.38399e10	−	6.58182e9i	−0.922276	−	0.438606i
$351$		0			0
$352$	9.30058e8	+	1.61091e9i	0.0605814	+	0.104930i
$353$	1.42207e10	+	8.21030e9i	0.915843	+	0.528762i	0.882306	−	0.470675i	$-0.155990\pi$
$353$	1.42207e10	+	8.21030e9i	0.915843	+	0.528762i	0.0335364	+	0.999437i	$0.489323\pi$
$354$		0			0
$355$	1.38504e10	+	2.39897e10i	0.872068	+	1.51047i
$356$			1.25914e9i			0.0783922i
$357$		0			0
$358$	−5.16010e7			−0.00314142
$359$	−1.05059e10	+	6.06556e9i	−0.632490	+	0.365168i	−0.781716	−	0.623635i	$-0.785655\pi$
$359$	−1.05059e10	+	6.06556e9i	−0.632490	+	0.365168i	0.149226	+	0.988803i	$0.452322\pi$
$360$		0			0
$361$	−7.75102e9	+	1.34252e10i	−0.456384	+	0.790480i
$362$	−1.28456e10	+	7.41641e9i	−0.748032	+	0.431876i
$363$		0			0
$364$	−4.94763e9	−	7.18118e9i	−0.281833	−	0.409063i
$365$		−	2.80951e10i		−	1.58292i
$366$		0			0
$367$	−6.94467e9	+	1.20285e10i	−0.382814	+	0.663052i	−0.991463	−	0.130387i	$-0.958378\pi$
$367$	−6.94467e9	+	1.20285e10i	−0.382814	+	0.663052i	0.608650	+	0.793439i	$0.291711\pi$
$368$	−2.93281e9	−	1.69326e9i	−0.159916	−	0.0923277i
$369$		0			0
$370$	−2.23648e10			−1.19332
$371$	2.31138e10	−	1.59248e10i	1.22005	−	0.840577i
$372$		0			0
$373$	−1.61745e10	−	2.80151e10i	−0.835597	−	1.44730i	−0.893544	−	0.448976i	$-0.851789\pi$
$373$	−1.61745e10	−	2.80151e10i	−0.835597	−	1.44730i	0.0579472	−	0.998320i	$-0.481545\pi$
$374$	1.48592e10	+	8.57898e9i	0.759469	+	0.438479i
$375$		0			0
$376$	2.30920e9	+	3.99965e9i	0.115534	+	0.200111i
$377$			3.38271e10i			1.67456i
$378$		0			0
$379$	−1.70023e10			−0.824046			−0.412023	−	0.911173i	$-0.635178\pi$
$379$	−1.70023e10			−0.824046			−0.412023	+	0.911173i	$0.635178\pi$
$380$	−1.95228e10	+	1.12715e10i	−0.936283	+	0.540563i
$381$		0			0
$382$	−2.26733e9	+	3.92713e9i	−0.106478	+	0.184426i
$383$	9.01879e9	−	5.20700e9i	0.419134	−	0.241987i	−0.275573	−	0.961280i	$-0.588867\pi$
$383$	9.01879e9	−	5.20700e9i	0.419134	−	0.241987i	0.694707	+	0.719293i	$0.255534\pi$
$384$		0			0
$385$	1.01112e10	−	2.12612e10i	0.460212	−	0.967710i
$386$		−	2.36425e10i		−	1.06499i
$387$		0			0
$388$	5.54619e9	−	9.60628e9i	0.244719	−	0.423866i
$389$	1.19242e10	+	6.88445e9i	0.520752	+	0.300656i	0.737242	−	0.675628i	$-0.236128\pi$
$389$	1.19242e10	+	6.88445e9i	0.520752	+	0.300656i	−0.216490	+	0.976285i	$0.569461\pi$
$390$		0			0
$391$	−3.12377e10			−1.33651
$392$	−6.47580e9	+	5.26864e9i	−0.274252	+	0.223128i
$393$		0			0
$394$	1.10940e10	+	1.92154e10i	0.460367	+	0.797379i
$395$	1.02292e10	+	5.90584e9i	0.420198	+	0.242601i
$396$		0			0
$397$	−7.97532e9	−	1.38137e10i	−0.321060	−	0.556092i	0.659647	−	0.751575i	$-0.270706\pi$
$397$	−7.97532e9	−	1.38137e10i	−0.321060	−	0.556092i	−0.980707	+	0.195483i	$0.937372\pi$
$398$		−	5.06042e9i		−	0.201676i
$399$		0			0
$400$	−9.24337e9			−0.361069
$401$	2.05250e10	−	1.18501e10i	0.793790	−	0.458295i	−0.0475048	−	0.998871i	$-0.515127\pi$
$401$	2.05250e10	−	1.18501e10i	0.793790	−	0.458295i	0.841295	+	0.540576i	$0.181794\pi$
$402$		0			0
$403$	−2.50549e10	+	4.33964e10i	−0.949890	+	1.64526i
$404$	1.59599e10	−	9.21443e9i	0.599106	−	0.345894i
$405$		0			0
$406$	3.22804e10	−	2.57778e9i	1.18805	−	0.0948726i
$407$		−	2.03011e10i		−	0.739847i
$408$		0			0
$409$	−9.56611e8	+	1.65690e9i	−0.0341855	+	0.0592111i	−0.882612	−	0.470102i	$-0.844217\pi$
$409$	−9.56611e8	+	1.65690e9i	−0.0341855	+	0.0592111i	0.848426	+	0.529313i	$0.177550\pi$
$410$	−3.47010e9	−	2.00346e9i	−0.122802	−	0.0708999i
$411$		0			0
$412$	1.65240e10			0.573491
$413$	−1.58414e10	+	1.09142e10i	−0.544493	+	0.375140i
$414$		0			0
$415$	−2.86878e10	−	4.96887e10i	−0.967174	−	1.67519i
$416$	−4.55511e9	−	2.62989e9i	−0.152099	−	0.0878142i
$417$		0			0
$418$	−1.02314e10	−	1.77213e10i	−0.335143	−	0.580485i
$419$		−	4.95708e10i		−	1.60831i	−0.594420	−	0.804155i	$-0.702618\pi$
$419$		−	4.95708e10i		−	1.60831i	0.594420	−	0.804155i	$-0.297382\pi$
$420$		0			0
$421$	2.82478e10			0.899200			0.449600	−	0.893230i	$-0.351567\pi$
$421$	2.82478e10			0.899200			0.449600	+	0.893230i	$0.351567\pi$
$422$	−1.01620e10	+	5.86706e9i	−0.320428	+	0.184999i
$423$		0			0
$424$	8.46475e9	−	1.46614e10i	0.261909	−	0.453640i
$425$	−7.38392e10	+	4.26311e10i	−2.26324	+	1.30668i
$426$		0			0
$427$	4.68190e10	−	3.73877e9i	1.40835	−	0.112465i
$428$			2.38492e10i			0.710720i
$429$		0			0
$430$	−8.25099e9	+	1.42911e10i	−0.241341	+	0.418016i
$431$	−4.08819e10	−	2.36032e10i	−1.18474	−	0.684008i	−0.227631	−	0.973747i	$-0.573098\pi$
$431$	−4.08819e10	−	2.36032e10i	−1.18474	−	0.684008i	−0.957106	+	0.289739i	$0.906431\pi$
$432$		0			0
$433$	6.08245e9			0.173032			0.0865161	−	0.996250i	$-0.472427\pi$
$433$	6.08245e9			0.173032			0.0865161	+	0.996250i	$0.472427\pi$
$434$	4.33214e10	+	2.06023e10i	1.22108	+	0.580707i
