LMFDB - Embedded newform 475.2.e.f.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$-0.975939 - 1.69038i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.f.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08504 + 1.87935i) q^{2} +(-1.47594 + 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 - 5.94669i) q^{13} +(-0.641933 + 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(2.61787 - 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 + 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(-2.79990 + 4.84957i) q^{22} +(-1.45072 - 2.51271i) q^{23} +(-2.27175 + 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 - 1.38812i) q^{28} +(-3.52494 - 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 + 6.57195i) q^{32} +(-3.80859 + 6.59667i) q^{33} +(5.68101 + 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 - 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(-1.89491 - 3.28208i) q^{42} +(-2.18013 + 3.77609i) q^{43} +(-3.49558 - 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 - 2.21600i) q^{47} +(3.06756 + 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(-9.30181 + 16.1112i) q^{52} +(4.79573 + 8.30645i) q^{53} +(-8.69138 + 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 - 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 - 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(7.39371 - 12.8063i) q^{62} +(-1.69013 - 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(-2.15122 - 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(-4.39714 - 7.61607i) q^{72} +(4.21337 - 7.29777i) q^{73} +(5.23574 - 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 + 38.0935i) q^{78} +(-2.93630 + 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(-6.75806 - 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 - 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(-3.93039 + 6.80764i) q^{92} +(10.0574 - 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 + 2.18732i) q^{97} +(7.21552 - 12.4977i) q^{98} +(-7.37182 - 12.7684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.08504	+	1.87935i	−0.767241	+	1.32890i	0.171812	+	0.985130i	$0.445038\pi$
$2$	−1.08504	+	1.87935i	−0.767241	+	1.32890i	−0.939053	+	0.343771i	$0.888295\pi$
$3$	−1.47594	+	2.55640i	−0.852134	+	1.47594i	0.0271449	+	0.999632i	$0.491358\pi$
$3$	−1.47594	+	2.55640i	−0.852134	+	1.47594i	−0.879279	+	0.476308i	$0.841975\pi$
$4$	−1.35464	−	2.34630i	−0.677319	−	1.17315i
$5$		0			0
$5$		0			0
$6$	−3.20292	−	5.54761i	−1.30758	−	2.26480i
$7$	0.591620			0.223611			0.111806	−	0.993730i	$-0.464337\pi$
$7$	0.591620			0.223611			0.111806	+	0.993730i	$0.464337\pi$
$8$	1.53919			0.544185
$9$	−2.85679	−	4.94811i	−0.952264	−	1.64937i
$10$		0			0
$11$	2.58045			0.778036			0.389018	−	0.921230i	$-0.372814\pi$
$11$	2.58045			0.778036			0.389018	+	0.921230i	$0.372814\pi$
$12$	7.99745			2.30867
$13$	−3.43332	−	5.94669i	−0.952232	−	1.64931i	−0.740579	−	0.671969i	$-0.765449\pi$
$13$	−3.43332	−	5.94669i	−0.952232	−	1.64931i	−0.211653	−	0.977345i	$-0.567885\pi$
$14$	−0.641933	+	1.11186i	−0.171564	+	0.297157i
$15$		0			0
$16$	1.03919	−	1.79993i	0.259797	−	0.449982i
$17$	2.61787	−	4.53429i	0.634927	−	1.09973i	−0.351603	−	0.936149i	$-0.614363\pi$
$17$	2.61787	−	4.53429i	0.634927	−	1.09973i	0.986531	−	0.163577i	$-0.0523033\pi$
$18$	12.3990			2.92247
$19$	−2.26423	+	3.72468i	−0.519449	+	0.854501i
$19$	−2.26423	+	3.72468i	−0.519449	+	0.854501i
$20$		0			0
$21$	−0.873195	+	1.51242i	−0.190547	+	0.330037i
$22$	−2.79990	+	4.84957i	−0.596941	+	1.03393i
$23$	−1.45072	−	2.51271i	−0.302495	−	0.523937i	0.674205	−	0.738544i	$-0.264486\pi$
$23$	−1.45072	−	2.51271i	−0.302495	−	0.523937i	−0.976701	+	0.214607i	$0.931153\pi$
$24$	−2.27175	+	3.93478i	−0.463719	+	0.803185i
$25$		0			0
$26$	14.9012			2.92237
$27$	8.01017			1.54156
$28$	−0.801431	−	1.38812i	−0.151456	−	0.262330i
$29$	−3.52494	−	6.10538i	−0.654565	−	1.13374i	−0.982003	−	0.188867i	$-0.939518\pi$
$29$	−3.52494	−	6.10538i	−0.654565	−	1.13374i	0.327438	−	0.944873i	$-0.393815\pi$
$30$		0			0
$31$	−6.81421			−1.22387			−0.611934	−	0.790909i	$-0.709608\pi$
$31$	−6.81421			−1.22387			−0.611934	+	0.790909i	$0.709608\pi$
$32$	3.79432	+	6.57195i	0.670747	+	1.16177i
$33$	−3.80859	+	6.59667i	−0.662990	+	1.14833i
$34$	5.68101	+	9.83980i	0.974285	+	1.68751i
$35$		0			0
$36$	−7.73984	+	13.4058i	−1.28997	+	2.23430i
$37$	−4.82538			−0.793287			−0.396644	−	0.917973i	$-0.629825\pi$
$37$	−4.82538			−0.793287			−0.396644	+	0.917973i	$0.629825\pi$
$38$	−4.54320	−	8.29672i	−0.737005	−	1.34591i
$39$	20.2695			3.24572
$40$		0			0
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	−0.999877	−	0.0156852i	$-0.995007\pi$
$41$	−3.11419	+	5.39393i	−0.486355	+	0.842391i	0.513522	+	0.858076i	$0.328340\pi$
$42$	−1.89491	−	3.28208i	−0.292391	−	0.506436i
$43$	−2.18013	+	3.77609i	−0.332467	+	0.575849i	−0.982995	−	0.183633i	$-0.941214\pi$
$43$	−2.18013	+	3.77609i	−0.332467	+	0.575849i	0.650528	+	0.759482i	$0.274548\pi$
$44$	−3.49558	−	6.05452i	−0.526978	−	0.912753i
$45$		0			0
$46$	6.29636			0.928348
$47$	−1.27941	−	2.21600i	−0.186621	−	0.323237i	0.757501	−	0.652834i	$-0.226420\pi$
$47$	−1.27941	−	2.21600i	−0.186621	−	0.323237i	−0.944121	+	0.329598i	$0.893087\pi$
$48$	3.06756	+	5.31317i	0.442764	+	0.766890i
$49$	−6.64999			−0.949998
$50$		0			0
$51$	7.72764	+	13.3847i	1.08209	+	1.87423i
$52$	−9.30181	+	16.1112i	−1.28993	+	2.23422i
$53$	4.79573	+	8.30645i	0.658745	+	1.14098i	0.980941	+	0.194306i	$0.0622456\pi$
$53$	4.79573	+	8.30645i	0.658745	+	1.14098i	−0.322196	+	0.946673i	$0.604421\pi$
$54$	−8.69138	+	15.0539i	−1.18275	+	2.04858i
$55$		0			0
$56$	0.910615			0.121686
$57$	−6.17993	−	11.2857i	−0.818551	−	1.49483i
$58$	15.2989			2.00884
$59$	1.46221	−	2.53263i	0.190364	−	0.329720i	−0.755007	−	0.655717i	$-0.772367\pi$
$59$	1.46221	−	2.53263i	0.190364	−	0.329720i	0.945371	+	0.325997i	$0.105700\pi$
$60$		0			0
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	0.781686	−	0.623672i	$-0.214360\pi$
$61$	−1.16586	−	2.01932i	−0.149273	−	0.258548i	−0.930959	+	0.365124i	$0.881027\pi$
$62$	7.39371	−	12.8063i	0.939003	−	1.62640i
$63$	−1.69013	−	2.92740i	−0.212937	−	0.368818i
$64$	−12.3112			−1.53891
$65$		0			0
$66$	−8.26497	−	14.3153i	−1.01735	−	1.76210i
$67$	−2.15122	−	3.72603i	−0.262814	−	0.455207i	0.704175	−	0.710027i	$-0.251317\pi$
$67$	−2.15122	−	3.72603i	−0.262814	−	0.455207i	−0.966989	+	0.254820i	$0.917984\pi$
$68$	−14.1851			−1.72019
$69$	8.56468			1.03107
$70$		0			0
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	−0.118528	−	0.992951i	$-0.537818\pi$
$71$	6.74645	−	11.6852i	0.800656	−	1.38678i	0.919185	−	0.393827i	$-0.128849\pi$
$72$	−4.39714	−	7.61607i	−0.518208	−	0.897563i
$73$	4.21337	−	7.29777i	0.493137	−	0.854139i	−0.506831	−	0.862045i	$-0.669183\pi$
$73$	4.21337	−	7.29777i	0.493137	−	0.854139i	0.999969	+	0.00790620i	$0.00251665\pi$
$74$	5.23574	−	9.06858i	0.608643	−	1.05420i
$75$		0			0
$76$	11.8064	+	0.266962i	1.35429	+	0.0306226i
$77$	1.52665			0.173978
$78$	−21.9933	+	38.0935i	−2.49025	+	4.31324i
$79$	−2.93630	+	5.08583i	−0.330360	+	0.572200i	−0.982582	−	0.185827i	$-0.940503\pi$
$79$	−2.93630	+	5.08583i	−0.330360	+	0.572200i	0.652222	+	0.758028i	$0.273837\pi$
$80$		0			0
$81$	−3.25215	+	5.63288i	−0.361350	+	0.625876i
$82$	−6.75806	−	11.7053i	−0.746303	−	1.29263i
$83$	−4.02036			−0.441292			−0.220646	−	0.975354i	$-0.570816\pi$
$83$	−4.02036			−0.441292			−0.220646	+	0.975354i	$0.570816\pi$
$84$	4.73145			0.516244
