LMFDB - Embedded newform 126.9.s.b.107.4

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} + 3140415 x^{18} - 28263450 x^{17} + 4166681580501 x^{16} - 33332812007100 x^{15} + \cdots + 75\!\cdots\!79 $ x^20 - 10x^19 + 3140415x^18 - 28263450x^17 + 4166681580501x^16 - 33332812007100x^15 + 3031999370323294994x^14 - 21223412270295167948x^13 + 1313283359586691659338157x^12 - 7879424254677270736897262x^11 + 343395008585647382793738362717x^10 - 1716902815378389725958443657694x^9 + 52358316972954959192126259265947855x^8 - 209422966561600366110762067553592180x^7 + 4229075043327500600602686549793780016622x^6 - 12686492156810441352359584184417459023348x^5 + 144254968239046675448003125054039788454888507x^4 - 288488792568822027386658361381507315488125730x^3 + 639027248533334160181502914078717624884446094987x^2 - 638883006251430205323520488726745011115535930034*x + 758989993652521448576631480355366113559097835556179
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{18}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.4
Root			$0.500000 + 325.242i$ of defining polynomial
Character	$\chi$	$=$	126.107
Dual form			126.9.s.b.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(282.418 + 163.054i) q^{5} +(-233.264 + 2389.64i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(282.418 + 163.054i) q^{5} +(-233.264 + 2389.64i) q^{7} -1448.15i q^{8} +(-1844.75 - 3195.20i) q^{10} +(-2675.11 + 1544.47i) q^{11} +53526.0 q^{13} +(15803.4 - 22094.1i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-7638.40 + 4410.03i) q^{17} +(-72729.7 + 125971. i) q^{19} +41741.9i q^{20} +34947.5 q^{22} +(390530. + 225472. i) q^{23} +(-142139. - 246192. i) q^{25} +(-524445. - 302789. i) q^{26} +(-279824. + 127080. i) q^{28} -1.00072e6i q^{29} +(-157103. - 272110. i) q^{31} +(160530. - 92681.9i) q^{32} +99787.6 q^{34} +(-455519. + 636844. i) q^{35} +(-1.87184e6 + 3.24211e6i) q^{37} +(1.42520e6 - 822842. i) q^{38} +(236128. - 408985. i) q^{40} -3.68191e6i q^{41} +150657. q^{43} +(-342414. - 197693. i) q^{44} +(-2.55093e6 - 4.41834e6i) q^{46} +(3.15179e6 + 1.81969e6i) q^{47} +(-5.65598e6 - 1.11483e6i) q^{49} +3.21624e6i q^{50} +(3.42566e6 + 5.93342e6i) q^{52} +(-7.75222e6 + 4.47575e6i) q^{53} -1.00733e6 q^{55} +(3.46057e6 + 337802. i) q^{56} +(-5.66095e6 + 9.80506e6i) q^{58} +(1.46455e7 - 8.45557e6i) q^{59} +(-9.60884e6 + 1.66430e7i) q^{61} +3.55482e6i q^{62} -2.09715e6 q^{64} +(1.51167e7 + 8.72764e6i) q^{65} +(1.36410e7 + 2.36269e7i) q^{67} +(-977715. - 564484. i) q^{68} +(8.06569e6 - 3.66296e6i) q^{70} +1.55777e7i q^{71} +(6.16601e6 + 1.06798e7i) q^{73} +(3.66803e7 - 2.11774e7i) q^{74} -1.86188e7 q^{76} +(-3.06674e6 - 6.75282e6i) q^{77} +(-1.93325e6 + 3.34848e6i) q^{79} +(-4.62714e6 + 2.67148e6i) q^{80} +(-2.08280e7 + 3.60752e7i) q^{82} +8.85749e7i q^{83} -2.87630e6 q^{85} +(-1.47613e6 - 852242. i) q^{86} +(2.23664e6 + 3.87397e6i) q^{88} +(8.05742e7 + 4.65195e7i) q^{89} +(-1.24857e7 + 1.27908e8i) q^{91} +5.77209e7i q^{92} +(-2.05874e7 - 3.56584e7i) q^{94} +(-4.10804e7 + 2.37178e7i) q^{95} -9.41324e7 q^{97} +(4.91106e7 + 4.29181e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} + 3778 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 + 3778 * q^7	$ 20 q + 1280 q^{4} + 3778 q^{7} + 14816 q^{10} + 17700 q^{13} - 163840 q^{16} - 267794 q^{19} + 453568 q^{22} - 765890 q^{25} - 232448 q^{28} - 2604342 q^{31} + 4087936 q^{34} + 1127530 q^{37} - 1896448 q^{40} - 4460924 q^{43} - 180416 q^{46} - 25278034 q^{49} + 1132800 q^{52} - 18833120 q^{55} + 5146496 q^{58} - 25730232 q^{61} - 41943040 q^{64} + 58134374 q^{67} - 76724864 q^{70} + 5811002 q^{73} - 68555264 q^{76} + 74799798 q^{79} - 9883296 q^{82} + 119739328 q^{85} + 29028352 q^{88} - 479039766 q^{91} + 169364448 q^{94} - 658133608 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 + 3778 * q^7 + 14816 * q^10 + 17700 * q^13 - 163840 * q^16 - 267794 * q^19 + 453568 * q^22 - 765890 * q^25 - 232448 * q^28 - 2604342 * q^31 + 4087936 * q^34 + 1127530 * q^37 - 1896448 * q^40 - 4460924 * q^43 - 180416 * q^46 - 25278034 * q^49 + 1132800 * q^52 - 18833120 * q^55 + 5146496 * q^58 - 25730232 * q^61 - 41943040 * q^64 + 58134374 * q^67 - 76724864 * q^70 + 5811002 * q^73 - 68555264 * q^76 + 74799798 * q^79 - 9883296 * q^82 + 119739328 * q^85 + 29028352 * q^88 - 479039766 * q^91 + 169364448 * q^94 - 658133608 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−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
$5$	282.418	+	163.054i	0.451869	+	0.260887i	0.708619	−	0.705591i	$-0.249318\pi$
$5$	282.418	+	163.054i	0.451869	+	0.260887i	−0.256750	+	0.966478i	$0.582652\pi$
$6$		0			0
$7$	−233.264	+	2389.64i	−0.0971527	+	0.995269i
$7$	−233.264	+	2389.64i	−0.0971527	+	0.995269i
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	−1844.75	−	3195.20i	−0.184475	−	0.319520i
$11$	−2675.11	+	1544.47i	−0.182714	+	0.105490i	−0.588567	−	0.808448i	$-0.700308\pi$
$11$	−2675.11	+	1544.47i	−0.182714	+	0.105490i	0.405853	+	0.913938i	$0.366974\pi$
$12$		0			0
$13$	53526.0			1.87409			0.937047	−	0.349204i	$-0.113548\pi$
$13$	53526.0			1.87409			0.937047	+	0.349204i	$0.113548\pi$
$14$	15803.4	−	22094.1i	0.411375	−	0.575127i
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	−7638.40	+	4410.03i	−0.0914548	+	0.0528015i	−0.545030	−	0.838417i	$-0.683482\pi$
$17$	−7638.40	+	4410.03i	−0.0914548	+	0.0528015i	0.453575	+	0.891218i	$0.350148\pi$
$18$		0			0
$19$	−72729.7	+	125971.i	−0.558081	+	0.966625i	0.439576	+	0.898206i	$0.355129\pi$
$19$	−72729.7	+	125971.i	−0.558081	+	0.966625i	−0.997657	+	0.0684190i	$0.978205\pi$
$20$			41741.9i			0.260887i
$21$		0			0
$22$	34947.5			0.149185
$23$	390530.	+	225472.i	1.39554	+	0.805716i	0.993922	−	0.110090i	$-0.0351140\pi$
$23$	390530.	+	225472.i	1.39554	+	0.805716i	0.401620	+	0.915806i	$0.368447\pi$
$24$		0			0
$25$	−142139.	−	246192.i	−0.363876	−	0.630252i
$26$	−524445.	−	302789.i	−1.14764	−	0.662592i
$27$		0			0
$28$	−279824.	+	127080.i	−0.455253	+	0.206749i
$29$		−	1.00072e6i		−	1.41489i	−0.706769	−	0.707445i	$-0.749848\pi$
$29$		−	1.00072e6i		−	1.41489i	0.706769	−	0.707445i	$-0.250152\pi$
$30$		0			0
$31$	−157103.	−	272110.i	−0.170113	−	0.294644i	0.768346	−	0.640034i	$-0.221080\pi$
$31$	−157103.	−	272110.i	−0.170113	−	0.294644i	−0.938459	+	0.345390i	$0.887746\pi$
$32$	160530.	−	92681.9i	0.153093	−	0.0883883i
$33$		0			0
$34$	99787.6			0.0746725
$35$	−455519.	+	636844.i	−0.303553	+	0.424386i
$36$		0			0
$37$	−1.87184e6	+	3.24211e6i	−0.998759	+	1.72990i	−0.456251	+	0.889851i	$0.650808\pi$
$37$	−1.87184e6	+	3.24211e6i	−0.998759	+	1.72990i	−0.542508	+	0.840051i	$0.682525\pi$
$38$	1.42520e6	−	822842.i	0.683507	−	0.394623i
$39$		0			0
$40$	236128.	−	408985.i	0.0922374	−	0.159760i
$41$		−	3.68191e6i		−	1.30298i	−0.758657	−	0.651490i	$-0.774144\pi$
$41$		−	3.68191e6i		−	1.30298i	0.758657	−	0.651490i	$-0.225856\pi$
$42$		0			0
$43$	150657.			0.0440671			0.0220335	−	0.999757i	$-0.492986\pi$
$43$	150657.			0.0440671			0.0220335	+	0.999757i	$0.492986\pi$
$44$	−342414.	−	197693.i	−0.0913568	−	0.0527448i
$45$		0			0
$46$	−2.55093e6	−	4.41834e6i	−0.569727	−	0.986797i
$47$	3.15179e6	+	1.81969e6i	0.645900	+	0.372911i	0.786884	−	0.617101i	$-0.211693\pi$
$47$	3.15179e6	+	1.81969e6i	0.645900	+	0.372911i	−0.140984	+	0.990012i	$0.545026\pi$
$48$		0			0
$49$	−5.65598e6	−	1.11483e6i	−0.981123	−	0.193386i
$50$			3.21624e6i			0.514599i
$51$		0			0
$52$	3.42566e6	+	5.93342e6i	0.468523	+	0.811506i
$53$	−7.75222e6	+	4.47575e6i	−0.982478	+	0.567234i	−0.903017	−	0.429604i	$-0.858653\pi$
$53$	−7.75222e6	+	4.47575e6i	−0.982478	+	0.567234i	−0.0794604	+	0.996838i	$0.525320\pi$
$54$		0			0
$55$	−1.00733e6			−0.110083
$56$	3.46057e6	+	337802.i	0.351881	+	0.0343487i
$57$		0			0
$58$	−5.66095e6	+	9.80506e6i	−0.500239	+	0.866439i
$59$	1.46455e7	−	8.45557e6i	1.20864	−	0.697806i	0.246175	−	0.969225i	$-0.420826\pi$