$435$		0			0
$436$	−2.97546e9	−	5.15364e9i	−0.0823394	−	0.142616i
$437$	3.22634e10	+	1.86273e10i	0.884675	+	0.510767i
$438$		0			0
$439$	2.63784e10	+	4.56887e10i	0.710215	+	1.23013i	0.964776	+	0.263072i	$0.0847358\pi$
$439$	2.63784e10	+	4.56887e10i	0.710215	+	1.23013i	−0.254561	+	0.967057i	$0.581931\pi$
$440$		−	1.41999e10i		−	0.378856i
$441$		0			0
$442$	−4.85170e10			−1.27117
$443$	6.25747e10	−	3.61275e10i	1.62474	−	0.938043i	0.639110	−	0.769115i	$-0.279303\pi$
$443$	6.25747e10	−	3.61275e10i	1.62474	−	0.938043i	0.985628	−	0.168928i	$-0.0540307\pi$
$444$		0			0
$445$	4.80605e9	−	8.32432e9i	0.122560	−	0.212280i
$446$	4.24864e9	−	2.45295e9i	0.107377	−	0.0619940i
$447$		0			0
$448$	−2.16252e9	+	4.54724e9i	−0.0536845	+	0.112885i
$449$		−	7.95127e9i		−	0.195637i	−0.995204	−	0.0978185i	$-0.968814\pi$
$449$		−	7.95127e9i		−	0.195637i	0.995204	−	0.0978185i	$-0.0311865\pi$
$450$		0			0
$451$	1.81859e9	−	3.14990e9i	0.0439572	−	0.0761361i
$452$	−3.66824e9	−	2.11786e9i	−0.0878827	−	0.0507391i
$453$		0			0
$454$	−3.31633e10			−0.780609
$455$	5.29927e9	+	6.63606e10i	0.123643	+	1.54833i
$456$		0			0
$457$	9.89100e9	+	1.71317e10i	0.226765	+	0.392768i	0.956847	−	0.290591i	$-0.0938518\pi$
$457$	9.89100e9	+	1.71317e10i	0.226765	+	0.392768i	−0.730083	+	0.683359i	$0.760518\pi$
$458$	−1.03745e10	−	5.98973e9i	−0.235780	−	0.136127i
$459$		0			0
$460$	1.29261e10	+	2.23887e10i	0.288694	+	0.500032i
$461$			5.18117e10i			1.14716i	0.819150	+	0.573580i	$0.194446\pi$
$461$			5.18117e10i			1.14716i	−0.819150	+	0.573580i	$0.805554\pi$
$462$		0			0
$463$	−1.02438e10			−0.222915			−0.111457	−	0.993769i	$-0.535552\pi$
$463$	−1.02438e10			−0.222915			−0.111457	+	0.993769i	$0.535552\pi$
$464$	1.69150e10	−	9.76590e9i	0.364923	−	0.210688i
$465$		0			0
$466$	−2.42563e9	+	4.20131e9i	−0.0514376	+	0.0890925i
$467$	−2.15789e10	+	1.24586e10i	−0.453693	+	0.261940i	−0.709389	−	0.704817i	$-0.751029\pi$
$467$	−2.15789e10	+	1.24586e10i	−0.453693	+	0.261940i	0.255695	+	0.966757i	$0.417696\pi$
$468$		0			0
$469$	−6.52524e9	−	9.47099e9i	−0.134867	−	0.195751i
$470$		−	3.52563e10i		−	0.722513i
$471$		0			0
$472$	−5.80142e9	+	1.00484e10i	−0.116887	+	0.202454i
$473$	−1.29724e10	−	7.48964e9i	−0.259165	−	0.149629i
$474$		0			0
$475$	1.01685e11			1.99748
$476$	3.69720e9	+	4.62985e10i	0.0720188	+	0.901861i
$477$		0			0
$478$	8.38485e9	+	1.45230e10i	0.160614	+	0.278192i
$479$	−5.22209e10	−	3.01498e10i	−0.991979	−	0.572719i	−0.0861135	−	0.996285i	$-0.527445\pi$
$479$	−5.22209e10	−	3.01498e10i	−0.991979	−	0.572719i	−0.905865	+	0.423566i	$0.860778\pi$
$480$		0			0
$481$	2.87023e10	+	4.97139e10i	0.536213	+	0.928747i
$482$		−	2.38295e10i		−	0.441496i
$483$		0			0
$484$	−1.45483e10			−0.265113
$485$	−7.33332e10	+	4.23389e10i	−1.32536	+	0.765197i
$486$		0			0
$487$	−6.15012e9	+	1.06523e10i	−0.109337	+	0.189378i	−0.915502	−	0.402314i	$-0.868206\pi$
$487$	−6.15012e9	+	1.06523e10i	−0.109337	+	0.189378i	0.806165	+	0.591691i	$0.201539\pi$
$488$	2.45333e10	−	1.41643e10i	0.432590	−	0.249756i
$489$		0			0
$490$	6.29224e10	−	1.01139e10i	1.09149	−	0.175443i
$491$			7.67869e10i			1.32118i	0.750748	+	0.660589i	$0.229693\pi$
$491$			7.67869e10i			1.32118i	−0.750748	+	0.660589i	$0.770307\pi$
$492$		0			0
$493$	9.00819e10	−	1.56027e11i	1.52493	−	2.64126i
$494$	5.01100e10	+	2.89310e10i	0.841427	+	0.485798i
$495$		0			0
$496$	2.89335e10			0.478050
$497$	−6.14690e10	−	2.92327e10i	−1.00747	−	0.479119i
$498$		0			0
$499$	2.51734e10	+	4.36016e10i	0.406013	+	0.703235i	0.994439	−	0.105316i	$-0.0335854\pi$
$499$	2.51734e10	+	4.36016e10i	0.406013	+	0.703235i	−0.588426	+	0.808551i	$0.700252\pi$
$500$	1.87979e10	+	1.08530e10i	0.300767	+	0.173648i
$501$		0			0
$502$	1.86685e10	+	3.23348e10i	0.293964	+	0.509161i
$503$		−	5.10365e10i		−	0.797276i	−0.917108	−	0.398638i	$-0.869483\pi$
$503$		−	5.10365e10i		−	0.797276i	0.917108	−	0.398638i	$-0.130517\pi$
$504$		0			0
$505$	−1.40684e11			−2.16311
$506$	−2.03228e10	+	1.17334e10i	−0.310015	+	0.178987i
$507$		0			0
$508$	−2.09952e10	+	3.63647e10i	−0.315257	+	0.546041i
$509$	−7.63635e10	+	4.40885e10i	−1.13767	+	0.656832i	−0.945852	−	0.324600i	$-0.894770\pi$
$509$	−7.63635e10	+	4.40885e10i	−1.13767	+	0.656832i	−0.191814	+	0.981431i	$0.561437\pi$
$510$		0			0
$511$	3.91669e10	+	5.68485e10i	0.574429	+	0.833749i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	−2.19523e9	+	3.80225e9i	−0.0314505	+	0.0544738i
$515$	−1.09243e11	−	6.30712e10i	−1.55297	−	0.896607i
$516$		0			0
$517$	3.20031e10			0.447950
$518$	4.52535e10	−	3.11784e10i	0.628541	−	0.433046i
$519$		0			0
$520$	2.00763e10	+	3.47731e10i	0.274581	+	0.475587i
$521$	−2.60547e10	−	1.50427e10i	−0.353618	−	0.204162i	0.312660	−	0.949865i	$-0.398780\pi$