$85$		0			0
$86$	−4.73107	−	8.19445i	−0.510164	−	0.883630i
$87$	20.8104			2.23111
$88$	3.97180			0.423396
$89$	−1.85823	−	3.21855i	−0.196972	−	0.341166i	0.750573	−	0.660787i	$-0.229778\pi$
$89$	−1.85823	−	3.21855i	−0.196972	−	0.341166i	−0.947545	+	0.319622i	$0.896444\pi$
$90$		0			0
$91$	−2.03122	−	3.51818i	−0.212930	−	0.368805i
$92$	−3.93039	+	6.80764i	−0.409772	+	0.709745i
$93$	10.0574	−	17.4199i	1.04290	−	1.80636i
$94$	5.55285			0.572733
$95$		0			0
$96$	−22.4007			−2.28627
$97$	−1.26285	+	2.18732i	−0.128223	+	0.222089i	−0.922988	−	0.384828i	$-0.874261\pi$
$97$	−1.26285	+	2.18732i	−0.128223	+	0.222089i	0.794765	+	0.606917i	$0.207594\pi$
$98$	7.21552	−	12.4977i	0.728878	−	1.26245i
$99$	−7.37182	−	12.7684i	−0.740895	−	1.28327i
$100$		0			0
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	0.829501	−	0.558506i	$-0.188625\pi$
$101$	−0.692736	−	1.19985i	−0.0689298	−	0.119390i	−0.898430	+	0.439116i	$0.855292\pi$
$102$	−33.5393			−3.32088
$103$	0.166774			0.0164328			0.00821638	−	0.999966i	$-0.497385\pi$
$103$	0.166774			0.0164328			0.00821638	+	0.999966i	$0.497385\pi$
$104$	−5.28453	−	9.15307i	−0.518191	−	0.897533i
$105$		0			0
$106$	−20.8143			−2.02166
$107$	−4.51729			−0.436703			−0.218351	−	0.975870i	$-0.570068\pi$
$107$	−4.51729			−0.436703			−0.218351	+	0.975870i	$0.570068\pi$
$108$	−10.8509	−	18.7943i	−1.04413	−	1.80848i
$109$	5.35464	−	9.27450i	0.512881	−	0.888336i	−0.487007	−	0.873398i	$-0.661911\pi$
$109$	5.35464	−	9.27450i	0.512881	−	0.888336i	0.999888	−	0.0149384i	$-0.00475523\pi$
$110$		0			0
$111$	7.12196	−	12.3356i	0.675987	−	1.17084i
$112$	0.614805	−	1.06487i	0.0580936	−	0.100621i
$113$	13.2065			1.24237			0.621183	−	0.783665i	$-0.286652\pi$
$113$	13.2065			1.24237			0.621183	+	0.783665i	$0.286652\pi$
$114$	27.9152	+	0.631206i	2.61450	+	0.0591178i
$115$		0			0
$116$	−9.55004	+	16.5411i	−0.886699	+	1.53581i
$117$	−19.6166	+	33.9769i	−1.81355	+	3.14117i
$118$	3.17313	+	5.49602i	0.292110	+	0.505950i
$119$	1.54879	−	2.68257i	0.141977	−	0.245911i
$120$		0			0
$121$	−4.34127			−0.394661
$122$	5.06002			0.458113
$123$	−9.19271	−	15.9222i	−0.828879	−	1.43566i
$124$	9.23079	+	15.9882i	0.828949	+	1.43578i
$125$		0			0
$126$	7.33548			0.653496
$127$	−0.860805	−	1.49096i	−0.0763841	−	0.132301i	0.825303	−	0.564690i	$-0.191004\pi$
$127$	−0.860805	−	1.49096i	−0.0763841	−	0.132301i	−0.901687	+	0.432389i	$0.857671\pi$
$128$	5.76959	−	9.99323i	0.509965	−	0.883285i
$129$	−6.43548	−	11.1466i	−0.566612	−	0.981401i
$130$		0			0
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	−0.928799	−	0.370585i	$-0.879157\pi$
$131$	−1.64201	+	2.84405i	−0.143463	+	0.248486i	0.785335	+	0.619071i	$0.212491\pi$
$132$	20.6370			1.79622
$133$	−1.33956	+	2.20360i	−0.116155	+	0.191076i
$134$	9.33668			0.806567
$135$		0			0
$136$	4.02940	−	6.97913i	0.345518	−	0.598455i
$137$	−4.07541	−	7.05882i	−0.348186	−	0.603075i	0.637741	−	0.770251i	$-0.279869\pi$
$137$	−4.07541	−	7.05882i	−0.348186	−	0.603075i	−0.985927	+	0.167175i	$0.946536\pi$
$138$	−9.29304	+	16.0960i	−0.791076	+	1.37018i
$139$	7.81401	+	13.5343i	0.662776	+	1.14796i	0.979883	+	0.199571i	$0.0639550\pi$
$139$	7.81401	+	13.5343i	0.662776	+	1.14796i	−0.317108	+	0.948390i	$0.602712\pi$
$140$		0			0
$141$	7.55331			0.636103
$142$	14.6404	+	25.3579i	1.22859	+	2.12799i
$143$	−8.85952	−	15.3451i	−0.740870	−	1.28323i
$144$	−11.8750			−0.989582
$145$		0			0
$146$	9.14337	+	15.8368i	0.756711	+	1.31066i
$147$	9.81497	−	17.0000i	0.809525	−	1.40214i
$148$	6.53664	+	11.3218i	0.537308	+	0.930646i
$149$	−1.61005	+	2.78869i	−0.131900	+	0.228458i	−0.924409	−	0.381402i	$-0.875441\pi$
$149$	−1.61005	+	2.78869i	−0.131900	+	0.228458i	0.792509	+	0.609861i	$0.208775\pi$
$150$		0			0
$151$	−11.1226			−0.905142			−0.452571	−	0.891728i	$-0.649493\pi$
$151$	−11.1226			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$152$	−3.48507	+	5.73299i	−0.282677	+	0.465007i
$153$	−29.9149			−2.41847
$154$	−1.65648	+	2.86910i	−0.133483	+	0.231199i
$155$		0			0
$156$	−27.4578	−	47.5583i	−2.19838	−	3.80771i
$157$	−10.7157	+	18.5602i	−0.855209	+	1.48127i	0.0212418	+	0.999774i	$0.493238\pi$
$157$	−10.7157	+	18.5602i	−0.855209	+	1.48127i	−0.876451	+	0.481491i	$0.840095\pi$
$158$	−6.37203	−	11.0367i	−0.506932	−	0.878032i
$159$	−28.3128			−2.24535
$160$		0			0
$161$	−0.858273	−	1.48657i	−0.0676414	−	0.117158i
$162$	−7.05744	−	12.2238i	−0.554485	−	0.960396i
$163$	10.3129			0.807768			0.403884	−	0.914810i	$-0.367660\pi$
$163$	10.3129			0.807768			0.403884	+	0.914810i	$0.367660\pi$
$164$	16.8744			1.31767
$165$		0			0
$166$	4.36226	−	7.55566i	0.338577	−	0.586433i
$167$	−3.25342	−	5.63509i	−0.251757	−	0.436056i	0.712252	−	0.701923i	$-0.247675\pi$
$167$	−3.25342	−	5.63509i	−0.251757	−	0.436056i	−0.964010	+	0.265867i	$0.914342\pi$
$168$	−1.34401	+	2.32790i	−0.103693	+	0.179601i
$169$	−17.0754	+	29.5754i	−1.31349	+	2.27503i
$170$		0			0
$171$	24.8986	+	0.562995i	1.90404	+	0.0430533i
$172$	11.8131			0.900744
$173$	−3.13027	+	5.42179i	−0.237990	+	0.412211i	−0.960137	−	0.279528i	$-0.909822\pi$
$173$	−3.13027	+	5.42179i	−0.237990	+	0.412211i	0.722147	+	0.691739i	$0.243155\pi$
$174$	−22.5802	+	39.1100i	−1.71180	+	2.96492i
$175$		0			0
$176$	2.68158	−	4.64463i	0.202131	−	0.350102i
$177$	4.31628	+	7.47601i	0.324431	+	0.561931i
$178$	8.06505			0.604501
$179$	23.1893			1.73325			0.866624	−	0.498961i	$-0.166285\pi$
$179$	23.1893			1.73325			0.866624	+	0.498961i	$0.166285\pi$
$180$		0			0
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	0.919328	−	0.393493i	$-0.128733\pi$
$181$	1.59948	+	2.77039i	0.118889	+	0.205921i	−0.800439	+	0.599414i	$0.795400\pi$
$182$	8.81585			0.653474
$183$	6.88294			0.508801
$184$	−2.23293	−	3.86754i	−0.164614	−	0.285119i
$185$		0			0
$186$	21.8253	+	37.8026i	1.60031	+	2.77182i
$187$	6.75529	−	11.7005i	0.493996	−	0.855626i
$188$	−3.46627	+	6.00375i	−0.252803	+	0.437868i
$189$	4.73898			0.344710
$190$		0			0
$191$	18.9443			1.37076			0.685382	−	0.728184i	$-0.259635\pi$
$191$	18.9443			1.37076			0.685382	+	0.728184i	$0.259635\pi$
$192$	18.1706	−	31.4725i	1.31135	−	2.27133i
$193$	0.515269	−	0.892472i	0.0370899	−	0.0642415i	−0.846885	−	0.531777i	$-0.821525\pi$
$193$	0.515269	−	0.892472i	0.0370899	−	0.0642415i	0.883974	+	0.467535i	$0.154858\pi$
$194$	−2.74049	−	4.74667i	−0.196756	−	0.340791i
$195$		0			0
$196$	9.00832	+	15.6029i	0.643452	+	1.11449i
$197$	−18.5515			−1.32174			−0.660868	−	0.750502i	$-0.729812\pi$
$197$	−18.5515			−1.32174			−0.660868	+	0.750502i	$0.729812\pi$
$198$	31.9950			2.27378
$199$	−11.3166	−	19.6010i	−0.802215	−	1.38948i	−0.918155	−	0.396221i	$-0.870321\pi$
$199$	−11.3166	−	19.6010i	−0.802215	−	1.38948i	0.115940	−	0.993256i	$-0.463012\pi$
$200$		0			0
$201$	12.7003			0.895810
$202$	3.00659			0.211543
$203$	−2.08542	−	3.61206i	−0.146368	−	0.253517i
$204$	20.9363	−	36.2627i	1.46583	−	2.53890i
$205$		0			0
$206$	−0.180957	+	0.313427i	−0.0126079	+	0.0218375i
$207$	−8.28879	+	14.3566i	−0.576111	+	0.997853i
$208$	−14.2715			−0.989549
$209$	−5.84273	+	9.61137i	−0.404150	+	0.664832i
$210$		0			0
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	−0.996712	−	0.0810240i	$-0.974181\pi$
$211$	−6.21978	+	10.7730i	−0.428187	+	0.741642i	0.568525	+	0.822666i	$0.307514\pi$
$212$	12.9930	−	22.5045i	0.892360	−	1.54561i
$213$	19.9147	+	34.4933i	1.36453	+	2.36344i
$214$	4.90145	−	8.48956i	0.335056	−	0.580335i
$215$		0			0
$216$	12.3292			0.838893
$217$	−4.03142			−0.273671
$218$	11.6200	+	20.1265i	0.787008	+	1.36314i