$59$	1.46455e7	−	8.45557e6i	1.20864	−	0.697806i	0.962461	+	0.271419i	$0.0874929\pi$
$60$		0			0
$61$	−9.60884e6	+	1.66430e7i	−0.693987	+	1.20202i	0.276534	+	0.961004i	$0.410814\pi$
$61$	−9.60884e6	+	1.66430e7i	−0.693987	+	1.20202i	−0.970521	+	0.241017i	$0.922519\pi$
$62$			3.55482e6i			0.240576i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	1.51167e7	+	8.72764e6i	0.846845	+	0.488926i
$66$		0			0
$67$	1.36410e7	+	2.36269e7i	0.676935	+	1.17249i	0.975899	+	0.218221i	$0.0700253\pi$
$67$	1.36410e7	+	2.36269e7i	0.676935	+	1.17249i	−0.298965	+	0.954264i	$0.596641\pi$
$68$	−977715.	−	564484.i	−0.0457274	−	0.0264007i
$69$		0			0
$70$	8.06569e6	−	3.66296e6i	0.335930	−	0.152560i
$71$			1.55777e7i			0.613014i	0.951868	+	0.306507i	$0.0991603\pi$
$71$			1.55777e7i			0.613014i	−0.951868	+	0.306507i	$0.900840\pi$
$72$		0			0
$73$	6.16601e6	+	1.06798e7i	0.217127	+	0.376074i	0.953928	−	0.300035i	$-0.0969982\pi$
$73$	6.16601e6	+	1.06798e7i	0.217127	+	0.376074i	−0.736802	+	0.676109i	$0.763665\pi$
$74$	3.66803e7	−	2.11774e7i	1.22323	−	0.706229i
$75$		0			0
$76$	−1.86188e7			−0.558081
$77$	−3.06674e6	−	6.75282e6i	−0.0872396	−	0.192098i
$78$		0			0
$79$	−1.93325e6	+	3.34848e6i	−0.0496339	+	0.0859685i	−0.889775	−	0.456400i	$-0.849139\pi$
$79$	−1.93325e6	+	3.34848e6i	−0.0496339	+	0.0859685i	0.840141	+	0.542368i	$0.182472\pi$
$80$	−4.62714e6	+	2.67148e6i	−0.112967	+	0.0652217i
$81$		0			0
$82$	−2.08280e7	+	3.60752e7i	−0.460673	+	0.797909i
$83$			8.85749e7i			1.86637i	0.359392	+	0.933187i	$0.382984\pi$
$83$			8.85749e7i			1.86637i	−0.359392	+	0.933187i	$0.617016\pi$
$84$		0			0
$85$	−2.87630e6			−0.0551008
$86$	−1.47613e6	−	852242.i	−0.0269855	−	0.0155801i
$87$		0			0
$88$	2.23664e6	+	3.87397e6i	0.0372962	+	0.0645990i
$89$	8.05742e7	+	4.65195e7i	1.28421	+	0.741439i	0.977615	−	0.210401i	$-0.0674771\pi$
$89$	8.05742e7	+	4.65195e7i	1.28421	+	0.741439i	0.306595	+	0.951840i	$0.400810\pi$
$90$		0			0
$91$	−1.24857e7	+	1.27908e8i	−0.182073	+	1.86523i
$92$			5.77209e7i			0.805716i
$93$		0			0
$94$	−2.05874e7	−	3.56584e7i	−0.263688	−	0.456720i
$95$	−4.10804e7	+	2.37178e7i	−0.504359	+	0.291192i
$96$		0			0
$97$	−9.41324e7			−1.06329			−0.531646	−	0.846967i	$-0.678426\pi$
$97$	−9.41324e7			−1.06329			−0.531646	+	0.846967i	$0.678426\pi$
$98$	4.91106e7	+	4.29181e7i	0.532440	+	0.465304i
$99$		0			0
$100$	1.81938e7	−	3.15126e7i	0.181938	−	0.315126i
$101$	3.62646e7	−	2.09374e7i	0.348496	−	0.201204i	−0.315527	−	0.948917i	$-0.602181\pi$
$101$	3.62646e7	−	2.09374e7i	0.348496	−	0.201204i	0.664023	+	0.747712i	$0.268848\pi$
$102$		0			0
$103$	8.40806e6	−	1.45632e7i	0.0747046	−	0.129392i	−0.826253	−	0.563299i	$-0.809532\pi$
$103$	8.40806e6	−	1.45632e7i	0.0747046	−	0.129392i	0.900958	+	0.433907i	$0.142865\pi$
$104$		−	7.75139e7i		−	0.662592i
$105$		0			0
$106$	1.01275e8			0.802190
$107$	−7.66010e7	−	4.42256e7i	−0.584385	−	0.337395i	0.178489	−	0.983942i	$-0.442879\pi$
$107$	−7.66010e7	−	4.42256e7i	−0.584385	−	0.337395i	−0.762874	+	0.646547i	$0.776212\pi$
$108$		0			0
$109$	5.81764e7	+	1.00764e8i	0.412136	+	0.713841i	0.995123	−	0.0986407i	$-0.0314494\pi$
$109$	5.81764e7	+	1.00764e8i	0.412136	+	0.713841i	−0.582987	+	0.812482i	$0.698116\pi$
$110$	9.86980e6	+	5.69833e6i	0.0674121	+	0.0389204i
$111$		0			0
$112$	−3.19956e7	−	2.28857e7i	−0.203338	−	0.145443i
$113$			1.21361e8i			0.744327i	0.928167	+	0.372164i	$0.121384\pi$
$113$			1.21361e8i			0.744327i	−0.928167	+	0.372164i	$0.878616\pi$
$114$		0			0
$115$	7.35285e7	+	1.27355e8i	0.420401	+	0.728157i
$116$	1.10932e8	−	6.40464e7i	0.612665	−	0.353722i
$117$		0			0
$118$	−1.91328e8			−0.986847
$119$	−8.75663e6	−	1.92817e7i	−0.0436666	−	0.0961520i
$120$		0			0
$121$	−1.02409e8	+	1.77377e8i	−0.477744	+	0.827477i
$122$	1.88294e8	−	1.08712e8i	0.849957	−	0.490723i
$123$		0			0
$124$	2.01091e7	−	3.48300e7i	0.0850563	−	0.147322i
$125$		−	2.20092e8i		−	0.901495i
$126$		0			0
$127$	1.17965e7			0.0453459			0.0226730	−	0.999743i	$-0.492782\pi$
$127$	1.17965e7			0.0453459			0.0226730	+	0.999743i	$0.492782\pi$
$128$	2.05478e7	+	1.18633e7i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−9.87420e7	−	1.71026e8i	−0.345723	−	0.598810i
$131$	−1.31326e8	−	7.58212e7i	−0.445930	−	0.257458i	0.260180	−	0.965560i	$-0.416218\pi$
$131$	−1.31326e8	−	7.58212e7i	−0.445930	−	0.257458i	−0.706110	+	0.708103i	$0.749551\pi$
$132$		0			0
$133$	−2.84062e8	−	2.03182e8i	−0.907833	−	0.649351i
$134$		−	3.08660e8i		−	0.957330i
$135$		0			0
$136$	6.38641e6	+	1.10616e7i	0.0186681	+	0.0323342i
$137$	−2.55842e8	+	1.47710e8i	−0.726255	+	0.419303i	−0.817050	−	0.576566i	$-0.804392\pi$
$137$	−2.55842e8	+	1.47710e8i	−0.726255	+	0.419303i	0.0907959	+	0.995870i	$0.471059\pi$
$138$		0			0
$139$	5.15687e8			1.38142			0.690712	−	0.723130i	$-0.257297\pi$
$139$	5.15687e8			1.38142			0.690712	+	0.723130i	$0.257297\pi$
$140$	−9.97482e7	−	9.73686e6i	−0.259653	−	0.0253459i
$141$		0			0
$142$	8.81208e7	−	1.52630e8i	0.216733	−	0.375393i
$143$	−1.43188e8	+	8.26695e7i	−0.342422	+	0.197698i
$144$		0			0
$145$	1.63172e8	−	2.82623e8i	0.369126	−	0.639345i
$146$		−	1.39521e8i		−	0.307063i
$147$		0			0
$148$	−4.79190e8			−0.998759
$149$	−5.11062e8	−	2.95062e8i	−1.03688	−	0.598643i	−0.117932	−	0.993022i	$-0.537627\pi$
$149$	−5.11062e8	−	2.95062e8i	−1.03688	−	0.598643i	−0.918948	+	0.394378i	$0.870960\pi$
$150$		0			0
$151$	−2.77344e8	−	4.80374e8i	−0.533471	−	0.924000i	−0.999236	−	0.0390908i	$-0.987554\pi$
$151$	−2.77344e8	−	4.80374e8i	−0.533471	−	0.924000i	0.465764	−	0.884909i	$-0.345779\pi$
$152$	1.82426e8	+	1.05324e8i	0.341753	+	0.197311i
$153$		0			0
$154$	−8.15197e6	+	8.35119e7i	−0.0144937	+	0.148479i
$155$		−	1.02465e8i		−	0.177520i
$156$		0			0
$157$	1.28899e8	+	2.23260e8i	0.212154	+	0.367462i	0.952389	−	0.304887i	$-0.0986187\pi$
$157$	1.28899e8	+	2.23260e8i	0.212154	+	0.367462i	−0.740234	+	0.672349i	$0.765285\pi$
$158$	3.78837e7	−	2.18722e7i	0.0607889	−	0.0350965i
$159$		0			0
$160$	6.04487e7			0.0922374
$161$	−6.29895e8	+	8.80632e8i	−0.937485	+	1.31066i
$162$		0			0
$163$	2.35858e8	−	4.08518e8i	0.334118	−	0.578709i	−0.649197	−	0.760620i	$-0.724895\pi$
$163$	2.35858e8	−	4.08518e8i	0.334118	−	0.578709i	0.983315	+	0.181911i	$0.0582283\pi$
$164$	4.08144e8	−	2.35642e8i	0.564207	−	0.325745i
$165$		0			0
$166$	5.01055e8	−	8.67854e8i	0.659863	−	1.14292i
$167$		−	1.71470e8i		−	0.220456i	−0.993906	−	0.110228i	$-0.964842\pi$
$167$		−	1.71470e8i		−	0.220456i	0.993906	−	0.110228i	$-0.0351581\pi$
$168$		0			0
$169$	2.04930e9			2.51223
$170$	2.81818e7	+	1.62708e7i	0.0337422	+	0.0194811i
$171$		0			0
$172$	9.64202e6	+	1.67005e7i	0.0110168	+	0.0190816i
$173$	−4.39586e8	−	2.53795e8i	−0.490749	−	0.283334i	0.234136	−	0.972204i	$-0.424774\pi$
$173$	−4.39586e8	−	2.53795e8i	−0.490749	−	0.283334i	−0.724885	+	0.688870i	$0.758107\pi$
$174$		0			0
$175$	6.21467e8	−	2.82234e8i	0.662622	−	0.300924i
$176$		−	5.06093e7i		−	0.0527448i
$177$		0			0
$178$	−5.26308e8	−	9.11593e8i	−0.524276	−	0.908073i
$179$	−1.02924e9	+	5.94233e8i	−1.00255	+	0.578822i	−0.909001	−	0.416793i	$-0.863154\pi$
$179$	−1.02924e9	+	5.94233e8i	−1.00255	+	0.578822i	−0.0935470	+	0.995615i	$0.529821\pi$
$180$		0			0
$181$	−1.60266e9			−1.49324			−0.746618	−	0.665253i	$-0.768324\pi$
$181$	−1.60266e9			−1.49324			−0.746618	+	0.665253i	$0.768324\pi$
$182$	8.45891e8	−	1.18261e9i	0.770954	−	1.07784i
$183$		0			0
$184$	3.26519e8	−	5.65547e8i	0.284864	−	0.493398i
$185$	−1.05728e9	+	6.10421e8i	−0.902617	+	0.521126i
$186$		0			0
$187$	1.36224e7	−	2.35946e7i	0.0111400	−	0.0192951i
$188$			4.65839e8i			0.372911i
$189$		0			0
$190$	5.36672e8			0.411807
$191$	−1.13158e9	−	6.53320e8i	−0.850262	−	0.490899i	0.0104769	−	0.999945i	$-0.496665\pi$
$191$	−1.13158e9	−	6.53320e8i	−0.850262	−	0.490899i	−0.860739	+	0.509046i	$0.829998\pi$
$192$		0			0
$193$	6.51135e8	+	1.12780e9i	0.469290	+	0.812835i	0.999384	−	0.0351047i	$-0.0111765\pi$
$193$	6.51135e8	+	1.12780e9i	0.469290	+	0.812835i	−0.530093	+	0.847939i	$0.677843\pi$