$521$	−2.60547e10	−	1.50427e10i	−0.353618	−	0.204162i	−0.666278	+	0.745704i	$0.732113\pi$
$522$		0			0
$523$	3.95244e10	+	6.84583e10i	0.528273	+	0.914996i	0.999457	+	0.0329609i	$0.0104937\pi$
$523$	3.95244e10	+	6.84583e10i	0.528273	+	0.914996i	−0.471183	+	0.882035i	$0.656173\pi$
$524$		−	5.07714e10i		−	0.673433i
$525$		0			0
$526$	5.68750e10			0.742982
$527$	2.31130e11	−	1.33443e11i	2.99650	−	1.73003i
$528$		0			0
$529$	−1.77937e10	+	3.08197e10i	−0.227219	+	0.393555i
$530$	−1.11923e11	+	6.46188e10i	−1.41846	+	0.818947i
$531$		0			0
$532$	2.37896e10	−	5.00234e10i	0.296989	−	0.624492i
$533$			1.02848e10i			0.127434i
$534$		0			0
$535$	9.10309e10	−	1.57670e11i	1.11115	−	1.92457i
$536$	−6.00756e9	−	3.46846e9i	−0.0727845	−	0.0420221i
$537$		0			0
$538$	5.19415e10			0.619990
$539$	9.18068e9	+	5.71163e10i	0.108773	+	0.676714i
$540$		0			0
$541$	−3.84892e10	−	6.66652e10i	−0.449314	−	0.778234i	0.549028	−	0.835804i	$-0.314998\pi$
$541$	−3.84892e10	−	6.66652e10i	−0.449314	−	0.778234i	−0.998341	+	0.0575698i	$0.981665\pi$
$542$	2.93745e10	+	1.69594e10i	0.340387	+	0.196523i
$543$		0			0
$544$	1.40069e10	+	2.42606e10i	0.159936	+	0.277016i
$545$			4.54286e10i			0.514924i
$546$		0			0
$547$	−9.53137e10			−1.06465			−0.532324	−	0.846541i	$-0.678681\pi$
$547$	−9.53137e10			−1.06465			−0.532324	+	0.846541i	$0.678681\pi$
$548$	3.29146e10	−	1.90033e10i	0.364978	−	0.210720i
$549$		0			0
$550$	−3.20258e10	+	5.54704e10i	−0.349985	+	0.606192i
$551$	−1.86079e11	+	1.07433e11i	−2.01879	+	1.16555i
$552$		0			0
$553$	−2.89313e10	+	2.31033e9i	−0.309362	+	0.0247044i
$554$			6.13735e10i			0.651541i
$555$		0			0
$556$	−3.45857e10	+	5.99042e10i	−0.361907	+	0.626842i
$557$	9.60917e10	+	5.54786e10i	0.998309	+	0.576374i	0.907748	−	0.419517i	$-0.137800\pi$
$557$	9.60917e10	+	5.54786e10i	0.998309	+	0.576374i	0.0905616	+	0.995891i	$0.471134\pi$
$558$		0			0
$559$	4.23563e10			0.433782
$560$	3.16533e10	−	2.18082e10i	0.321859	−	0.221752i
$561$		0			0
$562$	3.62673e10	+	6.28169e10i	0.363555	+	0.629696i
$563$	−3.20416e10	−	1.84992e10i	−0.318919	−	0.184128i	0.331992	−	0.943282i	$-0.392279\pi$
$563$	−3.20416e10	−	1.84992e10i	−0.318919	−	0.184128i	−0.650911	+	0.759154i	$0.725613\pi$
$564$		0			0
$565$	1.61675e10	+	2.80029e10i	0.158653	+	0.274795i
$566$			1.48470e10i			0.144668i
$567$		0			0
$568$	−4.10538e10			−0.394421
$569$	−3.94908e10	+	2.28000e10i	−0.376745	+	0.217514i	−0.676401	−	0.736534i	$-0.736461\pi$
$569$	−3.94908e10	+	2.28000e10i	−0.376745	+	0.217514i	0.299656	+	0.954047i	$0.403128\pi$
$570$		0			0
$571$	−3.78923e10	+	6.56314e10i	−0.356456	+	0.617401i	−0.987366	−	0.158456i	$-0.949348\pi$
$571$	−3.78923e10	+	6.56314e10i	−0.356456	+	0.617401i	0.630910	+	0.775856i	$0.282682\pi$
$572$	−3.15645e10	+	1.82238e10i	−0.294859	+	0.170237i
$573$		0			0
$574$	9.81449e9	−	7.83743e8i	0.0904108	−	0.00721982i
$575$		−	1.16612e11i		−	1.06677i
$576$		0			0
$577$	−7.59257e10	+	1.31507e11i	−0.684992	+	1.18644i	0.288447	+	0.957496i	$0.406861\pi$
$577$	−7.59257e10	+	1.31507e11i	−0.684992	+	1.18644i	−0.973439	+	0.228945i	$0.926472\pi$
$578$	1.55435e11	+	8.97402e10i	1.39263	+	0.804037i
$579$		0			0
$580$	−1.49103e11			−1.31758
$581$	1.27318e11	+	6.05484e10i	1.11734	+	0.531371i
$582$		0			0
$583$	−5.86562e10	−	1.01596e11i	−0.507738	−	0.879428i
$584$	3.60596e10	+	2.08190e10i	0.310006	+	0.178982i
$585$		0			0
$586$	7.22531e9	+	1.25146e10i	0.0612726	+	0.106127i
$587$		−	7.97697e10i		−	0.671871i	−0.941885	−	0.335935i	$-0.890948\pi$
$587$		−	7.97697e10i		−	0.671871i	0.941885	−	0.335935i	$-0.109052\pi$
$588$		0			0
$589$	−3.18292e11			−2.64463
$590$	7.67079e10	−	4.42873e10i	0.633041	−	0.365487i
$591$		0			0
$592$	1.65727e10	−	2.87048e10i	0.134930	−	0.233705i
$593$	−1.28600e11	+	7.42472e10i	−1.03997	+	0.600428i	−0.919825	−	0.392328i	$-0.871670\pi$
$593$	−1.28600e11	+	7.42472e10i	−1.03997	+	0.600428i	−0.120147	+	0.992756i	$0.538336\pi$
$594$		0			0
$595$	1.52276e11	−	3.20198e11i	1.21496	−	2.55476i
$596$			6.16664e10i			0.488724i
$597$		0			0
$598$	3.31781e10	−	5.74661e10i	0.259446	−	0.449373i
$599$	1.50721e11	+	8.70190e10i	1.17076	+	0.675938i	0.953859	−	0.300256i	$-0.0970721\pi$
$599$	1.50721e11	+	8.70190e10i	1.17076	+	0.675938i	0.216900	+	0.976194i	$0.430405\pi$
$600$		0			0
$601$	−5.90100e10			−0.452301			−0.226150	−	0.974092i	$-0.572614\pi$
$601$	−5.90100e10			−0.452301			−0.226150	+	0.974092i	$0.572614\pi$
$602$	−3.22774e9	−	4.04196e10i	−0.0245761	−	0.307756i
$603$		0			0
$604$	−2.20960e10	−	3.82715e10i	−0.166022	−	0.287559i
$605$	9.61808e10	+	5.55300e10i	0.717905	+	0.414483i
$606$		0			0
$607$	4.19303e10	+	7.26255e10i	0.308868	+	0.534976i	0.978115	−	0.208064i	$-0.0667164\pi$