$219$	12.4373	+	21.5421i	0.840438	+	1.45568i
$220$		0			0
$221$	−35.9520			−2.41839
$222$	15.4553	+	26.7693i	1.03729	+	1.79664i
$223$	9.58654	−	16.6044i	0.641962	−	1.11191i	−0.343032	−	0.939324i	$-0.611454\pi$
$223$	9.58654	−	16.6044i	0.641962	−	1.11191i	0.984994	−	0.172588i	$-0.0552128\pi$
$224$	2.24479	+	3.88810i	0.149987	+	0.259784i
$225$		0			0
$226$	−14.3297	+	24.8197i	−0.953195	+	1.65098i
$227$	−26.5208			−1.76025			−0.880123	−	0.474745i	$-0.842540\pi$
$227$	−26.5208			−1.76025			−0.880123	+	0.474745i	$0.842540\pi$
$228$	−18.1080	+	29.7880i	−1.19923	+	1.97276i
$229$	−8.81023			−0.582196			−0.291098	−	0.956693i	$-0.594021\pi$
$229$	−8.81023			−0.582196			−0.291098	+	0.956693i	$0.594021\pi$
$230$		0			0
$231$	−2.25324	+	3.90272i	−0.148252	+	0.256780i
$232$	−5.42555	−	9.39733i	−0.356205	−	0.616965i
$233$	2.25616	−	3.90778i	0.147806	−	0.256007i	−0.782610	−	0.622512i	$-0.786112\pi$
$233$	2.25616	−	3.90778i	0.147806	−	0.256007i	0.930416	+	0.366505i	$0.119446\pi$
$234$	−42.5697	−	73.7328i	−2.78287	−	4.82006i
$235$		0			0
$236$	−7.92308			−0.515749
$237$	−8.66761	−	15.0127i	−0.563022	−	0.975182i
$238$	3.36100	+	5.82142i	0.217861	+	0.377347i
$239$	−7.82431			−0.506112			−0.253056	−	0.967452i	$-0.581436\pi$
$239$	−7.82431			−0.506112			−0.253056	+	0.967452i	$0.581436\pi$
$240$		0			0
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.850740	−	0.525586i	$-0.823846\pi$
$241$	−13.6697	−	23.6766i	−0.880541	−	1.52514i	−0.0298010	−	0.999556i	$-0.509487\pi$
$242$	4.71046	−	8.15876i	0.302800	−	0.524465i
$243$	2.41531	+	4.18345i	0.154942	+	0.268368i
$244$	−3.15863	+	5.47091i	−0.202210	+	0.350239i
$245$		0			0
$246$	39.8979			2.54380
$247$	29.9233	+	0.676612i	1.90398	+	0.0430518i
$248$	−10.4884			−0.666011
$249$	5.93380	−	10.2777i	0.376040	−	0.651320i
$250$		0			0
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	0.999896	+	0.0144451i	$0.00459818\pi$
$251$	8.11886	+	14.0623i	0.512458	+	0.887603i	−0.487438	+	0.873158i	$0.662068\pi$
$252$	−4.57904	+	7.93113i	−0.288452	+	0.499614i
$253$	−3.74350	−	6.48394i	−0.235352	−	0.407642i
$254$	3.73604			0.234420
$255$		0			0
$256$	0.209275	+	0.362476i	0.0130797	+	0.0226547i
$257$	4.57174	+	7.91848i	0.285177	+	0.493941i	0.972652	−	0.232267i	$-0.0746143\pi$
$257$	4.57174	+	7.91848i	0.285177	+	0.493941i	−0.687475	+	0.726208i	$0.741281\pi$
$258$	27.9311			1.73891
$259$	−2.85479			−0.177388
$260$		0			0
$261$	−20.1400	+	34.8836i	−1.24664	+	2.15924i
$262$	−3.56331	−	6.17183i	−0.220142	−	0.381297i
$263$	7.64861	−	13.2478i	0.471634	−	0.816894i	−0.527840	−	0.849344i	$-0.676998\pi$
$263$	7.64861	−	13.2478i	0.471634	−	0.816894i	0.999473	+	0.0324505i	$0.0103311\pi$
$264$	−5.86214	+	10.1535i	−0.360790	+	0.624906i
$265$		0			0
$266$	−2.68785	−	4.90850i	−0.164803	−	0.300960i
$267$	10.9705			0.671386
$268$	−5.82826	+	10.0948i	−0.356017	+	0.616640i
$269$	7.07334	−	12.2514i	0.431269	−	0.746981i	−0.565714	−	0.824602i	$-0.691399\pi$
$269$	7.07334	−	12.2514i	0.431269	−	0.746981i	0.996983	+	0.0776213i	$0.0247325\pi$
$270$		0			0
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	−0.640246	−	0.768170i	$-0.721168\pi$
$271$	5.68158	−	9.84078i	0.345131	−	0.597785i	0.985378	+	0.170385i	$0.0545010\pi$
$272$	−5.44093	−	9.42396i	−0.329905	−	0.571412i
$273$	11.9918			0.725779
$274$	17.6880			1.06857
$275$		0			0
$276$	−11.6020	−	20.0953i	−0.698360	−	1.20960i
$277$	18.9102			1.13620			0.568101	−	0.822959i	$-0.307678\pi$
$277$	18.9102			1.13620			0.568101	+	0.822959i	$0.307678\pi$
$278$	−33.9142			−2.03404
$279$	19.4668	+	33.7175i	1.16545	+	2.01861i
$280$		0			0
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	0.896596	+	0.442849i	$0.146032\pi$
$281$	13.9438	+	24.1513i	0.831816	+	1.44075i	−0.0647802	+	0.997900i	$0.520635\pi$
$282$	−8.19567	+	14.1953i	−0.488045	+	0.845318i
$283$	−7.19798	+	12.4673i	−0.427876	+	0.741102i	−0.996684	−	0.0813677i	$-0.974071\pi$
$283$	−7.19798	+	12.4673i	−0.427876	+	0.741102i	0.568809	+	0.822470i	$0.307405\pi$
$284$	−36.5560			−2.16920
$285$		0			0
$286$	38.4519			2.27371
$287$	−1.84242	+	3.19116i	−0.108754	+	0.188368i
$288$	21.6792	−	37.5494i	1.27746	−	2.21262i
$289$	−5.20651	−	9.01794i	−0.306265	−	0.530467i
$290$		0			0
$291$	−3.72778	−	6.45670i	−0.218526	−	0.378498i
$292$	−22.8303			−1.33605
$293$	2.63178			0.153750			0.0768752	−	0.997041i	$-0.475506\pi$
$293$	2.63178			0.153750			0.0768752	+	0.997041i	$0.475506\pi$
$294$	21.2993	+	36.8915i	1.24220	+	2.15156i
$295$		0			0
$296$	−7.42717			−0.431695
$297$	20.6699			1.19939
$298$	−3.49395	−	6.05169i	−0.202399	−	0.350565i
$299$	−9.96155	+	17.2539i	−0.576091	+	0.997819i
$300$		0			0
$301$	−1.28981	+	2.23401i	−0.0743433	+	0.128766i
$302$	12.0685	−	20.9032i	0.694463	−	1.20284i
$303$	4.08974			0.234950
$304$	4.35120	+	7.94610i	0.249559	+	0.455740i
$305$		0			0
$306$	32.4589	−	56.2205i	1.85555	−	3.21391i
$307$	8.41257	−	14.5710i	0.480131	−	0.831611i	−0.519609	−	0.854404i	$-0.673923\pi$
$307$	8.41257	−	14.5710i	0.480131	−	0.831611i	0.999740	+	0.0227929i	$0.00725584\pi$
$308$	−2.06805	−	3.58197i	−0.117838	−	0.204102i
$309$	−0.246149	+	0.426342i	−0.0140029	+	0.0242538i
$310$		0			0
$311$	−18.3273			−1.03924			−0.519622	−	0.854396i	$-0.673927\pi$
$311$	−18.3273			−1.03924			−0.519622	+	0.854396i	$0.673927\pi$
$312$	31.1986			1.76627
$313$	11.7527	+	20.3562i	0.664299	+	1.15060i	0.979475	+	0.201567i	$0.0646033\pi$
$313$	11.7527	+	20.3562i	0.664299	+	1.15060i	−0.315176	+	0.949033i	$0.602063\pi$
$314$	−23.2541	−	40.2772i	−1.31230	−	2.27298i
$315$		0			0
$316$	15.9105			0.895036
$317$	1.94177	+	3.36324i	0.109061	+	0.188899i	0.915390	−	0.402568i	$-0.131882\pi$
$317$	1.94177	+	3.36324i	0.109061	+	0.188899i	−0.806329	+	0.591467i	$0.798549\pi$
$318$	30.7207	−	53.2097i	1.72273	−	2.98385i
$319$	−9.09594	−	15.7546i	−0.509275	−	0.882090i
$320$		0			0
$321$	6.66724	−	11.5480i	0.372129	−	0.644546i
$322$	3.72505			0.207589
$323$	10.9613	+	20.0174i	0.609905	+	1.11380i
$324$	17.6219			0.978996
$325$		0			0
$326$	−11.1899	+	19.3815i	−0.619753	+	1.07344i
$327$	15.8062	+	27.3772i	0.874087	+	1.51396i
$328$	−4.79333	+	8.30228i	−0.264667	+	0.458417i
$329$	−0.756923	−	1.31103i	−0.0417305	−	0.0722793i
$330$		0			0
$331$	3.25821			0.179087			0.0895437	−	0.995983i	$-0.471459\pi$
$331$	3.25821			0.179087			0.0895437	+	0.995983i	$0.471459\pi$
$332$	5.44613	+	9.43297i	0.298895	+	0.517702i
$333$	13.7851	+	23.8765i	0.755419	+	1.30842i
$334$	14.1204			0.772635
$335$		0			0
$336$	1.81483	+	3.14338i	0.0990070	+	0.171485i
$337$	11.0987	−	19.2234i	0.604582	−	1.04717i	−0.387535	−	0.921855i	$-0.626673\pi$
$337$	11.0987	−	19.2234i	0.604582	−	1.04717i	0.992117	−	0.125312i	$-0.0399933\pi$
$338$	−37.0551	−	64.1813i	−2.01553	−	3.49100i
$339$	−19.4921	+	33.7612i	−1.05866	+	1.83366i
$340$		0			0
$341$	−17.5837			−0.952213
$342$	−28.0741	+	46.1823i	−1.51807	+	2.49725i
$343$	−8.07560			−0.436042
$344$	−3.35563	+	5.81212i	−0.180923	+	0.313369i
$345$		0			0
$346$	−6.79296	−	11.7658i	−0.365192	−	0.632531i
$347$	1.49728	−	2.59336i	0.0803780	−	0.139219i	−0.823034	−	0.567992i	$-0.807721\pi$
$347$	1.49728	−	2.59336i	0.0803780	−	0.139219i	0.903412	+	0.428773i	$0.141054\pi$
$348$	−28.1905	−	48.8274i	−1.51117	−	2.61743i
$349$	15.1407			0.810461			0.405230	−	0.914215i	$-0.367191\pi$
$349$	15.1407			0.810461			0.405230	+	0.914215i	$0.367191\pi$
$350$		0			0
$351$	−27.5015	−	47.6340i	−1.46792	−	2.54251i
$352$	9.79106	+	16.9586i	0.521865	+	0.903897i