$194$	9.22305e8	+	5.32493e8i	0.651130	+	0.375930i
$195$		0			0
$196$	−2.38402e8	−	6.98321e8i	−0.161542	−	0.473185i
$197$			6.81884e8i			0.452737i	0.974042	+	0.226368i	$0.0726853\pi$
$197$			6.81884e8i			0.452737i	−0.974042	+	0.226368i	$0.927315\pi$
$198$		0			0
$199$	4.99514e8	+	8.65183e8i	0.318519	+	0.551691i	0.980179	−	0.198113i	$-0.0634813\pi$
$199$	4.99514e8	+	8.65183e8i	0.318519	+	0.551691i	−0.661660	+	0.749804i	$0.730148\pi$
$200$	−3.56524e8	+	2.05839e8i	−0.222828	+	0.128650i
$201$		0			0
$202$	−4.73759e8			−0.284546
$203$	2.39137e9	+	2.33433e8i	1.40820	+	0.137460i
$204$		0			0
$205$	6.00351e8	−	1.03984e9i	0.339930	−	0.588776i
$206$	−1.64764e8	+	9.51264e7i	−0.0914940	+	0.0528241i
$207$		0			0
$208$	−4.38485e8	+	7.59478e8i	−0.234262	+	0.405753i
$209$		−	4.49317e8i		−	0.235487i
$210$		0			0
$211$	−1.50350e9			−0.758530			−0.379265	−	0.925288i	$-0.623823\pi$
$211$	−1.50350e9			−0.758530			−0.379265	+	0.925288i	$0.623823\pi$
$212$	−9.92284e8	−	5.72896e8i	−0.491239	−	0.283617i
$213$		0			0
$214$	5.00356e8	+	8.66641e8i	0.238574	+	0.413223i
$215$	4.25481e7	+	2.45652e7i	0.0199125	+	0.0114965i
$216$		0			0
$217$	6.86891e8	−	3.11946e8i	0.309777	−	0.140682i
$218$		−	1.31638e9i		−	0.582849i
$219$		0			0
$220$	−6.44693e7	−	1.11664e8i	−0.0275209	−	0.0476675i
$221$	−4.08853e8	+	2.36051e8i	−0.171395	+	0.0989549i
$222$		0			0
$223$	1.72122e9			0.696011			0.348006	−	0.937492i	$-0.386859\pi$
$223$	1.72122e9			0.696011			0.348006	+	0.937492i	$0.386859\pi$
$224$	1.84031e8	+	4.05228e8i	0.0730968	+	0.160956i
$225$		0			0
$226$	6.86519e8	−	1.18909e9i	0.263159	−	0.455806i
$227$	−1.37033e9	+	7.91158e8i	−0.516084	+	0.297961i	−0.735331	−	0.677708i	$-0.762973\pi$
$227$	−1.37033e9	+	7.91158e8i	−0.516084	+	0.297961i	0.219247	+	0.975669i	$0.429640\pi$
$228$		0			0
$229$	−8.01260e8	+	1.38782e9i	−0.291361	+	0.504652i	−0.974132	−	0.225981i	$-0.927441\pi$
$229$	−8.01260e8	+	1.38782e9i	−0.291361	+	0.504652i	0.682771	+	0.730633i	$0.260775\pi$
$230$		−	1.66376e9i		−	0.594537i
$231$		0			0
$232$	−1.44920e9			−0.500239
$233$	3.32653e9	+	1.92058e9i	1.12867	+	0.651640i	0.943601	−	0.331085i	$-0.107415\pi$
$233$	3.32653e9	+	1.92058e9i	1.12867	+	0.651640i	0.185072	+	0.982725i	$0.440748\pi$
$234$		0			0
$235$	5.93415e8	+	1.02782e9i	0.194575	+	0.337014i
$236$	1.87462e9	+	1.08231e9i	0.604318	+	0.348903i
$237$		0			0
$238$	−2.32768e7	+	2.38457e8i	−0.00725464	+	0.0743193i
$239$			6.99315e8i			0.214329i	0.994241	+	0.107165i	$0.0341772\pi$
$239$			6.99315e8i			0.214329i	−0.994241	+	0.107165i	$0.965823\pi$
$240$		0			0
$241$	1.46670e7	+	2.54041e7i	0.00434785	+	0.00753070i	0.868191	−	0.496230i	$-0.165283\pi$
$241$	1.46670e7	+	2.54041e7i	0.00434785	+	0.00753070i	−0.863843	+	0.503761i	$0.831949\pi$
$242$	2.00679e9	−	1.15862e9i	0.585114	−	0.337816i
$243$		0			0
$244$	−2.45986e9			−0.693987
$245$	−1.41557e9	−	1.23708e9i	−0.392887	−	0.343347i
$246$		0			0
$247$	−3.89293e9	+	6.74275e9i	−1.04590	+	1.81155i
$248$	−3.94057e8	+	2.27509e8i	−0.104172	+	0.0601439i
$249$		0			0
$250$	−1.24503e9	+	2.15645e9i	−0.318727	+	0.552051i
$251$		−	3.39157e9i		−	0.854487i	−0.904137	−	0.427244i	$-0.859485\pi$
$251$		−	3.39157e9i		−	0.854487i	0.904137	−	0.427244i	$-0.140515\pi$
$252$		0			0
$253$	−1.39295e9			−0.339979
$254$	−1.15582e8	−	6.67311e7i	−0.0277686	−	0.0160322i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	2.19315e9	+	1.26622e9i	0.502731	+	0.290252i	0.729841	−	0.683617i	$-0.239594\pi$
$257$	2.19315e9	+	1.26622e9i	0.502731	+	0.290252i	−0.227110	+	0.973869i	$0.572928\pi$
$258$		0			0
$259$	−7.31086e9	−	5.22928e9i	−1.62469	−	1.16210i
$260$			2.23428e9i			0.488926i
$261$		0			0
$262$	8.57819e8	+	1.48579e9i	0.182050	+	0.315320i
$263$	−2.07156e9	+	1.19602e9i	−0.432987	+	0.249985i	−0.700618	−	0.713536i	$-0.747092\pi$
$263$	−2.07156e9	+	1.19602e9i	−0.432987	+	0.249985i	0.267632	+	0.963521i	$0.413759\pi$
$264$		0			0
$265$	−2.91916e9			−0.591935
$266$	1.63385e9	+	3.59767e9i	0.326352	+	0.718612i
$267$		0			0
$268$	−1.74605e9	+	3.02424e9i	−0.338467	+	0.586243i
$269$	4.48320e9	−	2.58838e9i	0.856207	−	0.494332i	−0.00653298	−	0.999979i	$-0.502080\pi$
$269$	4.48320e9	−	2.58838e9i	0.856207	−	0.494332i	0.862740	+	0.505647i	$0.168746\pi$
$270$		0			0
$271$	−1.94252e8	+	3.36455e8i	−0.0360155	+	0.0623806i	−0.883471	−	0.468485i	$-0.844800\pi$
$271$	−1.94252e8	+	3.36455e8i	−0.0360155	+	0.0623806i	0.847456	+	0.530866i	$0.178133\pi$
$272$		−	1.44508e8i		−	0.0264007i
$273$		0			0
$274$	3.34230e9			0.592984
$275$	7.60475e8	+	4.39061e8i	0.132970	+	0.0767704i
$276$		0			0
$277$	3.29627e9	+	5.70930e9i	0.559891	+	0.969759i	0.997505	+	0.0705965i	$0.0224903\pi$
$277$	3.29627e9	+	5.70930e9i	0.559891	+	0.969759i	−0.437614	+	0.899163i	$0.644176\pi$
$278$	−5.05268e9	−	2.91717e9i	−0.845946	−	0.488407i
$279$		0			0
$280$	9.22248e8	+	6.59662e8i	0.150043	+	0.107322i
$281$		−	4.99991e9i		−	0.801932i	−0.916093	−	0.400966i	$-0.868675\pi$
$281$		−	4.99991e9i		−	0.801932i	0.916093	−	0.400966i	$-0.131325\pi$
$282$		0			0
$283$	−1.84119e8	−	3.18903e8i	−0.0287046	−	0.0497179i	0.851316	−	0.524653i	$-0.175805\pi$
$283$	−1.84119e8	−	3.18903e8i	−0.0287046	−	0.0497179i	−0.880021	+	0.474935i	$0.842472\pi$
$284$	−1.72681e9	+	9.96974e8i	−0.265443	+	0.153253i
$285$		0			0
$286$	1.87060e9			0.279587
$287$	8.79845e9	+	8.58856e8i	1.29682	+	0.126588i
$288$		0			0
$289$	−3.44898e9	+	5.97381e9i	−0.494424	+	0.856368i
$290$	−3.19751e9	+	1.84608e9i	−0.452085	+	0.261011i
$291$		0			0
$292$	−7.89250e8	+	1.36702e9i	−0.108563	+	0.188037i
$293$		−	1.12225e10i		−	1.52271i	−0.648333	−	0.761357i	$-0.724534\pi$
$293$		−	1.12225e10i		−	1.52271i	0.648333	−	0.761357i	$-0.275466\pi$
$294$		0			0
$295$	5.51487e9			0.728194
$296$	4.69508e9	+	2.71071e9i	0.611613	+	0.353115i
$297$		0			0
$298$	3.33824e9	+	5.78201e9i	0.423305	+	0.733185i
$299$	2.09035e10	+	1.20686e10i	2.61538	+	1.50999i
$300$		0			0
$301$	−3.51427e7	+	3.60015e8i	−0.00428123	+	0.0438586i
$302$			6.27558e9i			0.754443i
$303$		0			0
$304$	−1.19160e9	−	2.06392e9i	−0.139520	−	0.241656i
$305$	−5.42742e9	+	3.13352e9i	−0.627183	+	0.362104i
$306$		0			0
$307$	2.12838e9			0.239605			0.119802	−	0.992798i	$-0.461774\pi$
$307$	2.12838e9			0.239605			0.119802	+	0.992798i	$0.461774\pi$
$308$	5.52288e8	−	7.72132e8i	0.0613709	−	0.0858003i
$309$		0			0
$310$	−5.79629e8	+	1.00395e9i	−0.0627630	+	0.108709i
$311$	−1.22047e10	+	7.04639e9i	−1.30462	+	0.753226i	−0.981194	−	0.193026i	$-0.938170\pi$
$311$	−1.22047e10	+	7.04639e9i	−1.30462	+	0.753226i	−0.323431	+	0.946252i	$0.604836\pi$
$312$		0			0
$313$	1.16191e9	−	2.01249e9i	0.121059	−	0.209680i	−0.799127	−	0.601163i	$-0.794704\pi$
$313$	1.16191e9	−	2.01249e9i	0.121059	−	0.209680i	0.920185	+	0.391483i	$0.128038\pi$
$314$		−	2.91666e9i		−	0.300032i
$315$		0			0
$316$	−4.94911e8			−0.0496339
$317$	−1.87159e9	−	1.08056e9i	−0.185342	−	0.107007i	0.404458	−	0.914556i	$-0.367460\pi$
$317$	−1.87159e9	−	1.08056e9i	−0.185342	−	0.107007i	−0.589800	+	0.807549i	$0.700793\pi$
$318$		0			0
$319$	1.54559e9	+	2.67705e9i	0.149256	+	0.258519i
$320$	−5.92274e8	−	3.41949e8i	−0.0564836	−	0.0326108i
$321$		0			0
$322$	1.11533e10	−	5.06517e9i	1.03748	−	0.471162i
$323$		−	1.28296e9i		−	0.117870i
$324$		0			0
$325$	−7.60814e9	−	1.31777e10i	−0.681938	−	1.18115i
$326$	−4.62185e9	+	2.66843e9i	−0.409209	+	0.236257i
$327$		0			0
$328$	−5.33198e9			−0.460673
$329$	−5.08359e9	+	7.10718e9i	−0.433898	+	0.606615i
$330$		0			0
$331$	8.95434e9	−	1.55094e10i	0.745970	−	1.29206i	−0.203770	−	0.979019i	$-0.565319\pi$
$331$	8.95434e9	−	1.55094e10i	0.745970	−	1.29206i	0.949740	−	0.313040i	$-0.101347\pi$
$332$	−9.81864e9	+	5.66880e9i	−0.808163	+	0.466593i
$333$		0			0
$334$	−9.69980e8	+	1.68005e9i	−0.0779429	+	0.135001i
$335$			8.89688e9i			0.706413i
$336$		0			0
$337$	2.08695e9			0.161805			0.0809026	−	0.996722i	$-0.474220\pi$
$337$	2.08695e9			0.161805			0.0809026	+	0.996722i	$0.474220\pi$