$607$	4.19303e10	+	7.26255e10i	0.308868	+	0.534976i	−0.669247	+	0.743040i	$0.733383\pi$
$608$		−	3.34095e10i		−	0.244487i
$609$		0			0
$610$	−2.16257e11			−1.56189
$611$	−7.83701e10	+	4.52470e10i	−0.562322	+	0.324657i
$612$		0			0
$613$	−2.07027e10	+	3.58582e10i	−0.146618	+	0.253949i	−0.929975	−	0.367622i	$-0.880172\pi$
$613$	−2.07027e10	+	3.58582e10i	−0.146618	+	0.253949i	0.783358	+	0.621571i	$0.213505\pi$
$614$	6.77770e10	−	3.91311e10i	0.476880	−	0.275327i
$615$		0			0
$616$	1.97958e10	+	2.87325e10i	0.137484	+	0.199549i
$617$		−	9.71102e10i		−	0.670076i	−0.942205	−	0.335038i	$-0.891251\pi$
$617$		−	9.71102e10i		−	0.670076i	0.942205	−	0.335038i	$-0.108749\pi$
$618$		0			0
$619$	6.35153e10	−	1.10012e11i	0.432629	−	0.749335i	−0.564470	−	0.825454i	$-0.690919\pi$
$619$	6.35153e10	−	1.10012e11i	0.432629	−	0.749335i	0.997099	+	0.0761183i	$0.0242527\pi$
$620$	−1.91283e11	−	1.10437e11i	−1.29452	−	0.747393i
$621$		0			0
$622$	4.65799e10			0.311198
$623$	1.88010e9	+	2.35437e10i	0.0124804	+	0.156287i
$624$		0			0
$625$	2.73392e10	+	4.73529e10i	0.179170	+	0.310332i
$626$	1.48341e11	+	8.56445e10i	0.965968	+	0.557702i
$627$		0			0
$628$	−6.23755e9	−	1.08038e10i	−0.0401029	−	0.0694603i
$629$		−	3.05738e11i		−	1.95320i
$630$		0			0
$631$	3.15863e11			1.99242			0.996210	−	0.0869861i	$-0.0277236\pi$
$631$	3.15863e11			1.99242			0.996210	+	0.0869861i	$0.0277236\pi$
$632$	−1.51601e10	+	8.75269e9i	−0.0950241	+	0.0548622i
$633$		0			0
$634$	2.29184e10	−	3.96958e10i	0.141849	−	0.245690i
$635$	2.77604e11	−	1.60275e11i	1.70738	−	0.985757i
$636$		0			0
$637$	−1.03235e11	−	1.26888e11i	−0.627001	−	0.770661i
$638$		−	1.35345e11i		−	0.816882i
$639$		0			0
$640$	1.15920e10	−	2.00780e10i	0.0690940	−	0.119674i
$641$	−2.68555e11	−	1.55050e11i	−1.59075	−	0.918418i	−0.993179	−	0.116600i	$-0.962800\pi$
$641$	−2.68555e11	−	1.55050e11i	−1.59075	−	0.918418i	−0.597568	−	0.801818i	$-0.703866\pi$
$642$		0			0
$643$	−1.93916e11			−1.13441			−0.567206	−	0.823576i	$-0.691976\pi$
$643$	−1.93916e11			−1.13441			−0.567206	+	0.823576i	$0.691976\pi$
$644$	−5.73669e10	−	2.72819e10i	−0.333517	−	0.158610i
$645$		0			0
$646$	−1.54087e11	−	2.66887e11i	−0.884781	−	1.53249i
$647$	1.36422e11	+	7.87631e10i	0.778514	+	0.449475i	0.835903	−	0.548877i	$-0.184944\pi$
$647$	1.36422e11	+	7.87631e10i	0.778514	+	0.449475i	−0.0573894	+	0.998352i	$0.518278\pi$
$648$		0			0
$649$	4.02008e10	+	6.96298e10i	0.226598	+	0.392479i
$650$		−	1.81117e11i		−	1.01462i
$651$		0			0
$652$	−7.21534e10			−0.399270
$653$	−6.48067e10	+	3.74161e10i	−0.356424	+	0.205781i	−0.667511	−	0.744600i	$-0.732640\pi$
$653$	−6.48067e10	+	3.74161e10i	−0.356424	+	0.205781i	0.311087	+	0.950381i	$0.399307\pi$
$654$		0			0
$655$	−1.93791e11	+	3.35657e11i	−1.05286	+	1.82360i
$656$	5.14282e9	−	2.96921e9i	0.0277707	−	0.0160334i
$657$		0			0
$658$	4.91502e10	+	7.13386e10i	0.262194	+	0.380558i
$659$		−	1.29203e11i		−	0.685062i	−0.939507	−	0.342531i	$-0.888716\pi$
$659$		−	1.29203e11i		−	0.685062i	0.939507	−	0.342531i	$-0.111284\pi$
$660$		0			0
$661$	1.41550e11	−	2.45172e11i	0.741487	−	1.28429i	−0.210330	−	0.977630i	$-0.567454\pi$
$661$	1.41550e11	−	2.45172e11i	0.741487	−	1.28429i	0.951818	−	0.306664i	$-0.0992127\pi$
$662$	−1.51049e11	−	8.72081e10i	−0.786476	−	0.454072i
$663$		0			0
$664$	8.50328e10			0.437436
$665$	−3.48212e11	+	2.39908e11i	−1.78056	+	1.22676i
$666$		0			0
$667$	1.23204e11	+	2.13396e11i	0.622475	+	1.07816i
$668$	6.92944e9	+	4.00071e9i	0.0348010	+	0.0200924i
$669$		0			0
$670$	2.64778e10	+	4.58610e10i	0.131396	+	0.227585i
$671$		−	1.96302e11i		−	0.968357i
$672$		0			0
$673$	−2.58046e11			−1.25787			−0.628937	−	0.777456i	$-0.716510\pi$
$673$	−2.58046e11			−1.25787			−0.628937	+	0.777456i	$0.716510\pi$
$674$	−1.64208e11	+	9.48053e10i	−0.795708	+	0.459402i
$675$		0			0
$676$	−6.76090e8	+	1.17102e9i	−0.00323756	+	0.00560762i
$677$	−1.43213e11	+	8.26842e10i	−0.681755	+	0.393612i	−0.800516	−	0.599311i	$-0.795441\pi$
$677$	−1.43213e11	+	8.26842e10i	−0.681755	+	0.393612i	0.118761	+	0.992923i	$0.462108\pi$
$678$		0			0
$679$	8.93605e10	−	1.87902e11i	0.420404	−	0.884002i
$680$		−	2.13853e11i		−	1.00018i
$681$		0			0
$682$	1.00247e11	−	1.73633e11i	0.463375	−	0.802590i
$683$	4.12418e10	+	2.38109e10i	0.189520	+	0.109419i	0.591758	−	0.806116i	$-0.298434\pi$
$683$	4.12418e10	+	2.38109e10i	0.189520	+	0.109419i	−0.402238	+	0.915535i	$0.631768\pi$
$684$		0			0
$685$	−2.90137e11			−1.31778
$686$	−1.13219e11	+	1.08184e11i	−0.511240	+	0.488502i
$687$		0			0
$688$	−1.22283e10	−	2.11800e10i	−0.0545773	−	0.0945306i
$689$	2.87278e11	+	1.65860e11i	1.27475	+	0.735978i
$690$		0			0
$691$	−4.16309e9	−	7.21068e9i	−0.0182601	−	0.0316275i	0.856751	−	0.515730i	$-0.172479\pi$