$353$	−34.4369			−1.83289			−0.916446	−	0.400159i	$-0.868955\pi$
$353$	−34.4369			−1.83289			−0.916446	+	0.400159i	$0.868955\pi$
$354$	−18.7334			−0.995668
$355$		0			0
$356$	−5.03446	+	8.71994i	−0.266826	+	0.462156i
$357$	4.57182	+	7.91863i	0.241967	+	0.419098i
$358$	−25.1614	+	43.5808i	−1.32982	+	2.30332i
$359$	−1.58165	+	2.73950i	−0.0834763	+	0.144585i	−0.904741	−	0.425962i	$-0.859936\pi$
$359$	−1.58165	+	2.73950i	−0.0834763	+	0.144585i	0.821265	+	0.570548i	$0.193269\pi$
$360$		0			0
$361$	−8.74655	−	16.8671i	−0.460345	−	0.887740i
$362$	−6.94204			−0.364865
$363$	6.40744	−	11.0980i	0.336304	−	0.582495i
$364$	−5.50314	+	9.53171i	−0.288443	+	0.499597i
$365$		0			0
$366$	−7.46829	+	12.9354i	−0.390374	+	0.676147i
$367$	−10.7270	−	18.5797i	−0.559945	−	0.969853i	−0.997500	−	0.0706615i	$-0.977489\pi$
$367$	−10.7270	−	18.5797i	−0.559945	−	0.969853i	0.437556	−	0.899191i	$-0.355844\pi$
$368$	−6.03027			−0.314350
$369$	35.5864			1.85255
$370$		0			0
$371$	2.83725	+	4.91426i	0.147303	+	0.255136i
$372$	−54.4963			−2.82550
$373$	−33.1587			−1.71689			−0.858446	−	0.512904i	$-0.828570\pi$
$373$	−33.1587			−1.71689			−0.858446	+	0.512904i	$0.828570\pi$
$374$	14.6596	+	25.3911i	0.758028	+	1.31294i
$375$		0			0
$376$	−1.96925	−	3.41084i	−0.101556	−	0.175901i
$377$	−24.2045	+	41.9234i	−1.24660	+	2.15917i
$378$	−5.14199	+	8.90619i	−0.264476	+	0.458085i
$379$	−14.1646			−0.727589			−0.363795	−	0.931479i	$-0.618519\pi$
$379$	−14.1646			−0.727589			−0.363795	+	0.931479i	$0.618519\pi$
$380$		0			0
$381$	5.08198			0.260358
$382$	−20.5554	+	35.6030i	−1.05171	+	1.82161i
$383$	−5.41036	+	9.37102i	−0.276457	+	0.478837i	−0.970502	−	0.241095i	$-0.922494\pi$
$383$	−5.41036	+	9.37102i	−0.276457	+	0.478837i	0.694045	+	0.719932i	$0.255827\pi$
$384$	17.0311	+	29.4988i	0.869117	+	1.50535i
$385$		0			0
$386$	1.11818	+	1.93674i	0.0569138	+	0.0985775i
$387$	24.9127			1.26638
$388$	6.84281			0.347391
$389$	−5.38703	−	9.33061i	−0.273133	−	0.473081i	0.696529	−	0.717529i	$-0.254727\pi$
$389$	−5.38703	−	9.33061i	−0.273133	−	0.473081i	−0.969662	+	0.244448i	$0.921393\pi$
$390$		0			0
$391$	−15.1912			−0.768250
$392$	−10.2356			−0.516975
$393$	−4.84702	−	8.39529i	−0.244500	−	0.423486i
$394$	20.1291	−	34.8647i	1.01409	−	1.75646i
$395$		0			0
$396$	−19.9723	+	34.5930i	−1.00364	+	1.73836i
$397$	1.55107	−	2.68653i	0.0778461	−	0.134833i	−0.824474	−	0.565899i	$-0.808529\pi$
$397$	1.55107	−	2.68653i	0.0778461	−	0.134833i	0.902320	+	0.431066i	$0.141862\pi$
$398$	49.1162			2.46197
$399$	−3.65617	−	6.67683i	−0.183037	−	0.334260i
$400$		0			0
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	−0.689513	−	0.724273i	$-0.742175\pi$
$401$	5.65671	−	9.79771i	0.282483	−	0.489274i	0.971996	+	0.234999i	$0.0755088\pi$
$402$	−13.7804	+	23.8683i	−0.687303	+	1.19044i
$403$	23.3954	+	40.5220i	1.16541	+	2.01854i
$404$	−1.87681	+	3.25074i	−0.0933749	+	0.161730i
$405$		0			0
$406$	9.05110			0.449199
$407$	−12.4517			−0.617206
$408$	11.8943	+	20.6015i	0.588855	+	1.01993i
$409$	−7.11186	−	12.3181i	−0.351659	−	0.609091i	0.634882	−	0.772609i	$-0.281049\pi$
$409$	−7.11186	−	12.3181i	−0.351659	−	0.609091i	−0.986540	+	0.163519i	$0.947716\pi$
$410$		0			0
$411$	24.0602			1.18680
$412$	−0.225919	−	0.391303i	−0.0111302	−	0.0192781i
$413$	0.865075	−	1.49835i	0.0425675	−	0.0737291i
$414$	−17.9874	−	31.1551i	−0.884032	−	1.53119i
$415$		0			0
$416$	26.0542	−	45.1272i	1.27741	−	2.21255i
$417$	−46.1320			−2.25909
$418$	−11.7235	−	21.4093i	−0.573416	−	1.04716i
$419$	−11.0053			−0.537643			−0.268821	−	0.963190i	$-0.586634\pi$
$419$	−11.0053			−0.537643			−0.268821	+	0.963190i	$0.586634\pi$
$420$		0			0
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	−0.438963	−	0.898505i	$-0.644654\pi$
$421$	11.4625	−	19.8536i	0.558646	−	0.967604i	0.997610	−	0.0690991i	$-0.0220125\pi$
$422$	−13.4975	−	23.3783i	−0.657046	−	1.13804i
$423$	−7.31000	+	12.6613i	−0.355424	+	0.615613i
$424$	7.38154	+	12.7852i	0.358479	+	0.620904i
$425$		0			0
$426$	−86.4332			−4.18770
$427$	−0.689744	−	1.19467i	−0.0333791	−	0.0578142i
$428$	6.11929	+	10.5989i	0.295787	+	0.512318i
$429$	52.3045			2.52528
$430$		0			0
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	0.994816	−	0.101693i	$-0.0324258\pi$
$431$	8.49811	+	14.7192i	0.409340	+	0.708997i	−0.585476	+	0.810690i	$0.699092\pi$
$432$	8.32408	−	14.4177i	0.400492	−	0.693673i
$433$	−15.7493	−	27.2786i	−0.756863	−	1.31093i	−0.944443	−	0.328676i	$-0.893398\pi$
$433$	−15.7493	−	27.2786i	−0.756863	−	1.31093i	0.187580	−	0.982249i	$-0.439936\pi$
$434$	4.37427	−	7.57645i	0.209972	−	0.363681i
$435$		0			0
$436$	−29.0144			−1.38954
$437$	12.6438	+	0.285896i	0.604836	+	0.0136763i
$438$	−53.9802			−2.57928
$439$	−1.57963	+	2.73600i	−0.0753916	+	0.130582i	−0.901256	−	0.433286i	$-0.857354\pi$
$439$	−1.57963	+	2.73600i	−0.0753916	+	0.130582i	0.825865	+	0.563868i	$0.190687\pi$
$440$		0			0
$441$	18.9976	+	32.9049i	0.904649	+	1.56690i
$442$	39.0095	−	67.5664i	1.85549	−	3.21380i
$443$	5.94720	+	10.3008i	0.282560	+	0.489408i	0.972015	−	0.234921i	$-0.0754831\pi$
$443$	5.94720	+	10.3008i	0.282560	+	0.489408i	−0.689455	+	0.724329i	$0.742150\pi$
$444$	−38.5907			−1.83143
$445$		0			0
$446$	20.8036	+	36.0329i	0.985080	+	1.70621i
$447$	−4.75267	−	8.23186i	−0.224794	−	0.389354i
$448$	−7.28358			−0.344117
$449$	21.2175			1.00132			0.500659	−	0.865645i	$-0.333091\pi$
$449$	21.2175			1.00132			0.500659	+	0.865645i	$0.333091\pi$
$450$		0			0
$451$	−8.03602	+	13.9188i	−0.378401	+	0.655410i
$452$	−17.8901	−	30.9865i	−0.841479	−	1.45748i
$453$	16.4162	−	28.4338i	0.771302	−	1.33593i
$454$	28.7762	−	49.8418i	1.35053	−	2.33919i
$455$		0			0
$456$	−9.51208	−	17.3708i	−0.445444	−	0.813462i
$457$	−9.41670			−0.440495			−0.220247	−	0.975444i	$-0.570686\pi$
$457$	−9.41670			−0.440495			−0.220247	+	0.975444i	$0.570686\pi$
$458$	9.55948	−	16.5575i	0.446685	−	0.773682i
$459$	20.9696	−	36.3204i	0.978777	−	1.69529i
$460$		0			0
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	−0.891775	−	0.452480i	$-0.850539\pi$
$461$	−1.16004	+	2.00924i	−0.0540282	+	0.0935797i	0.837746	+	0.546060i	$0.183873\pi$
$462$	−4.88972	−	8.46924i	−0.227490	−	0.394025i
$463$	−14.7160			−0.683909			−0.341955	−	0.939716i	$-0.611089\pi$
$463$	−14.7160			−0.683909			−0.341955	+	0.939716i	$0.611089\pi$
$464$	−14.6523			−0.680217
$465$		0			0
$466$	4.89606	+	8.48023i	0.226806	+	0.392839i
$467$	11.7747			0.544867			0.272434	−	0.962175i	$-0.412172\pi$
$467$	11.7747			0.544867			0.272434	+	0.962175i	$0.412172\pi$
$468$	106.293			4.91341
$469$	−1.27271	−	2.20439i	−0.0587681	−	0.101789i
$470$		0			0
$471$	−31.6316	−	54.7875i	−1.45751	−	2.52447i
$472$	2.25062	−	3.89819i	0.103593	−	0.179429i
$473$	−5.62572	+	9.74403i	−0.258671	+	0.448031i
$474$	37.6189			1.72789
$475$		0			0
$476$	−8.39217			−0.384655
$477$	27.4008	−	47.4596i	1.25460	−	2.17303i
$478$	8.48971	−	14.7046i	0.388310	−	0.672573i
$479$	−5.69219	−	9.85915i	−0.260083	−	0.450476i	0.706181	−	0.708031i	$-0.250416\pi$
$479$	−5.69219	−	9.85915i	−0.260083	−	0.450476i	−0.966264	+	0.257555i	$0.917083\pi$
$480$		0			0
$481$	16.5671	+	28.6950i	0.755394	+	1.30838i
$482$	59.3288			2.70235
$483$	5.06703			0.230558
$484$	5.88084	+	10.1859i	0.267311	+	0.462996i
$485$		0			0
$486$	−10.4829			−0.475513
$487$	4.77063			0.216178			0.108089	−	0.994141i	$-0.465527\pi$
$487$	4.77063			0.216178			0.108089	+	0.994141i	$0.465527\pi$
$488$	−1.79447	−	3.10812i	−0.0812321	−	0.140698i
$489$	−15.2212	+	26.3639i	−0.688326	+	1.19222i
$490$		0			0