$338$	−2.00790e10	−	1.15926e10i	−1.53842	−	0.888206i
$339$		0			0
$340$	−1.84083e8	−	3.18841e8i	−0.0137752	−	0.0238593i
$341$	8.40533e8	+	4.85282e8i	0.0621637	+	0.0358902i
$342$		0			0
$343$	3.98339e9	−	1.32557e10i	0.287790	−	0.957693i
$344$		−	2.18174e8i		−	0.0155801i
$345$		0			0
$346$	2.87137e9	+	4.97335e9i	0.200348	+	0.347012i
$347$	2.31196e10	−	1.33481e10i	1.59464	−	0.920663i	0.602139	−	0.798391i	$-0.294315\pi$
$347$	2.31196e10	−	1.33481e10i	1.59464	−	0.920663i	0.992497	−	0.122272i	$-0.0390181\pi$
$348$		0			0
$349$	−1.02360e10			−0.689967			−0.344984	−	0.938609i	$-0.612116\pi$
$349$	−1.02360e10			−0.689967			−0.344984	+	0.938609i	$0.612116\pi$
$350$	−7.68567e9	−	7.50232e8i	−0.512164	−	0.0499947i
$351$		0			0
$352$	−2.86290e8	+	4.95868e8i	−0.0186481	+	0.0322995i
$353$	1.08786e10	−	6.28075e9i	0.700605	−	0.404494i	−0.106968	−	0.994262i	$-0.534114\pi$
$353$	1.08786e10	−	6.28075e9i	0.700605	−	0.404494i	0.807573	+	0.589768i	$0.200781\pi$
$354$		0			0
$355$	−2.54001e9	+	4.39943e9i	−0.159927	+	0.277002i
$356$			1.19090e10i			0.741439i
$357$		0			0
$358$	1.34460e10			0.818577
$359$	−1.71752e10	−	9.91610e9i	−1.03401	−	0.596985i	−0.115878	−	0.993263i	$-0.536968\pi$
$359$	−1.71752e10	−	9.91610e9i	−1.03401	−	0.596985i	−0.918130	+	0.396279i	$0.870301\pi$
$360$		0			0
$361$	−2.08743e9	−	3.61553e9i	−0.122909	−	0.212884i
$362$	1.57028e10	+	9.06604e9i	0.914417	+	0.527939i
$363$		0			0
$364$	−1.49778e10	+	6.80206e9i	−0.853186	+	0.387467i
$365$			4.02158e9i			0.226582i
$366$		0			0
$367$	−1.13832e10	−	1.97162e10i	−0.627478	−	1.08682i	−0.988056	−	0.154094i	$-0.950754\pi$
$367$	−1.13832e10	−	1.97162e10i	−0.627478	−	1.08682i	0.360579	−	0.932729i	$-0.382579\pi$
$368$	−6.39844e9	+	3.69414e9i	−0.348885	+	0.201429i
$369$		0			0
$370$	1.38123e10			0.736984
$371$	−8.88712e9	−	1.95691e10i	−0.469100	−	1.03294i
$372$		0			0
$373$	1.40763e10	−	2.43808e10i	0.727198	−	1.25954i	−0.230864	−	0.972986i	$-0.574155\pi$
$373$	1.40763e10	−	2.43808e10i	0.727198	−	1.25954i	0.958063	−	0.286558i	$-0.0925113\pi$
$374$	−2.66943e8	+	1.54119e8i	−0.0136437	+	0.00787718i
$375$		0			0
$376$	2.63519e9	−	4.56428e9i	0.131844	−	0.228360i
$377$		−	5.35648e10i		−	2.65164i
$378$		0			0
$379$	2.76040e10			1.33788			0.668938	−	0.743318i	$-0.266749\pi$
$379$	2.76040e10			1.33788			0.668938	+	0.743318i	$0.266749\pi$
$380$	−5.25829e9	−	3.03587e9i	−0.252180	−	0.145596i
$381$		0			0
$382$	7.39147e9	+	1.28024e10i	0.347118	+	0.601226i
$383$	−6.72869e9	−	3.88481e9i	−0.312705	−	0.180540i	0.335431	−	0.942065i	$-0.391118\pi$
$383$	−6.72869e9	−	3.88481e9i	−0.312705	−	0.180540i	−0.648136	+	0.761524i	$0.724451\pi$
$384$		0			0
$385$	2.34974e8	−	2.40716e9i	0.0106949	−	0.109563i
$386$		−	1.47335e10i		−	0.663677i
$387$		0			0
$388$	−6.02447e9	−	1.04347e10i	−0.265823	−	0.460419i
$389$	−2.72144e10	+	1.57122e10i	−1.18850	+	0.686182i	−0.957966	−	0.286881i	$-0.907381\pi$
$389$	−2.72144e10	+	1.57122e10i	−1.18850	+	0.686182i	−0.230537	+	0.973064i	$0.574048\pi$
$390$		0			0
$391$	−3.97736e9			−0.170172
$392$	−1.61445e9	+	8.19073e9i	−0.0683724	+	0.346879i
$393$		0			0
$394$	3.85732e9	−	6.68108e9i	0.160067	−	0.277244i
$395$	−1.09197e9	+	6.30448e8i	−0.0448561	+	0.0258977i
$396$		0			0
$397$	−8.91087e9	+	1.54341e10i	−0.358722	+	0.621325i	−0.987748	−	0.156060i	$-0.950121\pi$
$397$	−8.91087e9	+	1.54341e10i	−0.358722	+	0.621325i	0.629026	+	0.777385i	$0.283454\pi$
$398$		−	1.13027e10i		−	0.450454i
$399$		0			0
$400$	4.65762e9			0.181938
$401$	−6.44409e9	−	3.72049e9i	−0.249221	−	0.143888i	0.370187	−	0.928957i	$-0.379294\pi$
$401$	−6.44409e9	−	3.72049e9i	−0.249221	−	0.143888i	−0.619407	+	0.785070i	$0.712627\pi$
$402$		0			0
$403$	−8.40907e9	−	1.45649e10i	−0.318807	−	0.552190i
$404$	4.64187e9	+	2.67999e9i	0.174248	+	0.100602i
$405$		0			0
$406$	−2.21101e10	−	1.58148e10i	−0.813741	−	0.582050i
$407$		−	1.15640e10i		−	0.421435i
$408$		0			0
$409$	−7.83007e8	−	1.35621e9i	−0.0279816	−	0.0484655i	0.851696	−	0.524037i	$-0.175575\pi$
$409$	−7.83007e8	−	1.35621e9i	−0.0279816	−	0.0484655i	−0.879677	+	0.475571i	$0.842241\pi$
$410$	−1.17644e10	+	6.79220e9i	−0.416328	+	0.240367i
$411$		0			0
$412$	2.15246e9			0.0747046
$413$	1.67895e10	+	3.69698e10i	0.577083	+	1.27071i
$414$		0			0
$415$	−1.44425e10	+	2.50152e10i	−0.486912	+	0.843356i
$416$	8.59251e9	−	4.96089e9i	0.286911	−	0.165648i
$417$		0			0
$418$	−2.54172e9	+	4.40238e9i	−0.0832573	+	0.144206i
$419$		−	2.00419e9i		−	0.0650255i	−0.999471	−	0.0325127i	$-0.989649\pi$
$419$		−	2.00419e9i		−	0.0650255i	0.999471	−	0.0325127i	$-0.0103509\pi$
$420$		0			0
$421$	3.04780e10			0.970193			0.485097	−	0.874461i	$-0.338784\pi$
$421$	3.04780e10			0.970193			0.485097	+	0.874461i	$0.338784\pi$
$422$	1.47312e10	+	8.50507e9i	0.464503	+	0.268181i
$423$		0			0
$424$	6.48157e9	+	1.12264e10i	0.200547	+	0.347358i
$425$	2.17143e9	+	1.25368e9i	0.0665565	+	0.0384264i
$426$		0			0
$427$	−3.75294e10	−	2.68439e10i	−1.12891	−	0.807484i
$428$		−	1.13218e10i		−	0.337395i
$429$		0			0
$430$	−2.77923e8	−	4.81377e8i	−0.00812926	−	0.0140803i
$431$	5.20244e10	−	3.00363e10i	1.50764	−	0.870437i	0.507681	−	0.861545i	$-0.330503\pi$
$431$	5.20244e10	−	3.00363e10i	1.50764	−	0.870437i	0.999960	−	0.00889211i	$-0.00283048\pi$
$432$		0			0
$433$	−9.25510e9			−0.263287			−0.131643	−	0.991297i	$-0.542025\pi$
$433$	−9.25510e9			−0.263287			−0.131643	+	0.991297i	$0.542025\pi$
$434$	−8.49476e9	−	8.29211e8i	−0.239437	−	0.0233726i
$435$		0			0
$436$	−7.44658e9	+	1.28979e10i	−0.206068	+	0.356920i
$437$	−5.68062e10	+	3.27971e10i	−1.55765	+	0.899310i
$438$		0			0
$439$	1.06988e10	−	1.85308e10i	0.288055	−	0.498926i	−0.685290	−	0.728270i	$-0.740325\pi$
$439$	1.06988e10	−	1.85308e10i	0.288055	−	0.498926i	0.973345	+	0.229344i	$0.0736580\pi$
$440$			1.45877e9i			0.0389204i
$441$		0			0
$442$	5.34123e9			0.139943
$443$	8.54052e9	+	4.93087e9i	0.221753	+	0.128029i	0.606762	−	0.794884i	$-0.292468\pi$
$443$	8.54052e9	+	4.93087e9i	0.221753	+	0.128029i	−0.385009	+	0.922913i	$0.625802\pi$
$444$		0			0
$445$	1.51704e10	+	2.62759e10i	0.386863	+	0.670067i
$446$	−1.68644e10	−	9.73667e9i	−0.426218	−	0.246077i
$447$		0			0
$448$	4.89189e8	−	5.01144e9i	0.0121441	−	0.124409i
$449$		−	4.45967e10i		−	1.09728i	−0.836059	−	0.548640i	$-0.815146\pi$
$449$		−	4.45967e10i		−	1.09728i	0.836059	−	0.548640i	$-0.184854\pi$
$450$		0			0
$451$	5.68662e9	+	9.84951e9i	0.137451	+	0.238072i
$452$	−1.34530e10	+	7.76708e9i	−0.322303	+	0.186082i
$453$		0			0
$454$	1.79019e10			0.421381
$455$	−2.43821e10	+	3.40877e10i	−0.568887	+	0.795339i
$456$		0			0
$457$	9.54870e9	−	1.65388e10i	0.218917	−	0.379175i	−0.735560	−	0.677459i	$-0.763081\pi$
$457$	9.54870e9	−	1.65388e10i	0.218917	−	0.379175i	0.954477	+	0.298284i	$0.0964143\pi$
$458$	1.57014e10	−	9.06522e9i	0.356843	−	0.206023i
$459$		0			0
$460$	−9.41164e9	+	1.63014e10i	−0.210201	+	0.364078i
$461$			4.82880e10i			1.06914i	0.845123	+	0.534571i	$0.179527\pi$
$461$			4.82880e10i			1.06914i	−0.845123	+	0.534571i	$0.820473\pi$
$462$		0			0
$463$	4.42971e10			0.963943			0.481972	−	0.876187i	$-0.339921\pi$
$463$	4.42971e10			0.963943			0.481972	+	0.876187i	$0.339921\pi$
$464$	1.41992e10	+	8.19793e9i	0.306333	+	0.176861i
$465$		0			0
$466$	−2.17288e10	−	3.76354e10i	−0.460779	−	0.798093i
$467$	7.07423e10	+	4.08431e10i	1.48735	+	0.858719i	0.999896	−	0.0144318i	$-0.00459395\pi$
$467$	7.07423e10	+	4.08431e10i	1.48735	+	0.858719i	0.487450	+	0.873151i	$0.337927\pi$
$468$		0			0
$469$	−5.96418e10	+	2.70858e10i	−1.23270	+	0.559822i
$470$		−	1.34274e10i		−	0.275170i
$471$		0			0
$472$	−1.22450e10	−	2.12089e10i	−0.246712	−	0.427317i
$473$	−4.03022e8	+	2.32685e8i	−0.00805165	+	0.00464862i
$474$		0			0
$475$	4.13509e10			0.812290
$476$	1.57698e9	−	2.20471e9i	0.0307184	−	0.0429462i
$477$		0			0
$478$	3.95592e9	−	6.85186e9i	0.0757768	−	0.131249i
$479$	3.75504e10	−	2.16797e10i	0.713301	−	0.411824i	−0.0989812	−	0.995089i	$-0.531558\pi$