$691$	−4.16309e9	−	7.21068e9i	−0.0182601	−	0.0316275i	−0.875011	+	0.484103i	$0.839146\pi$
$692$			3.99509e10i			0.174221i
$693$		0			0
$694$	1.77102e11			0.763457
$695$	4.57301e11	−	2.64023e11i	1.96003	−	1.13163i
$696$		0			0
$697$	2.73884e10	−	4.74381e10i	0.116047	−	0.201000i
$698$	−1.34760e11	+	7.78040e10i	−0.567729	+	0.327778i
$699$		0			0
$700$	−1.72835e11	+	1.38019e10i	−0.719847	+	0.0574839i
$701$		−	2.81248e11i		−	1.16471i	−0.812934	−	0.582355i	$-0.802131\pi$
$701$		−	2.81248e11i		−	1.16471i	0.812934	−	0.582355i	$-0.197869\pi$
$702$		0			0
$703$	−1.82314e11	+	3.15777e11i	−0.746446	+	1.29288i
$704$	1.82253e10	+	1.05224e10i	0.0741968	+	0.0428375i
$705$		0			0
$706$	1.85778e11			0.747783
$707$	2.84663e11	−	1.96125e11i	1.13934	−	0.784973i
$708$		0			0
$709$	−1.29441e11	−	2.24198e11i	−0.512255	−	0.887251i	−0.999899	−	0.0142088i	$-0.995477\pi$
$709$	−1.29441e11	−	2.24198e11i	−0.512255	−	0.887251i	0.487644	−	0.873042i	$-0.337856\pi$
$710$	2.71412e11	+	1.56700e11i	1.06806	+	0.616645i
$711$		0			0
$712$	7.12276e9	+	1.23370e10i	0.0277158	+	0.0480053i
$713$			3.65018e11i			1.41239i
$714$		0			0
$715$	2.78236e11			1.06461
$716$	−5.05584e8	+	2.91899e8i	−0.00192372	+	0.00111066i
$717$		0			0
$718$	−6.86240e10	+	1.18860e11i	−0.258213	+	0.447238i
$719$	−1.67169e11	+	9.65148e10i	−0.625517	+	0.361142i	−0.779014	−	0.627007i	$-0.784280\pi$
$719$	−1.67169e11	+	9.65148e10i	−0.625517	+	0.361142i	0.153497	+	0.988149i	$0.450946\pi$
$720$		0			0
$721$	3.08971e11	−	2.46731e10i	1.14334	−	0.0913025i
$722$			1.75386e11i			0.645424i
$723$		0			0
$724$	−8.39071e10	+	1.45331e11i	−0.305383	+	0.528938i
$725$	5.82456e11	+	3.36281e11i	2.10820	+	1.21717i
$726$		0			0
$727$	−1.85691e11			−0.664742			−0.332371	−	0.943149i	$-0.607849\pi$
$727$	−1.85691e11			−0.664742			−0.332371	+	0.943149i	$0.607849\pi$
$728$	−8.90995e10	−	4.23729e10i	−0.317212	−	0.150856i
$729$		0			0
$730$	−1.58930e11	−	2.75275e11i	−0.559647	−	0.969338i
$731$	−1.95367e11	−	1.12795e11i	−0.684199	−	0.395022i
$732$		0			0
$733$	−2.32208e10	−	4.02196e10i	−0.0804380	−	0.139323i	0.823000	−	0.568041i	$-0.192299\pi$
$733$	−2.32208e10	−	4.02196e10i	−0.0804380	−	0.139323i	−0.903438	+	0.428718i	$0.858965\pi$
$734$			1.57140e11i			0.541380i
$735$		0			0
$736$	−3.83141e10			−0.130571
$737$	−4.16292e10	+	2.40346e10i	−0.141100	+	0.0814643i
$738$		0			0
$739$	−2.17468e10	+	3.76666e10i	−0.0729151	+	0.126293i	−0.900178	−	0.435523i	$-0.856564\pi$
$739$	−2.17468e10	+	3.76666e10i	−0.0729151	+	0.126293i	0.827263	+	0.561815i	$0.189897\pi$
$740$	−2.19129e11	+	1.26514e11i	−0.730758	+	0.421903i
$741$		0			0
$742$	1.36384e11	−	2.86782e11i	0.449934	−	0.946098i
$743$		−	5.62557e11i		−	1.84591i	−0.384906	−	0.922956i	$-0.625766\pi$
$743$		−	5.62557e11i		−	1.84591i	0.384906	−	0.922956i	$-0.374234\pi$
$744$		0			0
$745$	2.35377e11	−	4.07685e11i	0.764080	−	1.32342i
$746$	−3.16955e11	−	1.82994e11i	−1.02339	−	0.590856i
$747$		0			0
$748$	1.94120e11			0.620104
$749$	3.56108e10	+	4.45939e11i	0.113150	+	1.41693i
$750$		0			0
$751$	1.66683e11	+	2.88703e11i	0.523999	+	0.907594i	0.999610	+	0.0279375i	$0.00889393\pi$
$751$	1.66683e11	+	2.88703e11i	0.523999	+	0.907594i	−0.475610	+	0.879656i	$0.657773\pi$
$752$	4.52509e10	+	2.61256e10i	0.141500	+	0.0816949i
$753$		0			0
$754$	1.91355e11	+	3.31437e11i	0.592045	+	1.02545i
$755$			3.37357e11i			1.03825i
$756$		0			0
$757$	−2.17560e11			−0.662514			−0.331257	−	0.943541i	$-0.607473\pi$
$757$	−2.17560e11			−0.662514			−0.331257	+	0.943541i	$0.607473\pi$
$758$	−1.66588e11	+	9.61797e10i	−0.504623	+	0.291344i
$759$		0			0
$760$	−1.27522e11	+	2.20875e11i	−0.382236	+	0.662052i
$761$	8.53154e10	−	4.92569e10i	0.254383	−	0.146868i	−0.367386	−	0.930068i	$-0.619747\pi$
$761$	8.53154e10	−	4.92569e10i	0.254383	−	0.146868i	0.621770	+	0.783200i	$0.286414\pi$
$762$		0			0
$763$	−6.33312e10	−	9.19215e10i	−0.186861	−	0.271218i
$764$			5.13039e10i			0.150583i
$765$		0			0
$766$	5.89105e10	−	1.02036e11i	0.171111	−	0.296373i
$767$	−1.96890e11	−	1.13674e11i	−0.568907	−	0.328459i
$768$		0			0
$769$	1.50574e11			0.430570			0.215285	−	0.976551i	$-0.430932\pi$
$769$	1.50574e11			0.430570			0.215285	+	0.976551i	$0.430932\pi$
$770$	−2.12028e10	−	2.65514e11i	−0.0603157	−	0.755308i
$771$		0			0
$772$	−1.33742e11	−	2.31648e11i	−0.376529	−	0.652168i
$773$	−3.03645e11	−	1.75309e11i	−0.850448	−	0.491006i	0.0103542	−	0.999946i	$-0.496704\pi$
$773$	−3.03645e11	−	1.75309e11i	−0.850448	−	0.491006i	−0.860802	+	0.508940i	$0.830037\pi$
$774$		0			0
$775$	4.98151e11	+	8.62823e11i	1.38087	+	2.39174i
$776$		−	1.25496e11i		−	0.346085i
$777$		0			0
$778$	1.55777e11			0.425192
$779$	−5.65753e10	+	3.26638e10i	−0.153630	+	0.0886986i
$780$		0			0