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	−0.803904	−	0.594758i	$-0.797248\pi$
$491$	2.50665	−	4.34165i	0.113124	−	0.195936i	0.917028	+	0.398822i	$0.130581\pi$
$492$	−24.9056	+	43.1377i	−1.12283	+	1.94480i
$493$	−36.9114			−1.66240
$494$	−33.7397	+	55.5023i	−1.51802	+	2.49717i
$495$		0			0
$496$	−7.08125	+	12.2651i	−0.317958	+	0.550719i
$497$	3.99133	−	6.91319i	0.179036	−	0.310099i
$498$	12.8769	+	22.3034i	0.577026	+	0.999439i
$499$	−10.9112	+	18.8987i	−0.488450	+	0.846021i	−0.999912	−	0.0132853i	$-0.995771\pi$
$499$	−10.9112	+	18.8987i	−0.488450	+	0.846021i	0.511461	+	0.859306i	$0.329104\pi$
$500$		0			0
$501$	19.2074			0.858124
$502$	−35.2372			−1.57272
$503$	7.58583	+	13.1391i	0.338236	+	0.585841i	0.984101	−	0.177610i	$-0.0568366\pi$
$503$	7.58583	+	13.1391i	0.338236	+	0.585841i	−0.645865	+	0.763451i	$0.723503\pi$
$504$	−2.60144	−	4.50582i	−0.115877	−	0.200705i
$505$		0			0
$506$	16.2475			0.722288
$507$	−50.4045	−	87.3031i	−2.23854	−	3.87727i
$508$	−2.33216	+	4.03941i	−0.103473	+	0.179220i
$509$	−2.59122	−	4.48812i	−0.114854	−	0.198933i	0.802868	−	0.596157i	$-0.203307\pi$
$509$	−2.59122	−	4.48812i	−0.114854	−	0.198933i	−0.917721	+	0.397225i	$0.869973\pi$
$510$		0			0
$511$	2.49271	−	4.31750i	0.110271	−	0.190995i
$512$	22.1701			0.979789
$513$	−18.1368	+	29.8354i	−0.800761	+	1.31726i
$514$	−19.8421			−0.875199
$515$		0			0
$516$	−17.4355	+	30.1991i	−0.767554	+	1.32944i
$517$	−3.30145	−	5.71828i	−0.145198	−	0.251490i
$518$	3.09757	−	5.36515i	0.136099	−	0.235731i
$519$	−9.24018	−	16.0045i	−0.405599	−	0.702518i
$520$		0			0
$521$	11.2091			0.491079			0.245540	−	0.969387i	$-0.421035\pi$
$521$	11.2091			0.491079			0.245540	+	0.969387i	$0.421035\pi$
$522$	−43.7056	−	75.7004i	−1.91294	−	3.31332i
$523$	−2.71940	−	4.71014i	−0.118911	−	0.205960i	0.800425	−	0.599433i	$-0.204607\pi$
$523$	−2.71940	−	4.71014i	−0.118911	−	0.205960i	−0.919336	+	0.393472i	$0.871274\pi$
$524$	8.89733			0.388682
$525$		0			0
$526$	16.5982	+	28.7488i	0.723714	+	1.25351i
$527$	−17.8387	+	30.8976i	−0.777067	+	1.34592i
$528$	7.91569	+	13.7104i	0.344486	+	0.596668i
$529$	7.29084	−	12.6281i	0.316993	−	0.549048i
$530$		0			0
$531$	−16.7090			−0.725107
$532$	6.98492	+	0.157940i	0.302835	+	0.00684756i
$533$	42.7680			1.85249
$534$	−11.9035	+	20.6175i	−0.515116	+	0.892206i
$535$		0			0
$536$	−3.31114	−	5.73506i	−0.143019	−	0.247717i
$537$	−34.2260	+	59.2811i	−1.47696	+	2.55817i
$538$	15.3498	+	26.5866i	0.661776	+	1.14623i
$539$	−17.1600			−0.739132
$540$		0			0
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	0.670689	−	0.741739i	$-0.265999\pi$
$541$	−7.14111	−	12.3688i	−0.307020	−	0.531775i	−0.977709	+	0.209964i	$0.932665\pi$
$542$	12.3295	+	21.3554i	0.529598	+	0.917291i
$543$	−9.44296			−0.405236
$544$	39.7322			1.70350
$545$		0			0
$546$	−13.0117	+	22.5369i	−0.556848	+	0.964488i
$547$	12.5122	+	21.6717i	0.534982	+	0.926616i	0.999164	+	0.0408766i	$0.0130151\pi$
$547$	12.5122	+	21.6717i	0.534982	+	0.926616i	−0.464182	+	0.885740i	$0.653652\pi$
$548$	−11.0414	+	19.1243i	−0.471666	+	0.816949i
$549$	−6.66122	+	11.5376i	−0.284294	+	0.492412i
$550$		0			0
$551$	30.7219	+	0.694668i	1.30880	+	0.0295939i
$552$	13.1827			0.561091
$553$	−1.73718	+	3.00888i	−0.0738722	+	0.127950i
$554$	−20.5184	+	35.5388i	−0.871741	+	1.50990i
$555$		0			0
$556$	21.1703	−	36.6680i	0.897821	−	1.55507i
$557$	3.57846	+	6.19807i	0.151624	+	0.262621i	0.931825	−	0.362909i	$-0.118216\pi$
$557$	3.57846	+	6.19807i	0.151624	+	0.262621i	−0.780201	+	0.625529i	$0.784883\pi$
$558$	−84.4892			−3.57671
$559$	29.9403			1.26634
$560$		0			0
$561$	19.9408	+	34.5385i	0.841901	+	1.45822i
$562$	−60.5184			−2.55282
$563$	28.9386			1.21962			0.609809	−	0.792548i	$-0.291246\pi$
$563$	28.9386			1.21962			0.609809	+	0.792548i	$0.291246\pi$
$564$	−10.2320	−	17.7223i	−0.430845	−	0.746245i
$565$		0			0
$566$	−15.6202	−	27.0551i	−0.656568	−	1.13721i
$567$	−1.92403	+	3.33253i	−0.0808019	+	0.139953i
$568$	10.3841	−	17.9857i	0.435706	−	0.754664i
$569$	38.8864			1.63020			0.815100	−	0.579320i	$-0.196682\pi$
$569$	38.8864			1.63020			0.815100	+	0.579320i	$0.196682\pi$
$570$		0			0
$571$	15.1613			0.634480			0.317240	−	0.948345i	$-0.397244\pi$
$571$	15.1613			0.634480			0.317240	+	0.948345i	$0.397244\pi$
$572$	−24.0029	+	41.5742i	−1.00361	+	1.73831i
$573$	−27.9607	+	48.4293i	−1.16807	+	2.02316i
$574$	−3.99820	−	6.92509i	−0.166882	−	0.289048i
$575$		0			0
$576$	35.1707	+	60.9174i	1.46544	+	2.53822i
$577$	20.6412			0.859303			0.429651	−	0.902995i	$-0.358636\pi$
$577$	20.6412			0.859303			0.429651	+	0.902995i	$0.358636\pi$
$578$	22.5972			0.939918
$579$	1.52101	+	2.63447i	0.0632111	+	0.109485i
$580$		0			0
$581$	−2.37852			−0.0986778
$582$	16.1792			0.670649
$583$	12.3752	+	21.4344i	0.512527	+	0.887723i
$584$	6.48517	−	11.2326i	0.268358	−	0.464810i
$585$		0			0
$586$	−2.85560	+	4.94604i	−0.117964	+	0.204319i
$587$	−3.58942	+	6.21706i	−0.148151	+	0.256606i	−0.930544	−	0.366180i	$-0.880666\pi$
$587$	−3.58942	+	6.21706i	−0.148151	+	0.256606i	0.782393	+	0.622785i	$0.213999\pi$
$588$	−53.1829			−2.19323
$589$	15.4289	−	25.3808i	0.635738	−	1.04580i
$590$		0			0
$591$	27.3808	−	47.4250i	1.12630	−	1.95080i
$592$	−5.01448	+	8.68533i	−0.206094	+	0.356965i
$593$	−18.3743	−	31.8253i	−0.754543	−	1.30691i	−0.945601	−	0.325328i	$-0.894525\pi$
$593$	−18.3743	−	31.8253i	−0.754543	−	1.30691i	0.191058	−	0.981579i	$-0.438808\pi$
$594$	−22.4277	+	38.8459i	−0.920219	+	1.59387i
$595$		0			0
$596$	8.72413			0.357354
$597$	66.8107			2.73438
$598$	−21.6174	−	37.4425i	−0.884002	−	1.53114i
$599$	0.926876	+	1.60540i	0.0378711	+	0.0655947i	0.884340	−	0.466844i	$-0.154609\pi$
$599$	0.926876	+	1.60540i	0.0378711	+	0.0655947i	−0.846469	+	0.532439i	$0.821276\pi$
$600$		0			0
$601$	−38.1633			−1.55671			−0.778356	−	0.627823i	$-0.783946\pi$
$601$	−38.1633			−1.55671			−0.778356	+	0.627823i	$0.783946\pi$
$602$	−2.79899	−	4.84800i	−0.114078	−	0.197590i
$603$	−12.2912	+	21.2890i	−0.500536	+	0.866954i
$604$	15.0671	+	26.0969i	0.613070	+	1.06187i
$605$		0			0
$606$	−4.43755	+	7.68606i	−0.180263	+	0.312225i
$607$	7.44914			0.302351			0.151176	−	0.988507i	$-0.451694\pi$
$607$	7.44914			0.302351			0.151176	+	0.988507i	$0.451694\pi$
$608$	−33.0696	−	0.747755i	−1.34115	−	0.0303255i
$609$	12.3118			0.498901
$610$		0			0
$611$	−8.78523	+	15.2165i	−0.355412	+	0.615592i
$612$	40.5238	+	70.1893i	1.63808	+	2.83723i
$613$	10.6049	−	18.3682i	0.428326	−	0.741883i	−0.568398	−	0.822754i	$-0.692437\pi$
$613$	10.6049	−	18.3682i	0.428326	−	0.741883i	0.996725	+	0.0808706i	$0.0257700\pi$
$614$	18.2560	+	31.6203i	0.736753	+	1.27609i
$615$		0			0
$616$	2.34980			0.0946760
$617$	15.4076	+	26.6868i	0.620287	+	1.07437i	0.989432	+	0.144997i	$0.0463172\pi$
$617$	15.4076	+	26.6868i	0.620287	+	1.07437i	−0.369145	+	0.929372i	$0.620349\pi$
$618$	−0.534164	−	0.925199i	−0.0214872	−	0.0372170i
$619$	7.32036			0.294230			0.147115	−	0.989119i	$-0.453001\pi$
$619$	7.32036			0.294230			0.147115	+	0.989119i	$0.453001\pi$
$620$		0			0
$621$	−11.6205	−	20.1273i	−0.466314	−	0.807680i
$622$	19.8859	−	34.4434i	0.797352	−	1.38105i
$623$	−1.09937	−	1.90416i	−0.0440452	−	0.0762885i
$624$	21.0638	−	36.4836i	0.843228	−	1.46051i
$625$		0			0
$626$	−51.0086			−2.03871
$627$	−15.9470	−	29.1222i	−0.636862	−	1.16303i
$628$	58.0638			2.31700
$629$	−12.6322	+	21.8797i	−0.503680	+	0.872399i
$630$		0			0
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	0.817664	−	0.575696i	$-0.195269\pi$