$479$	3.75504e10	−	2.16797e10i	0.713301	−	0.411824i	0.812282	+	0.583265i	$0.198225\pi$
$480$		0			0
$481$	−1.00192e11	+	1.73537e11i	−1.87177	+	3.24200i
$482$		−	3.31877e8i		−	0.00614879i
$483$		0			0
$484$	−2.62166e10			−0.477744
$485$	−2.65847e10	−	1.53487e10i	−0.480468	−	0.277399i
$486$		0			0
$487$	3.60605e10	+	6.24587e10i	0.641086	+	1.11039i	0.985191	+	0.171462i	$0.0548491\pi$
$487$	3.60605e10	+	6.24587e10i	0.641086	+	1.11039i	−0.344105	+	0.938931i	$0.611818\pi$
$488$	2.41016e10	+	1.39151e10i	0.424979	+	0.245362i
$489$		0			0
$490$	6.87174e9	+	2.01285e10i	0.119202	+	0.349163i
$491$			7.69409e10i			1.32383i	0.749580	+	0.661914i	$0.230255\pi$
$491$			7.69409e10i			1.32383i	−0.749580	+	0.661914i	$0.769745\pi$
$492$		0			0
$493$	4.41323e9	+	7.64393e9i	0.0747082	+	0.129398i
$494$	7.62855e10	−	4.40434e10i	1.28096	−	0.739560i
$495$		0			0
$496$	5.14794e9			0.0850563
$497$	−3.72252e10	−	3.63371e9i	−0.610114	−	0.0595560i
$498$		0			0
$499$	4.87595e10	−	8.44539e10i	0.786424	−	1.36213i	−0.141720	−	0.989907i	$-0.545263\pi$
$499$	4.87595e10	−	8.44539e10i	0.786424	−	1.36213i	0.928144	−	0.372220i	$-0.121403\pi$
$500$	2.43974e10	−	1.40859e10i	0.390359	−	0.225374i
$501$		0			0
$502$	−1.91856e10	+	3.32304e10i	−0.302107	+	0.523264i
$503$			1.19600e11i			1.86835i	0.356809	+	0.934177i	$0.383865\pi$
$503$			1.19600e11i			1.86835i	−0.356809	+	0.934177i	$0.616135\pi$
$504$		0			0
$505$	1.36557e10			0.209966
$506$	1.36480e10	+	7.87969e9i	0.208194	+	0.120201i
$507$		0			0
$508$	7.54976e8	+	1.30766e9i	0.0113365	+	0.0196354i
$509$	2.29880e9	+	1.32721e9i	0.0342476	+	0.0197728i	0.517026	−	0.855970i	$-0.327039\pi$
$509$	2.29880e9	+	1.32721e9i	0.0342476	+	0.0197728i	−0.482778	+	0.875743i	$0.660372\pi$
$510$		0			0
$511$	−2.69593e10	+	1.22433e10i	−0.395390	+	0.179563i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	−1.43256e10	−	2.48127e10i	−0.205239	−	0.355485i
$515$	4.74918e9	−	2.74194e9i	0.0675134	−	0.0389789i
$516$		0			0
$517$	−1.12418e10			−0.157353
$518$	4.20502e10	+	9.25928e10i	0.584049	+	1.28605i
$519$		0			0
$520$	1.26390e10	−	2.18913e10i	0.172862	−	0.299405i
$521$	−9.41519e10	+	5.43586e10i	−1.27784	+	0.737764i	−0.976452	−	0.215736i	$-0.930785\pi$
$521$	−9.41519e10	+	5.43586e10i	−1.27784	+	0.737764i	−0.301393	+	0.953500i	$0.597452\pi$
$522$		0			0
$523$	−5.53560e10	+	9.58794e10i	−0.739874	+	1.28150i	0.212677	+	0.977122i	$0.431782\pi$
$523$	−5.53560e10	+	9.58794e10i	−0.739874	+	1.28150i	−0.952552	+	0.304377i	$0.901552\pi$
$524$		−	1.94102e10i		−	0.257458i
$525$		0			0
$526$	2.70627e10			0.353532
$527$	2.40002e9	+	1.38565e9i	0.0311152	+	0.0179644i
$528$		0			0
$529$	6.25201e10	+	1.08288e11i	0.798357	+	1.38280i
$530$	2.86018e10	+	1.65133e10i	0.362485	+	0.209281i
$531$		0			0
$532$	4.34309e9	−	4.44923e10i	0.0542191	−	0.555441i
$533$		−	1.97078e11i		−	2.44191i
$534$		0			0
$535$	−1.44223e10	−	2.49802e10i	−0.176044	−	0.304917i
$536$	3.42154e10	−	1.97543e10i	0.414536	−	0.239333i
$537$		0			0
$538$	−5.85683e10			−0.699090
$539$	1.68522e10	−	5.75321e9i	0.199665	−	0.0681641i
$540$		0			0
$541$	1.28580e10	−	2.22706e10i	0.150101	−	0.259982i	−0.781164	−	0.624326i	$-0.785374\pi$
$541$	1.28580e10	−	2.22706e10i	0.150101	−	0.259982i	0.931264	+	0.364344i	$0.118707\pi$
$542$	3.80655e9	−	2.19771e9i	0.0441097	−	0.0254668i
$543$		0			0
$544$	−8.17460e8	+	1.41588e9i	−0.00933407	+	0.0161671i
$545$			3.79436e10i			0.430084i
$546$		0			0
$547$	8.93704e9			0.0998262			0.0499131	−	0.998754i	$-0.484106\pi$
$547$	8.93704e9			0.0998262			0.0499131	+	0.998754i	$0.484106\pi$
$548$	−3.27477e10	−	1.89069e10i	−0.363127	−	0.209652i
$549$		0			0
$550$	−4.96740e9	−	8.60380e9i	−0.0542849	−	0.0940241i
$551$	1.26063e11	+	7.27824e10i	1.36767	+	0.789623i
$552$		0			0
$553$	−7.55071e9	−	5.40084e9i	−0.0807397	−	0.0577512i
$554$		−	7.45860e10i		−	0.791805i
$555$		0			0
$556$	3.30040e10	+	5.71645e10i	0.345356	+	0.598174i
$557$	6.39247e10	−	3.69070e10i	0.664122	−	0.383431i	−0.129724	−	0.991550i	$-0.541409\pi$
$557$	6.39247e10	−	3.69070e10i	0.664122	−	0.383431i	0.793846	+	0.608119i	$0.208076\pi$
$558$		0			0
$559$	8.06404e9			0.0825858
$560$	−5.30454e9	−	1.16804e10i	−0.0539381	−	0.118769i
$561$		0			0
$562$	−2.82838e10	+	4.89890e10i	−0.283526	+	0.491081i
$563$	−1.24641e11	+	7.19613e10i	−1.24058	+	0.716251i	−0.969213	−	0.246224i	$-0.920810\pi$
$563$	−1.24641e11	+	7.19613e10i	−1.24058	+	0.716251i	−0.271370	+	0.962475i	$0.587477\pi$
$564$		0			0
$565$	−1.97884e10	+	3.42744e10i	−0.194185	+	0.336339i
$566$			4.16613e9i			0.0405945i
$567$		0			0
$568$	2.25589e10			0.216733
$569$	2.37871e10	+	1.37335e10i	0.226931	+	0.131018i	0.609155	−	0.793051i	$-0.291509\pi$
$569$	2.37871e10	+	1.37335e10i	0.226931	+	0.131018i	−0.382225	+	0.924069i	$0.624842\pi$
$570$		0			0
$571$	−3.50462e10	−	6.07018e10i	−0.329683	−	0.571028i	0.652766	−	0.757560i	$-0.273609\pi$
$571$	−3.50462e10	−	6.07018e10i	−0.329683	−	0.571028i	−0.982449	+	0.186532i	$0.940275\pi$
$572$	−1.83280e10	−	1.05817e10i	−0.171211	−	0.0988488i
$573$		0			0
$574$	−8.13484e10	−	5.81866e10i	−0.749379	−	0.536013i
$575$		−	1.28194e11i		−	1.17272i
$576$		0			0
$577$	−5.31290e10	−	9.20220e10i	−0.479323	−	0.830211i	0.520396	−	0.853925i	$-0.325784\pi$
$577$	−5.31290e10	−	9.20220e10i	−0.479323	−	0.830211i	−0.999719	+	0.0237137i	$0.992451\pi$
$578$	6.75860e10	−	3.90208e10i	0.605543	−	0.349611i
$579$		0			0
$580$	4.17721e10			0.369126
$581$	−2.11662e11	−	2.06613e10i	−1.85754	−	0.181323i
$582$		0			0
$583$	1.38254e10	−	2.39462e10i	0.119675	−	0.207283i
$584$	1.54661e10	−	8.92934e9i	0.132962	−	0.0767658i
$585$		0			0
$586$	−6.34839e10	+	1.09957e11i	−0.538360	+	0.932468i
$587$		−	1.40193e11i		−	1.18079i	−0.807114	−	0.590395i	$-0.798972\pi$
$587$		−	1.40193e11i		−	1.18079i	0.807114	−	0.590395i	$-0.201028\pi$
$588$		0			0
$589$	4.57041e10			0.379746
$590$	−5.40344e10	−	3.11968e10i	−0.445926	−	0.257455i
$591$		0			0
$592$	−3.06682e10	−	5.31188e10i	−0.249690	−	0.432475i
$593$	−1.02809e11	−	5.93569e10i	−0.831406	−	0.480012i	0.0229280	−	0.999737i	$-0.492701\pi$
$593$	−1.02809e11	−	5.93569e10i	−0.831406	−	0.480012i	−0.854334	+	0.519725i	$0.826034\pi$
$594$		0			0
$595$	6.70935e8	−	6.87332e9i	0.00535319	−	0.0548402i
$596$		−	7.55359e10i		−	0.598643i
$597$		0			0
$598$	−1.36541e11	−	2.36496e11i	−1.06772	−	1.84935i
$599$	−9.09320e10	+	5.24996e10i	−0.706333	+	0.407801i	−0.809702	−	0.586842i	$-0.800371\pi$
$599$	−9.09320e10	+	5.24996e10i	−0.706333	+	0.407801i	0.103369	+	0.994643i	$0.467038\pi$
$600$		0			0
$601$	1.45558e11			1.11567			0.557837	−	0.829951i	$-0.311632\pi$
$601$	1.45558e11			1.11567			0.557837	+	0.829951i	$0.311632\pi$
$602$	2.38088e9	−	3.32862e9i	0.0181281	−	0.0253442i
$603$		0			0
$604$	3.55000e10	−	6.14879e10i	0.266736	−	0.462000i
$605$	−5.78441e10	+	3.33963e10i	−0.431755	+	0.249274i
$606$		0			0
$607$	−6.43385e9	+	1.11438e10i	−0.0473932	+	0.0820874i	−0.888749	−	0.458394i	$-0.848425\pi$
$607$	−6.43385e9	+	1.11438e10i	−0.0473932	+	0.0820874i	0.841356	+	0.540482i	$0.181758\pi$
$608$			2.69629e10i			0.197311i
$609$		0			0
$610$	7.09035e10			0.512093
$611$	1.68703e11	+	9.74004e10i	1.21048	+	0.698870i
$612$		0			0
$613$	−4.81878e10	−	8.34638e10i	−0.341268	−	0.591093i	0.643401	−	0.765530i	$-0.277523\pi$
$613$	−4.81878e10	−	8.34638e10i	−0.341268	−	0.591093i	−0.984668	+	0.174436i	$0.944190\pi$
$614$	−2.08538e10	−	1.20399e10i	−0.146727	−	0.0847131i
$615$		0			0
$616$	−9.77913e9	+	4.44111e9i	−0.0679168	+	0.0308438i
$617$			1.76578e10i			0.121842i	0.998143	+	0.0609208i	$0.0194037\pi$
$617$			1.76578e10i			0.121842i	−0.998143	+	0.0609208i	$0.980596\pi$
$618$		0			0
$619$	−7.35111e10	−	1.27325e11i	−0.500715	−	0.867263i	−1.00000		0.000825367i	$-0.999737\pi$
$619$	−7.35111e10	−	1.27325e11i	−0.500715	−	0.867263i	0.499285	−	0.866438i	$-0.333596\pi$
$620$	1.13584e10	−	6.55776e9i	0.0768686	−	0.0443801i
$621$		0			0
$622$	1.59442e11			1.06522
$623$	−1.29960e11	+	1.81692e11i	−0.862696	+	1.20610i