$781$	−1.42241e11	+	2.46368e11i	−0.382313	+	0.662186i
$782$	−3.06066e11	+	1.76707e11i	−0.818441	+	0.472527i
$783$		0			0
$784$	−3.36457e10	+	8.82545e10i	−0.0890564	+	0.233600i
$785$			9.52335e10i			0.250790i
$786$		0			0
$787$	−3.24980e11	+	5.62881e11i	−0.847144	+	1.46730i	0.0366016	+	0.999330i	$0.488347\pi$
$787$	−3.24980e11	+	5.62881e11i	−0.847144	+	1.46730i	−0.883746	+	0.467967i	$0.844987\pi$
$788$	2.17398e11	+	1.25515e11i	0.563832	+	0.325529i
$789$		0			0
$790$	1.33634e11			0.343090
$791$	−7.17520e10	−	3.41230e10i	−0.183286	−	0.0871649i
$792$		0			0
$793$	2.77539e11	+	4.80711e11i	0.701828	+	1.21560i
$794$	−1.56284e11	−	9.02304e10i	−0.393216	−	0.227024i
$795$		0			0
$796$	−2.86260e10	−	4.95818e10i	−0.0713032	−	0.123501i
$797$			4.72971e11i			1.17220i	0.810239	+	0.586100i	$0.199337\pi$
$797$			4.72971e11i			1.17220i	−0.810239	+	0.586100i	$0.800663\pi$
$798$		0			0
$799$	4.81972e11			1.18259
$800$	−9.05662e10	+	5.22884e10i	−0.221109	+	0.127657i
$801$		0			0
$802$	1.34069e11	−	2.32214e11i	0.324064	−	0.561295i
$803$	2.49874e11	−	1.44265e11i	0.600979	−	0.346975i
$804$		0			0
$805$	2.75127e11	+	3.99330e11i	0.655163	+	0.950929i
$806$			5.66928e11i			1.34335i
$807$		0			0
$808$	1.04249e11	−	1.80565e11i	0.244584	−	0.423632i
$809$	4.06724e10	+	2.34822e10i	0.0949524	+	0.0548208i	0.546724	−	0.837313i	$-0.315875\pi$
$809$	4.06724e10	+	2.34822e10i	0.0949524	+	0.0548208i	−0.451772	+	0.892133i	$0.649208\pi$
$810$		0			0
$811$	−4.17500e11			−0.965102			−0.482551	−	0.875868i	$-0.660290\pi$
$811$	−4.17500e11			−0.965102			−0.482551	+	0.875868i	$0.660290\pi$
$812$	3.01700e11	−	2.07862e11i	0.693987	−	0.478137i
$813$		0			0
$814$	−1.14840e11	−	1.98909e11i	−0.261575	−	0.453062i
$815$	4.77016e11	+	2.75405e11i	1.08119	+	0.624226i
$816$		0			0
$817$	1.34521e11	+	2.32998e11i	0.301928	+	0.522954i
$818$			2.16456e10i			0.0483456i
$819$		0			0
$820$	−4.53332e10			−0.100268
$821$	−6.00612e11	+	3.46763e11i	−1.32197	+	0.763239i	−0.984043	−	0.177933i	$-0.943059\pi$
$821$	−6.00612e11	+	3.46763e11i	−1.32197	+	0.763239i	−0.337926	+	0.941173i	$0.609725\pi$
$822$		0			0
$823$	4.44713e11	−	7.70266e11i	0.969350	−	1.67896i	0.271906	−	0.962324i	$-0.412346\pi$
$823$	4.44713e11	−	7.70266e11i	0.969350	−	1.67896i	0.697444	−	0.716639i	$-0.254321\pi$
$824$	1.61902e11	−	9.34740e10i	0.351190	−	0.202760i
$825$		0			0
$826$	−9.34727e10	+	1.96549e11i	−0.200800	+	0.422232i
$827$			4.97905e11i			1.06445i	0.846603	+	0.532224i	$0.178644\pi$
$827$			4.97905e11i			1.06445i	−0.846603	+	0.532224i	$0.821356\pi$
$828$		0			0
$829$	3.68153e11	−	6.37659e11i	0.779488	−	1.35011i	−0.152748	−	0.988265i	$-0.548812\pi$
$829$	3.68153e11	−	6.37659e11i	0.779488	−	1.35011i	0.932237	−	0.361848i	$-0.117854\pi$
$830$	−5.62163e11	−	3.24565e11i	−1.18454	−	0.683895i
$831$		0			0
$832$	−5.95077e10			−0.124188
$833$	1.38263e11	+	8.60183e11i	0.287161	+	1.78653i
$834$		0			0
$835$	−3.05410e10	−	5.28985e10i	−0.0628256	−	0.108817i
$836$	−2.00494e11	−	1.15755e11i	−0.410465	−	0.236982i
$837$		0			0
$838$	−2.80415e11	−	4.85692e11i	−0.568623	−	0.984884i
$839$		−	3.11839e11i		−	0.629336i	−0.949202	−	0.314668i	$-0.898107\pi$
$839$		−	3.11839e11i		−	0.629336i	0.949202	−	0.314668i	$-0.101893\pi$
$840$		0			0
$841$	−9.20918e11			−1.84093
$842$	2.76771e11	−	1.59794e11i	0.550645	−	0.317915i
$843$		0			0
$844$	−6.63782e10	+	1.14970e11i	−0.130814	+	0.226577i
$845$	8.93944e9	−	5.16119e9i	0.0175341	−	0.0101233i
$846$		0			0
$847$	−2.72029e11	+	2.17230e10i	−0.528544	+	0.0422072i
$848$		−	1.91535e11i		−	0.370395i
$849$		0			0
$850$	−4.82315e11	+	8.35395e11i	−0.923965	+	1.60035i
$851$	3.62133e11	+	2.09078e11i	0.690478	+	0.398648i
$852$		0			0
$853$	6.66577e11			1.25908			0.629542	−	0.776967i	$-0.283243\pi$
$853$	6.66577e11			1.25908			0.629542	+	0.776967i	$0.283243\pi$
$854$	4.37581e11	−	3.01481e11i	0.822673	−	0.566797i
$855$		0			0
$856$	1.34911e11	+	2.33673e11i	0.251277	+	0.435225i
$857$	−3.66814e11	−	2.11780e11i	−0.680022	−	0.392611i	0.119841	−	0.992793i	$-0.461761\pi$
$857$	−3.66814e11	−	2.11780e11i	−0.680022	−	0.392611i	−0.799863	+	0.600182i	$0.795095\pi$
$858$		0			0
$859$	2.67760e11	+	4.63774e11i	0.491783	+	0.851792i	0.999955	−	0.00946285i	$-0.00301216\pi$
$859$	2.67760e11	+	4.63774e11i	0.491783	+	0.851792i	−0.508173	+	0.861255i	$0.669679\pi$
$860$			1.86698e11i			0.341308i
$861$		0			0
$862$	−5.34079e11			−0.967333
$863$	3.00771e11	−	1.73650e11i	0.542241	−	0.313063i	−0.203745	−	0.979024i	$-0.565311\pi$
$863$	3.00771e11	−	1.73650e11i	0.542241	−	0.313063i	0.745987	+	0.665961i	$0.231978\pi$
$864$		0			0
$865$	1.52490e11	−	2.64120e11i	0.272381	−	0.471778i
$866$	5.95956e10	−	3.44075e10i	0.105960	−	0.0611761i
$867$		0			0
$868$	5.41006e11	−	4.32024e10i	0.953067	−	0.0761078i