$631$	−2.25414	−	3.90429i	−0.0897360	−	0.155427i	−0.907399	+	0.420269i	$0.861936\pi$
$632$	−4.51953	+	7.82805i	−0.179777	+	0.311383i
$633$	−18.3600	−	31.8005i	−0.729746	−	1.26396i
$634$	−8.42762			−0.334704
$635$		0			0
$636$	38.3536	+	66.4305i	1.52082	+	2.63414i
$637$	22.8315	+	39.5454i	0.904618	+	1.56685i
$638$	39.4780			1.56295
$639$	−77.0928			−3.04975
$640$		0			0
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	−0.648483	−	0.761229i	$-0.724596\pi$
$641$	8.48158	−	14.6905i	0.335002	−	0.580241i	0.983485	+	0.180988i	$0.0579296\pi$
$642$	14.4685	+	25.0602i	0.571026	+	0.989046i
$643$	−4.64306	+	8.04202i	−0.183104	+	0.317146i	−0.942936	−	0.332974i	$-0.891948\pi$
$643$	−4.64306	+	8.04202i	−0.183104	+	0.317146i	0.759832	+	0.650120i	$0.225281\pi$
$644$	−2.32530	+	4.02753i	−0.0916295	+	0.158707i
$645$		0			0
$646$	−49.5132	−	1.11957i	−1.94807	−	0.0440489i
$647$	39.2779			1.54418			0.772088	−	0.635516i	$-0.219213\pi$
$647$	39.2779			1.54418			0.772088	+	0.635516i	$0.219213\pi$
$648$	−5.00567	+	8.67007i	−0.196641	+	0.340593i
$649$	3.77317	−	6.53533i	0.148110	−	0.256534i
$650$		0			0
$651$	5.95013	−	10.3059i	0.233204	−	0.403921i
$652$	−13.9702	−	24.1972i	−0.547116	−	0.947634i
$653$	26.5513			1.03903			0.519517	−	0.854460i	$-0.326112\pi$
$653$	26.5513			1.03903			0.519517	+	0.854460i	$0.326112\pi$
$654$	−68.6018			−2.68254
$655$		0			0
$656$	6.47246	+	11.2106i	0.252707	+	0.437702i
$657$	−48.1469			−1.87839
$658$	3.28518			0.128069
$659$	−16.3143	−	28.2573i	−0.635517	−	1.10075i	−0.986405	−	0.164330i	$-0.947454\pi$
$659$	−16.3143	−	28.2573i	−0.635517	−	1.10075i	0.350889	−	0.936417i	$-0.385880\pi$
$660$		0			0
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	0.798634	−	0.601817i	$-0.205556\pi$
$661$	−3.13332	−	5.42707i	−0.121872	−	0.211088i	−0.920506	+	0.390729i	$0.872223\pi$
$662$	−3.53530	+	6.12332i	−0.137403	+	0.237989i
$663$	53.0629	−	91.9077i	2.06079	−	3.56940i
$664$	−6.18809			−0.240145
$665$		0			0
$666$	−59.8297			−2.31836
$667$	−10.2274	+	17.7143i	−0.396006	+	0.685902i
$668$	−8.81442	+	15.2670i	−0.341040	+	0.590699i
$669$	28.2983	+	49.0141i	1.09408	+	1.89499i
$670$		0			0
$671$	−3.00844	−	5.21077i	−0.116140	−	0.201160i
$672$	−13.2527			−0.511235
$673$	−7.39044			−0.284881			−0.142440	−	0.989803i	$-0.545495\pi$
$673$	−7.39044			−0.284881			−0.142440	+	0.989803i	$0.545495\pi$
$674$	24.0850	+	41.7165i	0.927721	+	1.60686i
$675$		0			0
$676$	92.5238			3.55861
$677$	−20.2751			−0.779234			−0.389617	−	0.920977i	$-0.627393\pi$
$677$	−20.2751			−0.779234			−0.389617	+	0.920977i	$0.627393\pi$
$678$	−42.2994	−	73.2648i	−1.62450	−	2.81372i
$679$	−0.747127	+	1.29406i	−0.0286721	+	0.0496615i
$680$		0			0
$681$	39.1431	−	67.7978i	1.49997	−	2.59802i
$682$	19.0791	−	33.0460i	0.730577	−	1.26540i
$683$	24.6563			0.943448			0.471724	−	0.881746i	$-0.343632\pi$
$683$	24.6563			0.943448			0.471724	+	0.881746i	$0.343632\pi$
$684$	−32.4076	−	59.1822i	−1.23914	−	2.26289i
$685$		0			0
$686$	8.76238	−	15.1769i	0.334549	−	0.579456i
$687$	13.0034	−	22.5225i	0.496109	−	0.859286i
$688$	4.53113	+	7.84815i	0.172748	+	0.299208i
$689$	32.9306	−	57.0374i	1.25456	−	2.17295i
$690$		0			0
$691$	−41.7299			−1.58748			−0.793739	−	0.608258i	$-0.791869\pi$
$691$	−41.7299			−1.58748			−0.793739	+	0.608258i	$0.791869\pi$
$692$	16.9615			0.644781
$693$	−4.36131	−	7.55402i	−0.165673	−	0.286953i
$694$	3.24922	+	5.62782i	0.123339	+	0.213629i
$695$		0			0
$696$	32.0311			1.21414
$697$	16.3051	+	28.2413i	0.617600	+	1.06971i
$698$	−16.4283	+	28.4546i	−0.621819	+	1.07702i
$699$	6.65991	+	11.5353i	0.251901	+	0.436305i
$700$		0			0
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	−0.789801	−	0.613363i	$-0.789816\pi$
$701$	3.60840	−	6.24993i	0.136287	−	0.236057i	0.926089	+	0.377306i	$0.123150\pi$
$702$	119.361			4.50500
$703$	10.9258	−	17.9730i	0.412073	−	0.677865i
$704$	−31.7686			−1.19732
$705$		0			0
$706$	37.3655	−	64.7190i	1.40627	−	2.43573i
$707$	−0.409836	−	0.709857i	−0.0154135	−	0.0266969i
$708$	11.6940	−	20.2546i	0.439487	−	0.761213i
$709$	10.3172	+	17.8700i	0.387472	+	0.671122i	0.992109	−	0.125380i	$-0.0400149\pi$
$709$	10.3172	+	17.8700i	0.387472	+	0.671122i	−0.604636	+	0.796502i	$0.706682\pi$
$710$		0			0
$711$	33.5536			1.25836
$712$	−2.86017	−	4.95396i	−0.107189	−	0.185657i
$713$	9.88549	+	17.1222i	0.370214	+	0.641230i
$714$	−19.8425			−0.742587
$715$		0			0
$716$	−31.4131	−	54.4091i	−1.17396	−	2.03336i
$717$	11.5482	−	20.0021i	0.431275	−	0.746991i
$718$	−3.43232	−	5.94495i	−0.128093	−	0.221864i
$719$	−0.748958	+	1.29723i	−0.0279314	+	0.0483787i	−0.879653	−	0.475616i	$-0.842225\pi$
$719$	−0.748958	+	1.29723i	−0.0279314	+	0.0483787i	0.851722	+	0.523994i	$0.175559\pi$
$720$		0			0
$721$	0.0986670			0.00367455
$722$	41.1895	+	1.86367i	1.53291	+	0.0693585i
$723$	80.7024			3.00136
$724$	4.33344	−	7.50574i	0.161051	−	0.278949i
$725$		0			0
$726$	13.9047	+	24.0837i	0.516052	+	0.893828i
$727$	5.68222	−	9.84190i	0.210742	−	0.365016i	−0.741205	−	0.671279i	$-0.765745\pi$
$727$	5.68222	−	9.84190i	0.210742	−	0.365016i	0.951947	+	0.306263i	$0.0990787\pi$
$728$	−3.12643	−	5.41514i	−0.115873	−	0.200698i
$729$	−33.7723			−1.25083
$730$		0			0
$731$	11.4146	+	19.7707i	0.422184	+	0.731244i
$732$	−9.32389	−	16.1494i	−0.344621	−	0.596901i
$733$	45.6910			1.68764			0.843818	−	0.536630i	$-0.180303\pi$
$733$	45.6910			1.68764			0.843818	+	0.536630i	$0.180303\pi$
$734$	46.5570			1.71845
$735$		0			0
$736$	11.0090	−	19.0681i	0.405796	−	0.702859i
$737$	−5.55113	−	9.61484i	−0.204479	−	0.354167i
$738$	−38.6127	+	66.8792i	−1.42135	+	2.46186i
$739$	1.78276	−	3.08783i	0.0655799	−	0.113588i	−0.831371	−	0.555718i	$-0.812444\pi$
$739$	1.78276	−	3.08783i	0.0655799	−	0.113588i	0.896951	+	0.442130i	$0.145777\pi$
$740$		0			0
$741$	−45.8947	+	75.4975i	−1.68599	+	2.77347i
$742$	−12.3142			−0.452067
$743$	−21.2482	+	36.8030i	−0.779522	+	1.35017i	0.152696	+	0.988273i	$0.451205\pi$
$743$	−21.2482	+	36.8030i	−0.779522	+	1.35017i	−0.932218	+	0.361898i	$0.882129\pi$
$744$	15.4802	−	26.8125i	0.567531	−	0.982992i
$745$		0			0
$746$	35.9786	−	62.3168i	1.31727	−	2.28158i
$747$	11.4853	+	19.8932i	0.420226	+	0.727853i
$748$	−36.6039			−1.33837
$749$	−2.67252			−0.0976516
$750$		0			0
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	0.958697	−	0.284431i	$-0.0918045\pi$
$751$	6.38588	+	11.0607i	0.233024	+	0.403610i	−0.725672	+	0.688040i	$0.758471\pi$
$752$	−5.31818			−0.193934
$753$	−47.9317			−1.74673
$754$	−52.5259	−	90.9775i	−1.91288	−	3.31320i
$755$		0			0
$756$	−6.41960	−	11.1191i	−0.233478	−	0.404396i
$757$	5.67306	−	9.82603i	0.206191	−	0.357133i	−0.744321	−	0.667822i	$-0.767227\pi$
$757$	5.67306	−	9.82603i	0.206191	−	0.357133i	0.950512	+	0.310689i	$0.100560\pi$
$758$	15.3693	−	26.6203i	0.558237	−	0.966894i
$759$	22.1007			0.802206
$760$		0			0
$761$	−36.9214			−1.33840			−0.669199	−	0.743083i	$-0.733363\pi$
$761$	−36.9214			−1.33840			−0.669199	+	0.743083i	$0.733363\pi$
$762$	−5.51417	+	9.55082i	−0.199757	+	0.345990i
$763$	3.16791	−	5.48698i	0.114686	−	0.198642i
$764$	−25.6627	−	44.4491i	−0.928444	−	1.60811i
$765$		0			0
$766$	−11.7410	−	20.3359i	−0.424218	−	0.734767i
$767$	−20.0810			−0.725083
$768$	−1.23551			−0.0445827
$769$	−14.2528	−	24.6866i	−0.513971	−	0.890223i	−0.999869	−	0.0162076i	$-0.994841\pi$
$769$	−14.2528	−	24.6866i	−0.513971	−	0.890223i	0.485898	−	0.874015i	$-0.338493\pi$
$770$		0			0
$771$	−26.9904			−0.972036
$772$	−2.79201			−0.100487