$624$		0			0
$625$	−1.96362e10	+	3.40109e10i	−0.128688	+	0.222894i
$626$	−2.27687e10	+	1.31455e10i	−0.148266	+	0.0856014i
$627$		0			0
$628$	−1.64991e10	+	2.85773e10i	−0.106077	+	0.183731i
$629$		−	3.30194e10i		−	0.210944i
$630$		0			0
$631$	2.07592e11			1.30947			0.654733	−	0.755861i	$-0.272781\pi$
$631$	2.07592e11			1.30947			0.654733	+	0.755861i	$0.272781\pi$
$632$	4.84912e9	+	2.79964e9i	0.0303944	+	0.0175482i
$633$		0			0
$634$	1.22252e10	+	2.11746e10i	0.0756655	+	0.131056i
$635$	3.33154e9	+	1.92347e9i	0.0204904	+	0.0118301i
$636$		0			0
$637$	−3.02742e11	−	5.96726e10i	−1.83872	−	0.362424i
$638$		−	3.49728e10i		−	0.211080i
$639$		0			0
$640$	3.86872e9	+	6.70081e9i	0.0230593	+	0.0399400i
$641$	2.55827e11	−	1.47702e11i	1.51535	−	0.874890i	0.515517	−	0.856879i	$-0.327600\pi$
$641$	2.55827e11	−	1.47702e11i	1.51535	−	0.874890i	0.999838	−	0.0180109i	$-0.00573335\pi$
$642$		0			0
$643$	2.64367e11			1.54655			0.773273	−	0.634074i	$-0.218618\pi$
$643$	2.64367e11			1.54655			0.773273	+	0.634074i	$0.218618\pi$
$644$	−1.37932e11	−	1.34642e10i	−0.801905	−	0.0782775i
$645$		0			0
$646$	−7.25752e9	+	1.25704e10i	−0.0416733	+	0.0721803i
$647$	1.17368e11	−	6.77622e10i	0.669779	−	0.386697i	−0.126214	−	0.992003i	$-0.540283\pi$
$647$	1.17368e11	−	6.77622e10i	0.669779	−	0.386697i	0.795993	+	0.605306i	$0.206949\pi$
$648$		0			0
$649$	−2.61188e10	+	4.52391e10i	−0.147223	+	0.254997i
$650$			1.72153e11i			0.964406i
$651$		0			0
$652$	6.03796e10			0.334118
$653$	−2.63359e11	−	1.52051e11i	−1.44843	−	0.836249i	−0.450038	−	0.893009i	$-0.648590\pi$
$653$	−2.63359e11	−	1.52051e11i	−1.44843	−	0.836249i	−0.998388	+	0.0567605i	$0.981923\pi$
$654$		0			0
$655$	−2.47259e10	−	4.28266e10i	−0.134335	−	0.232674i
$656$	5.22425e10	+	3.01622e10i	0.282103	+	0.162872i
$657$		0			0
$658$	9.00131e10	−	4.08787e10i	0.480178	−	0.218069i
$659$			1.23424e11i			0.654424i	0.944951	+	0.327212i	$0.106109\pi$
$659$			1.23424e11i			0.654424i	−0.944951	+	0.327212i	$0.893891\pi$
$660$		0			0
$661$	7.24338e10	+	1.25459e11i	0.379433	+	0.657198i	0.990980	−	0.134011i	$-0.0427856\pi$
$661$	7.24338e10	+	1.25459e11i	0.379433	+	0.657198i	−0.611547	+	0.791208i	$0.709452\pi$
$662$	−1.75469e11	+	1.01307e11i	−0.913623	+	0.527481i
$663$		0			0
$664$	1.28270e11			0.659863
$665$	−4.70944e10	−	1.03700e11i	−0.240815	−	0.530263i
$666$		0			0
$667$	2.25636e11	−	3.90813e11i	1.14000	−	1.97454i
$668$	1.90076e10	−	1.09741e10i	0.0954602	−	0.0551140i
$669$		0			0
$670$	5.03284e10	−	8.71713e10i	0.249755	−	0.432588i
$671$		−	5.93624e10i		−	0.292834i
$672$		0			0
$673$	3.63874e11			1.77374			0.886871	−	0.462016i	$-0.152874\pi$
$673$	3.63874e11			1.77374			0.886871	+	0.462016i	$0.152874\pi$
$674$	−2.04479e10	−	1.18056e10i	−0.0990850	−	0.0572068i
$675$		0			0
$676$	1.31155e11	+	2.27168e11i	0.628057	+	1.08783i
$677$	−3.56360e10	−	2.05745e10i	−0.169643	−	0.0979432i	0.412775	−	0.910833i	$-0.364560\pi$
$677$	−3.56360e10	−	2.05745e10i	−0.169643	−	0.0979432i	−0.582417	+	0.812890i	$0.697893\pi$
$678$		0			0
$679$	2.19577e10	−	2.24943e11i	0.103302	−	1.05826i
$680$			4.16532e9i			0.0194811i
$681$		0			0
$682$	−5.49034e9	−	9.50954e9i	−0.0253782	−	0.0439564i
$683$	2.83671e11	−	1.63778e11i	1.30356	−	0.752613i	0.322550	−	0.946552i	$-0.395460\pi$
$683$	2.83671e11	−	1.63778e11i	1.30356	−	0.752613i	0.981013	+	0.193940i	$0.0621266\pi$
$684$		0			0
$685$	−9.63391e10			−0.437563
$686$	−1.14015e11	+	1.07345e11i	−0.514831	+	0.484716i
$687$		0			0
$688$	−1.23418e9	+	2.13766e9i	−0.00550838	+	0.00954080i
$689$	−4.14945e11	+	2.39569e11i	−1.84126	+	1.06305i
$690$		0			0
$691$	−1.95023e11	+	3.37790e11i	−0.855409	+	1.48161i	0.0208558	+	0.999782i	$0.493361\pi$
$691$	−1.95023e11	+	3.37790e11i	−0.855409	+	1.48161i	−0.876265	+	0.481830i	$0.839972\pi$
$692$		−	6.49716e10i		−	0.283334i
$693$		0			0
$694$	−3.02033e11			−1.30201
$695$	1.45639e11	+	8.40849e10i	0.624223	+	0.360395i
$696$		0			0
$697$	1.62373e10	+	2.81239e10i	0.0687992	+	0.119164i
$698$	1.00292e11	+	5.79035e10i	0.422517	+	0.243940i
$699$		0			0
$700$	7.10599e10	+	5.08274e10i	0.295960	+	0.211693i
$701$		−	8.35975e10i		−	0.346195i	−0.984905	−	0.173098i	$-0.944622\pi$
$701$		−	8.35975e10i		−	0.346195i	0.984905	−	0.173098i	$-0.0553776\pi$
$702$		0			0
$703$	−2.72276e11	−	4.71596e11i	−1.11478	−	1.93085i
$704$	5.61011e9	−	3.23900e9i	0.0228392	−	0.0131862i
$705$		0			0
$706$	−1.42117e11			−0.572041
$707$	4.15737e10	+	9.15434e10i	0.166395	+	0.366395i
$708$		0			0
$709$	−1.35952e11	+	2.35475e11i	−0.538021	+	0.931880i	0.460989	+	0.887406i	$0.347495\pi$
$709$	−1.35952e11	+	2.35475e11i	−0.538021	+	0.931880i	−0.999011	+	0.0444743i	$0.985839\pi$
$710$	4.97739e10	−	2.87370e10i	0.195870	−	0.113086i
$711$		0			0
$712$	6.73675e10	−	1.16684e11i	0.262138	−	0.454037i
$713$		−	1.41689e11i		−	0.548250i
$714$		0			0
$715$	−5.39185e10			−0.206307
$716$	−1.31743e11	−	7.60618e10i	−0.501274	−	0.289411i
$717$		0			0
$718$	1.12188e11	+	1.94315e11i	0.422132	+	0.731154i
$719$	4.32125e11	+	2.49488e11i	1.61694	+	0.933541i	0.987705	+	0.156326i	$0.0499651\pi$
$719$	4.32125e11	+	2.49488e11i	1.61694	+	0.933541i	0.629235	+	0.777215i	$0.283368\pi$
$720$		0			0
$721$	3.28395e10	+	2.34893e10i	0.121522	+	0.0869219i
$722$			4.72331e10i			0.173819i
$723$		0			0
$724$	−1.02571e11	−	1.77657e11i	−0.373309	−	0.646590i
$725$	−2.46371e11	+	1.42242e11i	−0.891737	+	0.514845i
$726$		0			0
$727$	−1.02834e11			−0.368128			−0.184064	−	0.982914i	$-0.558925\pi$
$727$	−1.02834e11			−0.368128			−0.184064	+	0.982914i	$0.558925\pi$
$728$	1.85231e11	+	1.80812e10i	0.659458	+	0.0643726i
$729$		0			0
$730$	2.27495e10	−	3.94033e10i	0.0801088	−	0.138752i
$731$	−1.15077e9	+	6.64400e8i	−0.00403014	+	0.00232681i
$732$		0			0
$733$	−4.09050e10	+	7.08496e10i	−0.141697	+	0.245426i	−0.928136	−	0.372242i	$-0.878589\pi$
$733$	−4.09050e10	+	7.08496e10i	−0.141697	+	0.245426i	0.786439	+	0.617668i	$0.211923\pi$
$734$			2.57571e11i			0.887387i
$735$		0			0
$736$	8.35889e10			0.284864
$737$	−7.29823e10	−	4.21363e10i	−0.247370	−	0.142819i
$738$		0			0
$739$	2.66771e10	+	4.62061e10i	0.0894459	+	0.154925i	0.907277	−	0.420533i	$-0.138157\pi$
$739$	2.66771e10	+	4.62061e10i	0.0894459	+	0.154925i	−0.817831	+	0.575458i	$0.804824\pi$
$740$	−1.35332e11	−	7.81339e10i	−0.451308	−	0.260563i
$741$		0			0
$742$	−2.36237e10	+	2.42010e11i	−0.0779349	+	0.798395i
$743$		−	2.44470e10i		−	0.0802177i	−0.999195	−	0.0401089i	$-0.987230\pi$
$743$		−	2.44470e10i		−	0.0802177i	0.999195	−	0.0401089i	$-0.0127705\pi$
$744$		0			0
$745$	−9.62222e10	−	1.66662e11i	−0.312356	−	0.541017i
$746$	−2.75838e11	+	1.59255e11i	−0.890632	+	0.514207i
$747$		0			0
$748$	3.48732e9			0.0111400
$749$	1.23552e11	−	1.72733e11i	0.392574	−	0.548842i
$750$		0			0
$751$	2.68646e11	−	4.65308e11i	0.844541	−	1.46279i	−0.0414788	−	0.999139i	$-0.513207\pi$
$751$	2.68646e11	−	4.65308e11i	0.844541	−	1.46279i	0.886019	−	0.463648i	$-0.153460\pi$
$752$	−5.16389e10	+	2.98137e10i	−0.161475	+	0.0932277i
$753$		0			0
$754$	−3.03008e11	+	5.24825e11i	−0.937495	+	1.62379i
$755$		−	1.80889e11i		−	0.556703i
$756$		0			0
$757$	1.29854e11			0.395433			0.197717	−	0.980259i	$-0.436647\pi$
$757$	1.29854e11			0.395433			0.197717	+	0.980259i	$0.436647\pi$
$758$	−2.70463e11	−	1.56152e11i	−0.819278	−	0.473011i
$759$		0			0
$760$	3.43470e10	+	5.94907e10i	0.102952	+	0.178318i
$761$	1.40832e11	+	8.13094e10i	0.419916	+	0.242439i	0.695042	−	0.718970i	$-0.255386\pi$
$761$	1.40832e11	+	8.13094e10i	0.419916	+	0.242439i	−0.275125	+	0.961408i	$0.588719\pi$
$762$		0			0
$763$	−2.54361e11	+	1.15516e11i	−0.750504	+	0.340835i
$764$		−	1.67250e11i		−	0.490899i
$765$		0			0
$766$	4.39516e10	+	7.61264e10i	0.127661	+	0.221116i
$767$	7.83914e11	−	4.52593e11i	2.26510	−	1.30775i
$768$		0			0
$769$	−2.89162e11			−0.826867			−0.413434	−	0.910534i	$-0.635671\pi$
$769$	−2.89162e11			−0.826867			−0.413434	+	0.910534i	$0.635671\pi$
$770$	−1.59192e10	+	2.22561e10i	−0.0452855	+	0.0633120i