$869$			1.21303e11i			0.212712i
$870$		0			0
$871$	6.79618e10	−	1.17713e11i	0.118084	−	0.204528i
$872$	−5.83068e10	−	3.36635e10i	−0.100845	−	0.0582228i
$873$		0			0
$874$	4.21487e11			0.722334
$875$	3.67694e11	+	1.74864e11i	0.627270	+	0.298310i
$876$		0			0
$877$	5.73082e11	+	9.92607e11i	0.968765	+	1.67795i	0.699141	+	0.714984i	$0.253566\pi$
$877$	5.73082e11	+	9.92607e11i	0.968765	+	1.67795i	0.269623	+	0.962966i	$0.413101\pi$
$878$	5.16909e11	+	2.98437e11i	0.869833	+	0.502198i
$879$		0			0
$880$	−8.03268e10	−	1.39130e11i	−0.133946	−	0.232001i
$881$			1.09062e10i			0.0181038i	0.999959	+	0.00905189i	$0.00288135\pi$
$881$			1.09062e10i			0.0181038i	−0.999959	+	0.00905189i	$0.997119\pi$
$882$		0			0
$883$	−7.76508e11			−1.27733			−0.638665	−	0.769485i	$-0.720513\pi$
$883$	−7.76508e11			−1.27733			−0.638665	+	0.769485i	$0.720513\pi$
$884$	−4.75367e11	+	2.74453e11i	−0.778431	+	0.449427i
$885$		0			0
$886$	4.08736e11	−	7.07951e11i	0.663297	−	1.14886i
$887$	−1.95564e11	+	1.12909e11i	−0.315933	+	0.182404i	−0.649578	−	0.760295i	$-0.725055\pi$
$887$	−1.95564e11	+	1.12909e11i	−0.315933	+	0.182404i	0.333645	+	0.942699i	$0.391721\pi$
$888$		0			0
$889$	−3.38275e11	+	7.11307e11i	−0.541581	+	1.13881i
$890$		−	1.08749e11i		−	0.173326i
$891$		0			0
$892$	2.77520e10	−	4.80679e10i	0.0438364	−	0.0759269i
$893$	−4.97798e11	−	2.87404e11i	−0.782793	−	0.451946i
$894$		0			0
$895$	4.45665e9			0.00694570
$896$	4.53474e9	+	5.67867e10i	0.00703592	+	0.0881079i
$897$		0			0
$898$	−4.49792e10	−	7.79062e10i	−0.0691681	−	0.119803i
$899$	−1.82320e12	−	1.05262e12i	−2.79122	−	1.61151i
$900$		0			0
$901$	−8.83374e11	−	1.53005e12i	−1.34043	−	2.32170i
$902$		−	4.11501e10i		−	0.0621648i
$903$		0			0
$904$	−4.79216e10			−0.0717559
$905$	1.10944e12	−	6.40537e11i	1.65390	−	0.954882i
$906$		0			0
$907$	1.64487e11	−	2.84901e11i	0.243054	−	0.420983i	−0.718528	−	0.695498i	$-0.755184\pi$
$907$	1.64487e11	−	2.84901e11i	0.243054	−	0.420983i	0.961583	+	0.274515i	$0.0885173\pi$
$908$	−3.24932e11	+	1.87600e11i	−0.478024	+	0.275987i
$909$		0			0
$910$	4.27314e11	+	6.20221e11i	0.623134	+	0.904442i
$911$			1.20936e11i			0.175583i	0.996139	+	0.0877914i	$0.0279809\pi$
$911$			1.20936e11i			0.175583i	−0.996139	+	0.0877914i	$0.972019\pi$
$912$		0			0
$913$	2.94616e11	−	5.10291e11i	0.424008	−	0.734403i
$914$	1.93823e11	+	1.11904e11i	0.277729	+	0.160347i
$915$		0			0
$916$	−1.35532e11			−0.192513
$917$	−7.58101e10	−	9.49339e11i	−0.107214	−	1.34259i
$918$		0			0
$919$	−6.89228e11	−	1.19378e12i	−0.966276	−	1.67364i	−0.706148	−	0.708065i	$-0.749569\pi$
$919$	−6.89228e11	−	1.19378e12i	−0.966276	−	1.67364i	−0.260128	−	0.965574i	$-0.583765\pi$
$920$	2.53299e11	+	1.46243e11i	0.353576	+	0.204137i
$921$		0			0
$922$	2.93091e11	+	5.07649e11i	0.405582	+	0.702489i
$923$		−	8.04417e11i		−	1.10834i
$924$		0			0
$925$	1.14134e12			1.55901
$926$	−1.00369e11	+	5.79480e10i	−0.136507	+	0.0788123i
$927$		0			0
$928$	1.10489e11	−	1.91372e11i	0.148979	−	0.258039i
$929$	1.12124e12	−	6.47346e11i	1.50534	−	0.869107i	0.505357	−	0.862910i	$-0.331361\pi$
$929$	1.12124e12	−	6.47346e11i	1.50534	−	0.869107i	0.999981	−	0.00619685i	$-0.00197253\pi$
$930$		0			0
$931$	3.70131e11	−	9.70873e11i	0.492670	−	1.29230i
$932$			5.48857e10i			0.0727437i
$933$		0			0
$934$	−1.40953e11	+	2.44138e11i	−0.185220	+	0.320810i
$935$	−1.28335e12	−	7.40945e11i	−1.67919	−	0.969481i
$936$		0			0
$937$	−1.42808e12			−1.85265			−0.926324	−	0.376729i	$-0.877049\pi$
$937$	−1.42808e12			−1.85265			−0.926324	+	0.376729i	$0.877049\pi$
$938$	−1.17510e11	−	5.58841e10i	−0.151797	−	0.0721899i
$939$		0			0
$940$	−1.99440e11	−	3.45440e11i	−0.255447	−	0.442447i
$941$	−1.03303e12	−	5.96420e11i	−1.31751	−	0.760665i	−0.334183	−	0.942508i	$-0.608460\pi$
$941$	−1.03303e12	−	5.96420e11i	−1.31751	−	0.760665i	−0.983328	+	0.181843i	$0.941794\pi$
$942$		0			0
$943$	3.74588e10	+	6.48806e10i	0.0473705	+	0.0820480i
$944$			1.31271e11i			0.165303i
$945$		0			0
$946$	−1.69471e11			−0.211608
$947$	7.96482e11	−	4.59849e11i	0.990322	−	0.571762i	0.0849512	−	0.996385i	$-0.472927\pi$
$947$	7.96482e11	−	4.59849e11i	0.990322	−	0.571762i	0.905370	+	0.424623i	$0.139593\pi$
$948$		0			0
$949$	−4.07933e11	+	7.06560e11i	−0.502949	+	0.871133i
$950$	9.96304e11	−	5.75216e11i	1.22320	−	0.706215i
$951$		0			0
$952$	2.98129e11	+	4.32717e11i	0.362958	+	0.526812i
$953$			1.36900e11i			0.165971i	0.996551	+	0.0829854i	$0.0264455\pi$
$953$			1.36900e11i			0.165971i	−0.996551	+	0.0829854i	$0.973554\pi$
$954$		0			0
$955$	1.95824e11	−	3.39177e11i	0.235425	−	0.407767i
$956$	1.64309e11	+	9.48638e10i	0.196711	+	0.113571i
$957$		0			0
$958$	−6.82211e11			−0.809947
$959$	5.87072e11	−	4.04476e11i	0.694092	−	0.478209i