$773$	7.60956	+	13.1801i	0.273697	+	0.474057i	0.969805	−	0.243880i	$-0.0784202\pi$
$773$	7.60956	+	13.1801i	0.273697	+	0.474057i	−0.696109	+	0.717936i	$0.745087\pi$
$774$	−27.0314	+	46.8197i	−0.971622	+	1.68290i
$775$		0			0
$776$	−1.94376	+	3.36670i	−0.0697770	+	0.120857i
$777$	4.21350	−	7.29799i	0.151158	−	0.261814i
$778$	23.3807			0.838237
$779$	−13.0395	−	23.8125i	−0.467188	−	0.853170i
$780$		0			0
$781$	17.4089	−	30.1531i	0.622939	−	1.07896i
$782$	16.4831	−	28.5495i	0.589433	−	1.02093i
$783$	−28.2354	−	48.9051i	−1.00905	−	1.74773i
$784$	−6.91059	+	11.9695i	−0.246807	+	0.427482i
$785$		0			0
$786$	21.0369			0.750362
$787$	−46.5712			−1.66008			−0.830042	−	0.557700i	$-0.811684\pi$
$787$	−46.5712			−1.66008			−0.830042	+	0.557700i	$0.811684\pi$
$788$	25.1305	+	43.5273i	0.895237	+	1.55060i
$789$	22.5778	+	39.1059i	0.803790	+	1.39221i
$790$		0			0
$791$	7.81325			0.277807
$792$	−11.3466	−	19.6529i	−0.403184	−	0.698336i
$793$	−8.00553	+	13.8660i	−0.284285	+	0.492395i
$794$	3.36596	+	5.83001i	0.119453	+	0.206899i
$795$		0			0
$796$	−30.6599	+	53.1045i	−1.08671	+	1.88224i
$797$	−8.32080			−0.294738			−0.147369	−	0.989082i	$-0.547080\pi$
$797$	−8.32080			−0.294738			−0.147369	+	0.989082i	$0.547080\pi$
$798$	16.5152	+	0.373434i	0.584632	+	0.0132194i
$799$	−13.3973			−0.473962
$800$		0			0
$801$	−10.6172	+	18.3895i	−0.375139	+	0.649760i
$802$	12.2755	+	21.2619i	0.433465	+	0.750783i
$803$	10.8724	−	18.8315i	0.383678	−	0.664551i
$804$	−17.2043	−	29.7987i	−0.606749	−	1.05092i
$805$		0			0
$806$	−101.540			−3.57659
$807$	20.8796	+	36.1646i	0.734998	+	1.27305i
$808$	−1.06625	−	1.84680i	−0.0375106	−	0.0649703i
$809$	−14.2469			−0.500893			−0.250447	−	0.968130i	$-0.580577\pi$
$809$	−14.2469			−0.500893			−0.250447	+	0.968130i	$0.580577\pi$
$810$		0			0
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	0.995816	+	0.0913794i	$0.0291276\pi$
$811$	16.4331	+	28.4630i	0.577045	+	0.999471i	−0.418771	+	0.908092i	$0.637539\pi$
$812$	−5.64999	+	9.78607i	−0.198276	+	0.343424i
$813$	16.7713	+	29.0488i	0.588196	+	1.01879i
$814$	13.5106	−	23.4010i	0.473546	−	0.820206i
$815$		0			0
$816$	32.1219			1.12449
$817$	−9.12845	−	16.6702i	−0.319364	−	0.583218i
$818$	30.8667			1.07923
$819$	−11.6056	+	20.1014i	−0.405531	+	0.702400i
$820$		0			0
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	0.727878	−	0.685706i	$-0.240507\pi$
$821$	−6.58734	−	11.4096i	−0.229900	−	0.398198i	−0.957778	+	0.287508i	$0.907173\pi$
$822$	−26.1064	+	45.2176i	−0.910565	+	1.57714i
$823$	−15.5045	−	26.8545i	−0.540452	−	0.936090i	−0.998878	−	0.0473572i	$-0.984920\pi$
$823$	−15.5045	−	26.8545i	−0.540452	−	0.936090i	0.458426	−	0.888732i	$-0.348413\pi$
$824$	0.256697			0.00894247
$825$		0			0
$826$	1.87729	+	3.25156i	0.0653192	+	0.113136i
$827$	−9.79469	−	16.9649i	−0.340595	−	0.589927i	0.643949	−	0.765069i	$-0.277295\pi$
$827$	−9.79469	−	16.9649i	−0.340595	−	0.589927i	−0.984543	+	0.175141i	$0.943962\pi$
$828$	44.9132			1.56084
$829$	−14.9634			−0.519699			−0.259850	−	0.965649i	$-0.583673\pi$
$829$	−14.9634			−0.519699			−0.259850	+	0.965649i	$0.583673\pi$
$830$		0			0
$831$	−27.9103	+	48.3420i	−0.968196	+	1.67697i
$832$	42.2685	+	73.2111i	1.46539	+	2.53814i
$833$	−17.4088	+	30.1529i	−0.603180	+	1.04474i
$834$	50.0552	−	86.6982i	1.73327	−	3.00211i
$835$		0			0
$836$	30.4660	+	0.688881i	1.05369	+	0.0238255i
$837$	−54.5830			−1.88666
$838$	11.9412	−	20.6828i	0.412502	−	0.714474i
$839$	13.2661	−	22.9776i	0.457997	−	0.793274i	−0.540858	−	0.841114i	$-0.681900\pi$
$839$	13.2661	−	22.9776i	0.457997	−	0.793274i	0.998855	+	0.0478399i	$0.0152337\pi$
$840$		0			0
$841$	−10.3504	+	17.9274i	−0.356911	+	0.618188i
$842$	24.8745	+	43.0840i	0.857233	+	1.48477i
$843$	−82.3207			−2.83528
$844$	33.7022			1.16008
$845$		0			0
$846$	−15.8633	−	27.4761i	−0.545393	−	0.944648i
$847$	−2.56838			−0.0882505
$848$	19.9347			0.684560
$849$	−21.2476	−	36.8019i	−0.729215	−	1.26304i
$850$		0			0
$851$	7.00026	+	12.1248i	0.239966	+	0.415633i
$852$	53.9544	−	93.4518i	1.84845	−	3.20160i
$853$	3.10745	−	5.38226i	0.106397	−	0.184285i	−0.807911	−	0.589304i	$-0.799402\pi$
$853$	3.10745	−	5.38226i	0.106397	−	0.184285i	0.914308	+	0.405019i	$0.132735\pi$
$854$	2.99361			0.102439
$855$		0			0
$856$	−6.95296			−0.237647
$857$	−18.6965	+	32.3832i	−0.638659	+	1.10619i	0.347068	+	0.937840i	$0.387177\pi$
$857$	−18.6965	+	32.3832i	−0.638659	+	1.10619i	−0.985727	+	0.168350i	$0.946156\pi$
$858$	−56.7526	+	98.2984i	−1.93750	+	3.35585i
$859$	21.4745	+	37.1950i	0.732701	+	1.26908i	0.955725	+	0.294263i	$0.0950741\pi$
$859$	21.4745	+	37.1950i	0.732701	+	1.26908i	−0.223023	+	0.974813i	$0.571593\pi$
$860$		0			0
$861$	−5.43859	−	9.41991i	−0.185347	−	0.321030i
$862$	−36.8833			−1.25625
$863$	−37.3005			−1.26972			−0.634862	−	0.772625i	$-0.718943\pi$
$863$	−37.3005			−1.26972			−0.634862	+	0.772625i	$0.718943\pi$
$864$	30.3931	+	52.6425i	1.03400	+	1.79093i
$865$		0			0
$866$	68.3547			2.32279
$867$	30.7380			1.04392
$868$	5.46112	+	9.45893i	0.185362	+	0.321057i
$869$	−7.57699	+	13.1237i	−0.257032	+	0.445192i
$870$		0			0
$871$	−14.7717	+	25.5853i	−0.500519	+	0.866925i
$872$	8.24180	−	14.2752i	0.279103	−	0.483420i
$873$	14.4308			0.488408
$874$	−14.2564	+	23.4520i	−0.482230	+	0.793274i
$875$		0			0
$876$	33.6962	−	58.3635i	1.13849	−	1.97192i
$877$	18.7681	−	32.5073i	0.633754	−	1.09769i	−0.353024	−	0.935614i	$-0.614847\pi$
$877$	18.7681	−	32.5073i	0.633754	−	1.09769i	0.986778	−	0.162079i	$-0.0518200\pi$
$878$	−3.42793	−	5.93735i	−0.115687	−	0.200376i
$879$	−3.88435	+	6.72789i	−0.131016	+	0.226926i
$880$		0			0
$881$	24.1432			0.813404			0.406702	−	0.913561i	$-0.366679\pi$
$881$	24.1432			0.813404			0.406702	+	0.913561i	$0.366679\pi$
$882$	−82.4530			−2.77634
$883$	−15.5062	−	26.8575i	−0.521825	−	0.903827i	−0.999678	−	0.0253873i	$-0.991918\pi$
$883$	−15.5062	−	26.8575i	−0.521825	−	0.903827i	0.477853	−	0.878440i	$-0.341415\pi$
$884$	48.7019	+	84.3542i	1.63802	+	2.83714i
$885$		0			0
$886$	−25.8119			−0.867167
$887$	−18.6066	−	32.2276i	−0.624750	−	1.08210i	−0.988589	−	0.150637i	$-0.951868\pi$
$887$	−18.6066	−	32.2276i	−0.624750	−	1.08210i	0.363839	−	0.931462i	$-0.381466\pi$
$888$	10.9620	−	18.9868i	0.367862	−	0.637156i
$889$	−0.509269	−	0.882080i	−0.0170803	−	0.0295840i
$890$		0			0
$891$	−8.39201	+	14.5354i	−0.281143	+	0.486954i
$892$	−51.9452			−1.73925
$893$	11.1508	+	0.252136i	0.373146	+	0.00843740i
$894$	20.6274			0.689884
$895$		0			0
$896$	3.41341	−	5.91219i	0.114034	−	0.197513i
$897$	−29.4053	−	50.9314i	−0.981814	−	1.70055i
$898$	−23.0219	+	39.8752i	−0.768252	+	1.33065i
$899$	24.0197	+	41.6033i	0.801102	+	1.38755i
$900$		0			0
$901$	50.2185			1.67302
$902$	−17.4389	−	30.2050i	−0.580650	−	1.00572i
$903$	−3.80735	−	6.59453i	−0.126701	−	0.219452i
$904$	20.3274			0.676078
$905$		0			0
$906$	35.6247	+	61.7037i	1.18355	+	2.04997i
$907$	−4.44080	+	7.69168i	−0.147454	+	0.255398i	−0.930286	−	0.366835i	$-0.880441\pi$
$907$	−4.44080	+	7.69168i	−0.147454	+	0.255398i	0.782832	+	0.622234i	$0.213775\pi$
$908$	35.9261	+	62.2258i	1.19225	+	2.06503i
$909$	−3.95801	+	6.85547i	−0.131279	+	0.227382i
$910$		0			0
$911$	−7.31703			−0.242424			−0.121212	−	0.992627i	$-0.538678\pi$
$911$	−7.31703			−0.242424			−0.121212	+	0.992627i	$0.538678\pi$
$912$	−26.7355	−	0.604531i	−0.885302	−	0.0200180i
$913$	−10.3743			−0.343341
$914$	10.2175	−	17.6973i	0.337966	−	0.585374i
$915$		0			0
$916$	11.9347	+	20.6715i	0.394333	+	0.683004i
$917$	−0.971448	+	1.68260i	−0.0320800	+	0.0555642i