$771$		0			0
$772$	−8.33452e10	+	1.44358e11i	−0.234645	+	0.406417i
$773$	2.46579e11	−	1.42363e11i	0.690619	−	0.398729i	−0.113225	−	0.993569i	$-0.536118\pi$
$773$	2.46579e11	−	1.42363e11i	0.690619	−	0.398729i	0.803844	+	0.594840i	$0.202785\pi$
$774$		0			0
$775$	−4.46608e10	+	7.73548e10i	−0.123800	+	0.214428i
$776$			1.36318e11i			0.375930i
$777$		0			0
$778$	3.55527e11			0.970408
$779$	4.63816e11	+	2.67784e11i	1.25949	+	0.727168i
$780$		0			0
$781$	−2.40594e10	−	4.16721e10i	−0.0646666	−	0.112006i
$782$	3.89700e10	+	2.24994e10i	0.104209	+	0.0601649i
$783$		0			0
$784$	6.21521e10	−	7.11197e10i	0.164510	−	0.188246i
$785$			8.40704e10i			0.221393i
$786$		0			0
$787$	2.83161e11	+	4.90448e11i	0.738132	+	1.27848i	0.953336	+	0.301912i	$0.0976250\pi$
$787$	2.83161e11	+	4.90448e11i	0.738132	+	1.27848i	−0.215204	+	0.976569i	$0.569042\pi$
$788$	−7.55877e10	+	4.36406e10i	−0.196041	+	0.113184i
$789$		0			0
$790$	1.42654e10			0.0366248
$791$	−2.90008e11	−	2.83090e10i	−0.740806	−	0.0723134i
$792$		0			0
$793$	−5.14322e11	+	8.90833e11i	−1.30060	+	2.25270i
$794$	1.74617e11	−	1.00815e11i	0.439343	−	0.253655i
$795$		0			0
$796$	−6.39377e10	+	1.10743e11i	−0.159259	+	0.275845i
$797$			1.77659e11i			0.440305i	0.975465	+	0.220152i	$0.0706555\pi$
$797$			1.77659e11i			0.440305i	−0.975465	+	0.220152i	$0.929345\pi$
$798$		0			0
$799$	−3.20995e10			−0.0787609
$800$	−4.56351e10	−	2.63475e10i	−0.111414	−	0.0643248i
$801$		0			0
$802$	4.20926e10	+	7.29065e10i	0.101744	+	0.176226i
$803$	−3.29895e10	−	1.90465e10i	−0.0793439	−	0.0458092i
$804$		0			0
$805$	−3.21484e11	+	1.45999e11i	−0.765555	+	0.347670i
$806$			1.90276e11i			0.450861i
$807$		0			0
$808$	−3.03206e10	−	5.25168e10i	−0.0711364	−	0.123212i
$809$	1.58129e11	−	9.12961e10i	0.369163	−	0.213137i	−0.303930	−	0.952695i	$-0.598299\pi$
$809$	1.58129e11	−	9.12961e10i	0.369163	−	0.213137i	0.673093	+	0.739558i	$0.264965\pi$
$810$		0			0
$811$	−2.70434e11			−0.625140			−0.312570	−	0.949895i	$-0.601190\pi$
$811$	−2.70434e11			−0.625140			−0.312570	+	0.949895i	$0.601190\pi$
$812$	1.27172e11	+	2.80026e11i	0.292527	+	0.644132i
$813$		0			0
$814$	−6.54159e10	+	1.13304e11i	−0.149000	+	0.258075i
$815$	1.33221e11	−	7.69152e10i	0.301955	−	0.174334i
$816$		0			0
$817$	−1.09572e10	+	1.89784e10i	−0.0245930	+	0.0425963i
$818$			1.77174e10i			0.0395719i
$819$		0			0
$820$	1.53690e11			0.339930
$821$	−1.58943e10	−	9.17655e9i	−0.0349838	−	0.0201979i	0.482406	−	0.875948i	$-0.339763\pi$
$821$	−1.58943e10	−	9.17655e9i	−0.0349838	−	0.0201979i	−0.517390	+	0.855750i	$0.673096\pi$
$822$		0			0
$823$	6.62489e10	+	1.14747e11i	0.144404	+	0.250115i	0.929150	−	0.369702i	$-0.120540\pi$
$823$	6.62489e10	+	1.14747e11i	0.144404	+	0.250115i	−0.784746	+	0.619817i	$0.787207\pi$
$824$	−2.10898e10	−	1.21762e10i	−0.0457470	−	0.0264120i
$825$		0			0
$826$	4.46298e10	−	4.57205e11i	0.0958749	−	0.982179i
$827$		−	5.05744e11i		−	1.08121i	−0.841277	−	0.540604i	$-0.818196\pi$
$827$		−	5.05744e11i		−	1.08121i	0.841277	−	0.540604i	$-0.181804\pi$
$828$		0			0
$829$	1.17149e11	+	2.02909e11i	0.248040	+	0.429618i	0.962982	−	0.269566i	$-0.0868802\pi$
$829$	1.17149e11	+	2.02909e11i	0.248040	+	0.429618i	−0.714942	+	0.699184i	$0.753547\pi$
$830$	2.83014e11	−	1.63398e11i	0.596343	−	0.344299i
$831$		0			0
$832$	−1.12252e11			−0.234262
$833$	4.81190e10	−	1.64275e10i	0.0999395	−	0.0341186i
$834$		0			0
$835$	2.79589e10	−	4.84262e10i	0.0575140	−	0.0996172i
$836$	4.98073e10	−	2.87563e10i	0.101969	−	0.0588718i
$837$		0			0
$838$	−1.13374e10	+	1.96370e10i	−0.0229900	+	0.0398198i
$839$		−	5.18393e11i		−	1.04619i	−0.852274	−	0.523096i	$-0.824777\pi$
$839$		−	5.18393e11i		−	1.04619i	0.852274	−	0.523096i	$-0.175223\pi$
$840$		0			0
$841$	−5.01203e11			−1.00191
$842$	−2.98622e11	−	1.72410e11i	−0.594120	−	0.343015i
$843$		0			0
$844$	−9.62239e10	−	1.66665e11i	−0.189633	−	0.328453i
$845$	5.78760e11	+	3.34147e11i	1.13520	+	0.655407i
$846$		0			0
$847$	−3.99979e11	−	2.86096e11i	−0.777148	−	0.555875i
$848$		−	1.46661e11i		−	0.283617i
$849$		0			0
$850$	−1.41837e10	−	2.45669e10i	−0.0271716	−	0.0470625i
$851$	−1.46201e12	+	8.44095e11i	−2.78762	+	1.60943i
$852$		0			0
$853$	−8.84268e10			−0.167027			−0.0835137	−	0.996507i	$-0.526614\pi$
$853$	−8.84268e10			−0.167027			−0.0835137	+	0.996507i	$0.526614\pi$
$854$	2.15860e11	+	4.75314e11i	0.405826	+	0.893612i
$855$		0			0
$856$	−6.40455e10	+	1.10930e11i	−0.119287	+	0.206611i
$857$	−3.45780e11	+	1.99636e11i	−0.641027	+	0.370097i	−0.785010	−	0.619483i	$-0.787342\pi$
$857$	−3.45780e11	+	1.99636e11i	−0.641027	+	0.370097i	0.143983	+	0.989580i	$0.454009\pi$
$858$		0			0
$859$	2.82062e11	−	4.88545e11i	0.518050	−	0.897288i	−0.481730	−	0.876319i	$-0.659992\pi$
$859$	2.82062e11	−	4.88545e11i	0.518050	−	0.897288i	0.999780	−	0.0209689i	$-0.00667511\pi$
$860$			6.28869e9i			0.0114965i
$861$		0			0
$862$	−6.79644e11			−1.23098
$863$	7.72403e11	+	4.45947e11i	1.39252	+	0.803970i	0.993593	−	0.113014i	$-0.0360504\pi$
$863$	7.72403e11	+	4.45947e11i	1.39252	+	0.803970i	0.398924	+	0.916984i	$0.369384\pi$
$864$		0			0
$865$	−8.27648e10	−	1.43353e11i	−0.147836	−	0.256060i
$866$	9.06811e10	+	5.23547e10i	0.161230	+	0.0930860i
$867$		0			0
$868$	7.85406e10	+	5.61782e10i	0.138361	+	0.0989666i
$869$		−	1.19434e10i		−	0.0209435i
$870$		0			0
$871$	7.30148e11	+	1.26465e12i	1.26864	+	2.19735i
$872$	1.45923e11	−	8.42484e10i	0.252381	−	0.145712i
$873$		0			0
$874$	7.42113e11			1.27182
$875$	5.25940e11	+	5.13394e10i	0.897231	+	0.0875827i
$876$		0			0
$877$	5.29291e11	−	9.16758e11i	0.894738	−	1.54973i	0.0606094	−	0.998162i	$-0.480696\pi$
$877$	5.29291e11	−	9.16758e11i	0.894738	−	1.54973i	0.834129	−	0.551570i	$-0.185971\pi$
$878$	−2.09652e11	+	1.21043e11i	−0.352794	+	0.203686i
$879$		0			0
$880$	8.25207e9	−	1.42930e10i	0.0137604	−	0.0238338i
$881$		−	1.13214e12i		−	1.87930i	−0.342132	−	0.939652i	$-0.611149\pi$
$881$		−	1.13214e12i		−	1.87930i	0.342132	−	0.939652i	$-0.388851\pi$
$882$		0			0
$883$	2.17582e11			0.357915			0.178957	−	0.983857i	$-0.442728\pi$
$883$	2.17582e11			0.357915			0.178957	+	0.983857i	$0.442728\pi$
$884$	−5.23332e10	−	3.02146e10i	−0.0856974	−	0.0494774i
$885$		0			0
$886$	−5.57864e10	−	9.66249e10i	−0.0905303	−	0.156803i
$887$	2.91630e11	+	1.68373e11i	0.471127	+	0.272005i	0.716711	−	0.697370i	$-0.245647\pi$
$887$	2.91630e11	+	1.68373e11i	0.471127	+	0.272005i	−0.245584	+	0.969375i	$0.578980\pi$
$888$		0			0
$889$	−2.75169e9	+	2.81894e10i	−0.00440548	+	0.0451314i
$890$		−	3.43267e11i		−	0.547107i
$891$		0			0
$892$	1.10158e11	+	1.90799e11i	0.174003	+	0.301382i
$893$	−4.58457e11	+	2.64690e11i	−0.720929	+	0.416229i
$894$		0			0
$895$	−3.87569e11			−0.604027
$896$	−3.31421e10	+	4.63346e10i	−0.0514218	+	0.0718909i
$897$		0			0
$898$	−2.52277e11	+	4.36957e11i	−0.387947	+	0.671944i
$899$	−2.72307e11	+	1.57216e11i	−0.416888	+	0.240691i
$900$		0			0
$901$	3.94764e10	−	6.83751e10i	0.0599015	−	0.103753i
$902$		−	1.28673e11i		−	0.194385i
$903$		0			0
$904$	1.75749e11			0.263159
$905$	−4.52622e11	−	2.61321e11i	−0.674747	−	0.389565i
$906$		0			0
$907$	1.27854e11	+	2.21449e11i	0.188923	+	0.327224i	0.944891	−	0.327384i	$-0.106167\pi$
$907$	1.27854e11	+	2.21449e11i	0.188923	+	0.327224i	−0.755969	+	0.654608i	$0.772834\pi$
$908$	−1.75402e11	−	1.01268e11i	−0.258042	−	0.148981i
$909$		0			0
$910$	4.31724e11	−	1.96064e11i	0.629565	−	0.285912i
$911$			1.19690e12i			1.73774i	0.495039	+	0.868871i	$0.335154\pi$
$911$			1.19690e12i			1.73774i	−0.495039	+	0.868871i	$0.664846\pi$
$912$		0			0
$913$	−1.36802e11	−	2.36948e11i	−0.196883	−	0.341012i
$914$	−1.87116e11	+	1.08031e11i	−0.268117	+	0.154798i
$915$		0			0
$916$	−2.05122e11			−0.291361
$917$	2.11819e11	−	2.96136e11i	0.299563	−	0.418807i
$918$		0			0
$919$	1.27826e11	−	2.21402e11i	0.179209	−	0.310398i	−0.762401	−	0.647105i	$-0.775980\pi$
$919$	1.27826e11	−	2.21402e11i	0.179209	−	0.310398i	0.941610	+	0.336706i	$0.109313\pi$