$960$		0			0
$961$	−1.13286e12	−	1.96217e12i	−1.32826	−	2.30061i
$962$	5.62449e11	+	3.24730e11i	0.656724	+	0.379160i
$963$		0			0
$964$	−1.34800e11	−	2.33480e11i	−0.156092	−	0.270360i
$965$			2.04194e12i			2.35469i
$966$		0			0
$967$	1.55691e12			1.78057			0.890283	−	0.455408i	$-0.150507\pi$
$967$	1.55691e12			1.78057			0.890283	+	0.455408i	$0.150507\pi$
$968$	−1.42544e11	+	8.22977e10i	−0.162348	+	0.0937316i
$969$		0			0
$970$	−4.79011e11	+	8.29671e11i	−0.541076	+	0.937171i
$971$	−4.80792e11	+	2.77585e11i	−0.540854	+	0.312262i	−0.745425	−	0.666589i	$-0.767753\pi$
$971$	−4.80792e11	+	2.77585e11i	−0.540854	+	0.312262i	0.204571	+	0.978852i	$0.434420\pi$
$972$		0			0
$973$	−5.57247e11	+	1.17175e12i	−0.621722	+	1.30732i
$974$			1.39161e11i			0.154626i
$975$		0			0
$976$	1.60251e11	−	2.77563e11i	0.176604	−	0.305887i
$977$	−9.32931e10	−	5.38628e10i	−0.102393	−	0.0591168i	0.447929	−	0.894069i	$-0.352162\pi$
$977$	−9.32931e10	−	5.38628e10i	−0.102393	−	0.0591168i	−0.550322	+	0.834952i	$0.685495\pi$
$978$		0			0
$979$	9.87139e10			0.107460
$980$	5.59298e11	−	4.55039e11i	0.606372	−	0.493338i
$981$		0			0
$982$	4.34372e11	+	7.52355e11i	0.467107	+	0.809052i
$983$	−2.18396e11	−	1.26091e11i	−0.233900	−	0.135042i	0.378470	−	0.925614i	$-0.376450\pi$
$983$	−2.18396e11	−	1.26091e11i	−0.233900	−	0.135042i	−0.612370	+	0.790571i	$0.709784\pi$
$984$		0			0
$985$	−9.58163e11	−	1.65959e12i	−1.01787	−	1.76301i
$986$		−	2.03832e12i		−	2.15658i
$987$		0			0
$988$	6.54634e11			0.687022
$989$	2.67202e11	−	1.54269e11i	0.279289	−	0.161248i
$990$		0			0
$991$	−4.64000e11	+	8.03671e11i	−0.481086	+	0.833266i	−0.999764	−	0.0217035i	$-0.993091\pi$
$991$	−4.64000e11	+	8.03671e11i	−0.481086	+	0.833266i	0.518678	+	0.854970i	$0.326424\pi$
$992$	2.83489e11	−	1.63672e11i	0.292745	−	0.169016i
$993$		0			0
$994$	−7.67636e11	+	6.13001e10i	−0.786339	+	0.0627936i
$995$			4.37055e11i			0.445907i
$996$		0			0
$997$	−2.77895e11	+	4.81327e11i	−0.281254	+	0.487147i	−0.971694	−	0.236243i	$-0.924084\pi$
$997$	−2.77895e11	+	4.81327e11i	−0.281254	+	0.487147i	0.690440	+	0.723390i	$0.257417\pi$
$998$	4.93296e11	+	2.84805e11i	0.497262	+	0.287095i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.a.53.6	yes	20
3.2	odd	2	inner	126.9.s.a.53.5	✓	20
7.2	even	3	inner	126.9.s.a.107.5	yes	20
21.2	odd	6	inner	126.9.s.a.107.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.a.53.5	✓	20	3.2	odd	2	inner
126.9.s.a.53.6	yes	20	1.1	even	1	trivial
126.9.s.a.107.5	yes	20	7.2	even	3	inner
126.9.s.a.107.6	yes	20	21.2	odd	6	inner

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-846.225 + 488.568i) q^{5} +(1031.17 - 2168.29i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-846.225 + 488.568i) q^{5} +(1031.17 - 2168.29i) q^{7} -1448.15i q^{8} +(-5527.52 + 9573.94i) q^{10} +(-8690.52 - 5017.47i) q^{11} +28375.5 q^{13} +(-2162.33 - 27078.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(-130881. - 75564.1i) q^{17} +(90118.8 + 156090. i) q^{19} +125073. i q^{20} -113532. q^{22} +(179005. - 103348. i) q^{23} +(282085. - 488586. i) q^{25} +(278022. - 160516. i) q^{26} +(-174363. - 253077. i) q^{28} +1.19213e6i q^{29} +(-882979. + 1.52936e6i) q^{31} +(-160530. - 92681.9i) q^{32} -1.70982e6 q^{34} +(186755. + 2.33866e6i) q^{35} +(1.01152e6 + 1.75200e6i) q^{37} +(1.76596e6 + 1.01958e6i) q^{38} +(707522. + 1.22546e6i) q^{40} +362452. i q^{41} +1.49271e6 q^{43} +(-1.11239e6 + 642237. i) q^{44} +(1.16925e6 - 2.02521e6i) q^{46} +(-2.76190e6 + 1.59458e6i) q^{47} +(-3.63817e6 - 4.47176e6i) q^{49} -6.38286e6i q^{50} +(1.81603e6 - 3.14546e6i) q^{52} +(1.01242e7 + 5.84519e6i) q^{53} +9.80551e6 q^{55} +(-3.14002e6 - 1.49330e6i) q^{56} +(6.74368e6 + 1.16804e7i) q^{58} +(-6.93873e6 - 4.00608e6i) q^{59} +(9.78093e6 + 1.69411e7i) q^{61} +1.99795e7i q^{62} -2.09715e6 q^{64} +(-2.40120e7 + 1.38633e7i) q^{65} +(2.39509e6 - 4.14842e6i) q^{67} +(-1.67528e7 + 9.67221e6i) q^{68} +(1.50593e7 + 2.18576e7i) q^{70} -2.83490e7i q^{71} +(-1.43763e7 + 2.49004e7i) q^{73} +(1.98217e7 + 1.14440e7i) q^{74} +2.30704e7 q^{76} +(-1.98408e7 + 1.36697e7i) q^{77} +(-6.04403e6 - 1.04686e7i) q^{79} +(1.38646e7 + 8.00470e6i) q^{80} +(2.05034e6 + 3.55129e6i) q^{82} +5.87181e7i q^{83} +1.47673e8 q^{85} +(1.46255e7 - 8.44405e6i) q^{86} +(-7.26608e6 + 1.25852e7i) q^{88} +(-8.51910e6 + 4.91851e6i) q^{89} +(2.92600e7 - 6.15263e7i) q^{91} -2.64572e7i q^{92} +(-1.80406e7 + 3.12473e7i) q^{94} +(-1.52522e8 - 8.80584e7i) q^{95} +8.66592e7 q^{97} +(-6.09428e7 - 2.32335e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 - 3710 * q^7	\( 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

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