$918$	45.5059	+	78.8184i	1.50192	+	2.60140i
$919$	−18.1725			−0.599454			−0.299727	−	0.954025i	$-0.596896\pi$
$919$	−18.1725			−0.599454			−0.299727	+	0.954025i	$0.596896\pi$
$920$		0			0
$921$	24.8329	+	43.0118i	0.818271	+	1.41729i
$922$	−2.51738	−	4.36023i	−0.0829054	−	0.143596i
$923$	−92.6509			−3.04964
$924$	12.2093			0.401656
$925$		0			0
$926$	15.9675	−	27.6565i	0.524724	−	0.908848i
$927$	−0.476440	−	0.825218i	−0.0156483	−	0.0271037i
$928$	26.7495	−	46.3315i	0.878095	−	1.52091i
$929$	−3.62348	+	6.27605i	−0.118882	+	0.205910i	−0.919325	−	0.393499i	$-0.871265\pi$
$929$	−3.62348	+	6.27605i	−0.118882	+	0.205910i	0.800443	+	0.599409i	$0.204598\pi$
$930$		0			0
$931$	15.0571	−	24.7691i	0.493476	−	0.811774i
$932$	−12.2251			−0.400447
$933$	27.0500	−	46.8519i	0.885576	−	1.53386i
$934$	−12.7760	+	22.1287i	−0.418045	+	0.724074i
$935$		0			0
$936$	−30.1936	+	52.2969i	−0.986909	+	1.70938i
$937$	0.874288	+	1.51431i	0.0285618	+	0.0494704i	0.879953	−	0.475061i	$-0.157574\pi$
$937$	0.874288	+	1.51431i	0.0285618	+	0.0494704i	−0.851391	+	0.524531i	$0.824241\pi$
$938$	5.52377			0.180357
$939$	−69.3848			−2.26429
$940$		0			0
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	0.535328	−	0.844644i	$-0.320188\pi$
$941$	−14.2280	−	24.6436i	−0.463819	−	0.803359i	−0.999147	+	0.0412856i	$0.986855\pi$
$942$	137.286			4.47303
$943$	18.0712			0.588480
$944$	−3.03903	−	5.26376i	−0.0989121	−	0.171321i
$945$		0			0
$946$	−12.2083	−	21.1454i	−0.396926	−	0.687496i
$947$	−5.53560	+	9.58793i	−0.179883	+	0.311566i	−0.941840	−	0.336061i	$-0.890905\pi$
$947$	−5.53560	+	9.58793i	−0.179883	+	0.311566i	0.761957	+	0.647627i	$0.224238\pi$
$948$	−23.4829	+	40.6737i	−0.762691	+	1.32102i
$949$	−57.8634			−1.87832
$950$		0			0
$951$	−11.4637			−0.371737
$952$	2.38387	−	4.12899i	0.0772618	−	0.133821i
$953$	26.2385	−	45.4464i	0.849949	−	1.47215i	−0.0313045	−	0.999510i	$-0.509966\pi$
$953$	26.2385	−	45.4464i	0.849949	−	1.47215i	0.881253	−	0.472644i	$-0.156701\pi$
$954$	59.4622	+	102.992i	1.92516	+	3.33447i
$955$		0			0
$956$	10.5991	+	18.3582i	0.342799	+	0.593746i
$957$	53.7002			1.73588
$958$	24.7051			0.798185
$959$	−2.41109	−	4.17614i	−0.0778583	−	0.134854i
$960$		0			0
$961$	15.4335			0.497854
$962$	−71.9040			−2.31828
$963$	12.9050	+	22.3520i	0.415856	+	0.720284i
$964$	−37.0349	+	64.1464i	−1.19281	+	2.06602i
$965$		0			0
$966$	−5.49795	+	9.52273i	−0.176894	+	0.306389i
$967$	−7.63706	+	13.2278i	−0.245591	+	0.425376i	−0.962298	−	0.271999i	$-0.912315\pi$
$967$	−7.63706	+	13.2278i	−0.245591	+	0.425376i	0.716707	+	0.697375i	$0.245649\pi$
$968$	−6.68203			−0.214769
$969$	−67.3508	−	1.52290i	−2.16362	−	0.0489227i
$970$		0			0
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	0.0402194	+	0.999191i	$0.487194\pi$
$971$	−26.3376	+	45.6181i	−0.845215	+	1.46396i	−0.885434	+	0.464764i	$0.846139\pi$
$972$	6.54375	−	11.3341i	0.209891	−	0.363542i
$973$	4.62292	+	8.00714i	0.148204	+	0.256697i
$974$	−5.17634	+	8.96568i	−0.165861	+	0.287279i
$975$		0			0
$976$	−4.84618			−0.155123
$977$	56.5695			1.80982			0.904909	−	0.425605i	$-0.139939\pi$
$977$	56.5695			1.80982			0.904909	+	0.425605i	$0.139939\pi$
$978$	−33.0313	−	57.2119i	−1.05623	−	1.82944i
$979$	−4.79508	−	8.30532i	−0.153251	−	0.265439i
$980$		0			0
$981$	−61.1883			−1.95359
$982$	5.43965	+	9.42176i	0.173586	+	0.300660i
$983$	−30.8770	+	53.4806i	−0.984825	+	1.70577i	−0.342111	+	0.939659i	$0.611142\pi$
$983$	−30.8770	+	53.4806i	−0.984825	+	1.70577i	−0.642713	+	0.766107i	$0.722191\pi$
$984$	−14.1493	−	24.5073i	−0.451064	−	0.781265i
$985$		0			0
$986$	40.0504	−	69.3694i	1.27547	−	2.20917i
$987$	4.46869			0.142240
$988$	−38.9478	−	71.1258i	−1.23909	−	2.26281i
$989$	12.6510			0.402278
$990$		0			0
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.0921233	−	0.995748i	$-0.470635\pi$
$991$	28.5967	−	49.5310i	0.908404	−	1.57340i	0.816281	−	0.577655i	$-0.196032\pi$
$992$	−25.8553	−	44.7827i	−0.820906	−	1.42185i
$993$	−4.80892	+	8.32929i	−0.152606	+	0.264322i
$994$	8.66154	+	15.0022i	0.274727	+	0.475842i
$995$		0			0
$996$	−32.1526			−1.01879
$997$	15.4592	+	26.7761i	0.489597	+	0.848007i	0.999928	−	0.0119712i	$-0.00381063\pi$
$997$	15.4592	+	26.7761i	0.489597	+	0.848007i	−0.510332	+	0.859978i	$0.670477\pi$
$998$	−23.6782	−	41.0118i	−0.749519	−	1.29820i
$999$	−38.6521			−1.22290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.f.201.1	yes	12
5.2	odd	4		475.2.j.d.49.2		24
5.3	odd	4		475.2.j.d.49.11		24
5.4	even	2		475.2.e.h.201.6	yes	12
19.7	even	3	inner	475.2.e.f.26.1	✓	12
19.8	odd	6		9025.2.a.bs.1.1		6
19.11	even	3		9025.2.a.bz.1.6		6
95.7	odd	12		475.2.j.d.349.11		24
95.49	even	6		9025.2.a.br.1.1		6
95.64	even	6		475.2.e.h.26.6	yes	12
95.83	odd	12		475.2.j.d.349.2		24
95.84	odd	6		9025.2.a.by.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.e.f.26.1	✓	12	19.7	even	3	inner
475.2.e.f.201.1	yes	12	1.1	even	1	trivial
475.2.e.h.26.6	yes	12	95.64	even	6
475.2.e.h.201.6	yes	12	5.4	even	2
475.2.j.d.49.2		24	5.2	odd	4
475.2.j.d.49.11		24	5.3	odd	4
475.2.j.d.349.2		24	95.83	odd	12
475.2.j.d.349.11		24	95.7	odd	12
9025.2.a.br.1.1		6	95.49	even	6
9025.2.a.bs.1.1		6	19.8	odd	6
9025.2.a.by.1.6		6	95.84	odd	6
9025.2.a.bz.1.6		6	19.11	even	3

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08504 + 1.87935i) q^{2} +(-1.47594 + 2.55640i) q^{3} +(-1.35464 - 2.34630i) q^{4} +(-3.20292 - 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 - 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 - 5.94669i) q^{13} +(-0.641933 + 1.11186i) q^{14} +(1.03919 - 1.79993i) q^{16} +(2.61787 - 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 + 3.72468i) q^{19} +(-0.873195 + 1.51242i) q^{21} +(-2.79990 + 4.84957i) q^{22} +(-1.45072 - 2.51271i) q^{23} +(-2.27175 + 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 - 1.38812i) q^{28} +(-3.52494 - 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 + 6.57195i) q^{32} +(-3.80859 + 6.59667i) q^{33} +(5.68101 + 9.83980i) q^{34} +(-7.73984 + 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 - 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 + 5.39393i) q^{41} +(-1.89491 - 3.28208i) q^{42} +(-2.18013 + 3.77609i) q^{43} +(-3.49558 - 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 - 2.21600i) q^{47} +(3.06756 + 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 + 13.3847i) q^{51} +(-9.30181 + 16.1112i) q^{52} +(4.79573 + 8.30645i) q^{53} +(-8.69138 + 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 - 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 - 2.53263i) q^{59} +(-1.16586 - 2.01932i) q^{61} +(7.39371 - 12.8063i) q^{62} +(-1.69013 - 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 - 14.3153i) q^{66} +(-2.15122 - 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 - 11.6852i) q^{71} +(-4.39714 - 7.61607i) q^{72} +(4.21337 - 7.29777i) q^{73} +(5.23574 - 9.06858i) q^{74} +(11.8064 + 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 + 38.0935i) q^{78} +(-2.93630 + 5.08583i) q^{79} +(-3.25215 + 5.63288i) q^{81} +(-6.75806 - 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 - 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 - 3.21855i) q^{89} +(-2.03122 - 3.51818i) q^{91} +(-3.93039 + 6.80764i) q^{92} +(10.0574 - 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 + 2.18732i) q^{97} +(7.21552 - 12.4977i) q^{98} +(-7.37182 - 12.7684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

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