$920$	1.84430e11	−	1.06481e11i	0.257442	−	0.148634i
$921$		0			0
$922$	2.73158e11	−	4.73124e11i	0.377999	−	0.654713i
$923$			8.33812e11i			1.14885i
$924$		0			0
$925$	1.06424e12			1.45370
$926$	−4.34021e11	−	2.50582e11i	−0.590292	−	0.340805i
$927$		0			0
$928$	−9.27490e10	−	1.60646e11i	−0.125060	−	0.216610i
$929$	−8.06751e11	−	4.65778e11i	−1.08312	−	0.625340i	−0.151384	−	0.988475i	$-0.548373\pi$
$929$	−8.06751e11	−	4.65778e11i	−1.08312	−	0.625340i	−0.931737	+	0.363135i	$0.881706\pi$
$930$		0			0
$931$	5.51795e11	−	6.31410e11i	0.734478	−	0.840452i
$932$			4.91667e11i			0.651640i
$933$		0			0
$934$	−4.62087e11	−	8.00358e11i	−0.607206	−	1.05171i
$935$	7.69441e9	−	4.44237e9i	0.0100677	−	0.00581257i
$936$		0			0
$937$	−7.75482e10			−0.100604			−0.0503018	−	0.998734i	$-0.516018\pi$
$937$	−7.75482e10			−0.100604			−0.0503018	+	0.998734i	$0.516018\pi$
$938$	7.37588e11	+	7.19992e10i	0.952801	+	0.0930072i
$939$		0			0
$940$	−7.59571e10	+	1.31562e11i	−0.0972875	+	0.168507i
$941$	−1.01791e12	+	5.87691e11i	−1.29823	+	0.749532i	−0.980098	−	0.198515i	$-0.936388\pi$
$941$	−1.01791e12	+	5.87691e11i	−1.29823	+	0.749532i	−0.318130	+	0.948047i	$0.603055\pi$
$942$		0			0
$943$	8.30169e11	−	1.43790e12i	1.04983	−	1.81836i
$944$			2.77072e11i			0.348903i
$945$		0			0
$946$	5.26506e9			0.00657414
$947$	−4.41365e11	−	2.54822e11i	−0.548780	−	0.316838i	0.199850	−	0.979827i	$-0.435955\pi$
$947$	−4.41365e11	−	2.54822e11i	−0.548780	−	0.316838i	−0.748630	+	0.662988i	$0.769288\pi$
$948$		0			0
$949$	3.30042e11	+	5.71649e11i	0.406916	+	0.704798i
$950$	−4.05155e11	−	2.33916e11i	−0.497424	−	0.287188i
$951$		0			0
$952$	−2.79229e10	+	1.26810e10i	−0.0339949	+	0.0154385i
$953$			6.09471e10i			0.0738893i	0.999317	+	0.0369446i	$0.0117625\pi$
$953$			6.09471e10i			0.0738893i	−0.999317	+	0.0369446i	$0.988237\pi$
$954$		0			0
$955$	−2.13053e11	−	3.69019e11i	−0.256138	−	0.443644i
$956$	−7.75199e10	+	4.47562e10i	−0.0928072	+	0.0535823i
$957$		0			0
$958$	−4.90557e11			−0.582408
$959$	−2.93296e11	−	6.45825e11i	−0.346762	−	0.763555i
$960$		0			0
$961$	3.77083e11	−	6.53127e11i	0.442123	−	0.765780i
$962$	1.96335e12	−	1.13354e12i	2.29244	−	1.32354i
$963$		0			0
$964$	−1.87738e9	+	3.25172e9i	−0.00217392	+	0.00376535i
$965$			4.24681e11i			0.489726i
$966$		0			0
$967$	−6.91316e10			−0.0790626			−0.0395313	−	0.999218i	$-0.512586\pi$
$967$	−6.91316e10			−0.0790626			−0.0395313	+	0.999218i	$0.512586\pi$
$968$	2.56869e11	+	1.48304e11i	0.292557	+	0.168908i
$969$		0			0
$970$	1.73651e11	+	3.00772e11i	0.196150	+	0.339742i
$971$	−3.75707e11	−	2.16915e11i	−0.422642	−	0.244012i	0.273565	−	0.961853i	$-0.411797\pi$
$971$	−3.75707e11	−	2.16915e11i	−0.422642	−	0.244012i	−0.696207	+	0.717841i	$0.745130\pi$
$972$		0			0
$973$	−1.20291e11	+	1.23231e12i	−0.134209	+	1.37489i
$974$		−	8.15957e11i		−	0.906632i
$975$		0			0
$976$	−1.57431e11	−	2.72679e11i	−0.173497	−	0.300505i
$977$	3.35469e11	−	1.93683e11i	0.368192	−	0.212576i	−0.304476	−	0.952520i	$-0.598481\pi$
$977$	3.35469e11	−	1.93683e11i	0.368192	−	0.212576i	0.672668	+	0.739944i	$0.265148\pi$
$978$		0			0
$979$	−2.87393e11			−0.312857
$980$	4.65352e10	−	2.36091e11i	0.0504519	−	0.255962i
$981$		0			0
$982$	4.35243e11	−	7.53864e11i	0.468044	−	0.810675i
$983$	−8.42064e11	+	4.86166e11i	−0.901843	+	0.520679i	−0.877798	−	0.479032i	$-0.840988\pi$
$983$	−8.42064e11	+	4.86166e11i	−0.901843	+	0.520679i	−0.0240453	+	0.999711i	$0.507655\pi$
$984$		0			0
$985$	−1.11184e11	+	1.92577e11i	−0.118113	+	0.204578i
$986$		−	9.98599e10i		−	0.105653i
$987$		0			0
$988$	−9.96589e11			−1.04590
$989$	5.88358e10	+	3.39689e10i	0.0614974	+	0.0355055i
$990$		0			0
$991$	−1.09986e11	−	1.90502e11i	−0.114037	−	0.197517i	0.803358	−	0.595497i	$-0.203045\pi$
$991$	−1.09986e11	−	1.90502e11i	−0.114037	−	0.197517i	−0.917394	+	0.397980i	$0.869711\pi$
$992$	−5.04393e10	−	2.91211e10i	−0.0520861	−	0.0300719i
$993$		0			0
$994$	3.44175e11	+	2.46180e11i	0.352561	+	0.252178i
$995$			3.25791e11i			0.332389i
$996$		0			0
$997$	3.41905e11	+	5.92196e11i	0.346038	+	0.599356i	0.985542	−	0.169432i	$-0.0541934\pi$
$997$	3.41905e11	+	5.92196e11i	0.346038	+	0.599356i	−0.639504	+	0.768788i	$0.720860\pi$
$998$	−9.55487e11	+	5.51651e11i	−0.963169	+	0.556086i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.b.107.4	yes	20
3.2	odd	2	inner	126.9.s.b.107.7	yes	20
7.4	even	3	inner	126.9.s.b.53.7	yes	20
21.11	odd	6	inner	126.9.s.b.53.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.b.53.4	✓	20	21.11	odd	6	inner
126.9.s.b.53.7	yes	20	7.4	even	3	inner
126.9.s.b.107.4	yes	20	1.1	even	1	trivial
126.9.s.b.107.7	yes	20	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(282.418 + 163.054i) q^{5} +(-233.264 + 2389.64i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(282.418 + 163.054i) q^{5} +(-233.264 + 2389.64i) q^{7} -1448.15i q^{8} +(-1844.75 - 3195.20i) q^{10} +(-2675.11 + 1544.47i) q^{11} +53526.0 q^{13} +(15803.4 - 22094.1i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-7638.40 + 4410.03i) q^{17} +(-72729.7 + 125971. i) q^{19} +41741.9i q^{20} +34947.5 q^{22} +(390530. + 225472. i) q^{23} +(-142139. - 246192. i) q^{25} +(-524445. - 302789. i) q^{26} +(-279824. + 127080. i) q^{28} -1.00072e6i q^{29} +(-157103. - 272110. i) q^{31} +(160530. - 92681.9i) q^{32} +99787.6 q^{34} +(-455519. + 636844. i) q^{35} +(-1.87184e6 + 3.24211e6i) q^{37} +(1.42520e6 - 822842. i) q^{38} +(236128. - 408985. i) q^{40} -3.68191e6i q^{41} +150657. q^{43} +(-342414. - 197693. i) q^{44} +(-2.55093e6 - 4.41834e6i) q^{46} +(3.15179e6 + 1.81969e6i) q^{47} +(-5.65598e6 - 1.11483e6i) q^{49} +3.21624e6i q^{50} +(3.42566e6 + 5.93342e6i) q^{52} +(-7.75222e6 + 4.47575e6i) q^{53} -1.00733e6 q^{55} +(3.46057e6 + 337802. i) q^{56} +(-5.66095e6 + 9.80506e6i) q^{58} +(1.46455e7 - 8.45557e6i) q^{59} +(-9.60884e6 + 1.66430e7i) q^{61} +3.55482e6i q^{62} -2.09715e6 q^{64} +(1.51167e7 + 8.72764e6i) q^{65} +(1.36410e7 + 2.36269e7i) q^{67} +(-977715. - 564484. i) q^{68} +(8.06569e6 - 3.66296e6i) q^{70} +1.55777e7i q^{71} +(6.16601e6 + 1.06798e7i) q^{73} +(3.66803e7 - 2.11774e7i) q^{74} -1.86188e7 q^{76} +(-3.06674e6 - 6.75282e6i) q^{77} +(-1.93325e6 + 3.34848e6i) q^{79} +(-4.62714e6 + 2.67148e6i) q^{80} +(-2.08280e7 + 3.60752e7i) q^{82} +8.85749e7i q^{83} -2.87630e6 q^{85} +(-1.47613e6 - 852242. i) q^{86} +(2.23664e6 + 3.87397e6i) q^{88} +(8.05742e7 + 4.65195e7i) q^{89} +(-1.24857e7 + 1.27908e8i) q^{91} +5.77209e7i q^{92} +(-2.05874e7 - 3.56584e7i) q^{94} +(-4.10804e7 + 2.37178e7i) q^{95} -9.41324e7 q^{97} +(4.91106e7 + 4.29181e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} + 3778 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 + 3778 * q^7	\( 20 q + 1280 q^{4} + 3778 q^{7} + 14816 q^{10} + 17700 q^{13} - 163840 q^{16} - 267794 q^{19} + 453568 q^{22} - 765890 q^{25} - 232448 q^{28} - 2604342 q^{31} + 4087936 q^{34} + 1127530 q^{37} - 1896448 q^{40} - 4460924 q^{43} - 180416 q^{46} - 25278034 q^{49} + 1132800 q^{52} - 18833120 q^{55} + 5146496 q^{58} - 25730232 q^{61} - 41943040 q^{64} + 58134374 q^{67} - 76724864 q^{70} + 5811002 q^{73} - 68555264 q^{76} + 74799798 q^{79} - 9883296 q^{82} + 119739328 q^{85} + 29028352 q^{88} - 479039766 q^{91} + 169364448 q^{94} - 658133608 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 + 3778 * q^7 + 14816 * q^10 + 17700 * q^13 - 163840 * q^16 - 267794 * q^19 + 453568 * q^22 - 765890 * q^25 - 232448 * q^28 - 2604342 * q^31 + 4087936 * q^34 + 1127530 * q^37 - 1896448 * q^40 - 4460924 * q^43 - 180416 * q^46 - 25278034 * q^49 + 1132800 * q^52 - 18833120 * q^55 + 5146496 * q^58 - 25730232 * q^61 - 41943040 * q^64 + 58134374 * q^67 - 76724864 * q^70 + 5811002 * q^73 - 68555264 * q^76 + 74799798 * q^79 - 9883296 * q^82 + 119739328 * q^85 + 29028352 * q^88 - 479039766 * q^91 + 169364448 * q^94 - 658133608 * q^97

Introduction

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