LMFDB - Embedded newform 594.2.f.k.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [594,2,Mod(163,594)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(594, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("594.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 594 = 2 \cdot 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	594.f (of order $5$, degree $4$, 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:	$4.74311388006$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} + 35x^{10} + 470x^{8} + 3060x^{6} + 10105x^{4} + 16040x^{2} + 9680 $ x^12 + 35x^10 + 470x^8 + 3060x^6 + 10105x^4 + 16040*x^2 + 9680
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			433.1
Root			$-2.48352i$ of defining polynomial
Character	$\chi$	$=$	594.433
Dual form			594.2.f.k.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-3.14677 + 2.28626i) q^{5} +(1.15076 + 3.54167i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-3.14677 + 2.28626i) q^{5} +(1.15076 + 3.54167i) q^{7} +(0.309017 - 0.951057i) q^{8} +3.88962 q^{10} +(-3.30503 - 0.277057i) q^{11} +(-4.45753 - 3.23859i) q^{13} +(1.15076 - 3.54167i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.53693 - 2.56973i) q^{17} +(1.35164 - 4.15992i) q^{19} +(-3.14677 - 2.28626i) q^{20} +(2.51098 + 2.16679i) q^{22} +0.169185 q^{23} +(3.13009 - 9.63342i) q^{25} +(1.70263 + 5.24015i) q^{26} +(-3.01272 + 2.18887i) q^{28} +(-2.59490 - 7.98629i) q^{29} +(0.272669 + 0.198105i) q^{31} +1.00000 q^{32} -4.37189 q^{34} +(-11.7184 - 8.51388i) q^{35} +(0.587055 + 1.80677i) q^{37} +(-3.53864 + 2.57097i) q^{38} +(1.20196 + 3.69925i) q^{40} +(-1.53799 + 4.73343i) q^{41} -3.84121 q^{43} +(-0.757814 - 3.22889i) q^{44} +(-0.136873 - 0.0994443i) q^{46} +(-0.320660 + 0.986891i) q^{47} +(-5.55604 + 4.03670i) q^{49} +(-8.19468 + 5.95378i) q^{50} +(1.70263 - 5.24015i) q^{52} +(5.59333 + 4.06379i) q^{53} +(11.0336 - 6.68434i) q^{55} +3.72393 q^{56} +(-2.59490 + 7.98629i) q^{58} +(-0.831841 - 2.56014i) q^{59} +(-8.64453 + 6.28062i) q^{61} +(-0.104150 - 0.320541i) q^{62} +(-0.809017 - 0.587785i) q^{64} +21.4311 q^{65} -11.4875 q^{67} +(3.53693 + 2.56973i) q^{68} +(4.47601 + 13.7758i) q^{70} +(-10.3127 + 7.49261i) q^{71} +(-1.62901 - 5.01358i) q^{73} +(0.587055 - 1.80677i) q^{74} +4.37400 q^{76} +(-2.82205 - 12.0241i) q^{77} +(8.27471 + 6.01193i) q^{79} +(1.20196 - 3.69925i) q^{80} +(4.02650 - 2.92542i) q^{82} +(5.38143 - 3.90984i) q^{83} +(-5.25483 + 16.1727i) q^{85} +(3.10760 + 2.25781i) q^{86} +(-1.28481 + 3.05766i) q^{88} -12.2110 q^{89} +(6.34046 - 19.5139i) q^{91} +(0.0522810 + 0.160904i) q^{92} +(0.839500 - 0.609932i) q^{94} +(5.25737 + 16.1805i) q^{95} +(-14.1868 - 10.3073i) q^{97} +6.86764 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 - 3 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8} + 4 q^{10} - 7 q^{11} + 2 q^{13} + 3 q^{14} - 3 q^{16} + 15 q^{17} - 6 q^{19} - q^{20} + 8 q^{22} - 18 q^{23} - 2 q^{25} - 3 q^{26} - 2 q^{28} - 7 q^{29} - 30 q^{31} + 12 q^{32} - 9 q^{35} - 21 q^{37} - q^{38} - q^{40} + 2 q^{41} + 10 q^{43} - 7 q^{44} + 17 q^{46} + 33 q^{47} - 22 q^{49} - 12 q^{50} - 3 q^{52} - 3 q^{53} + 71 q^{55} - 2 q^{56} - 7 q^{58} - 24 q^{59} - 29 q^{61} + 20 q^{62} - 3 q^{64} + 4 q^{65} + 28 q^{67} + 15 q^{68} - 9 q^{70} - 35 q^{71} + 16 q^{73} - 21 q^{74} + 14 q^{76} + 17 q^{77} + 31 q^{79} - q^{80} - 13 q^{82} + 26 q^{83} - 40 q^{85} - 10 q^{86} - 2 q^{88} - 24 q^{89} + 3 q^{91} - 8 q^{92} - 32 q^{94} + 13 q^{95} - 67 q^{97} + 58 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 - 3 * q^8 + 4 * q^10 - 7 * q^11 + 2 * q^13 + 3 * q^14 - 3 * q^16 + 15 * q^17 - 6 * q^19 - q^20 + 8 * q^22 - 18 * q^23 - 2 * q^25 - 3 * q^26 - 2 * q^28 - 7 * q^29 - 30 * q^31 + 12 * q^32 - 9 * q^35 - 21 * q^37 - q^38 - q^40 + 2 * q^41 + 10 * q^43 - 7 * q^44 + 17 * q^46 + 33 * q^47 - 22 * q^49 - 12 * q^50 - 3 * q^52 - 3 * q^53 + 71 * q^55 - 2 * q^56 - 7 * q^58 - 24 * q^59 - 29 * q^61 + 20 * q^62 - 3 * q^64 + 4 * q^65 + 28 * q^67 + 15 * q^68 - 9 * q^70 - 35 * q^71 + 16 * q^73 - 21 * q^74 + 14 * q^76 + 17 * q^77 + 31 * q^79 - q^80 - 13 * q^82 + 26 * q^83 - 40 * q^85 - 10 * q^86 - 2 * q^88 - 24 * q^89 + 3 * q^91 - 8 * q^92 - 32 * q^94 + 13 * q^95 - 67 * q^97 + 58 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/594\mathbb{Z}\right)^\times$.

$n$	$353$	$541$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−3.14677	+	2.28626i	−1.40728	+	1.02245i	−0.413568	+	0.910473i	$0.635718\pi$
$5$	−3.14677	+	2.28626i	−1.40728	+	1.02245i	−0.993711	+	0.111975i	$0.964282\pi$
$6$		0			0
$7$	1.15076	+	3.54167i	0.434945	+	1.33862i	0.893143	+	0.449774i	$0.148495\pi$
$7$	1.15076	+	3.54167i	0.434945	+	1.33862i	−0.458197	+	0.888851i	$0.651505\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	3.88962			1.23001
$11$	−3.30503	−	0.277057i	−0.996505	−	0.0835359i
$11$	−3.30503	−	0.277057i	−0.996505	−	0.0835359i
$12$		0			0
$13$	−4.45753	−	3.23859i	−1.23630	−	0.898223i	−0.238952	−	0.971032i	$-0.576804\pi$
$13$	−4.45753	−	3.23859i	−1.23630	−	0.898223i	−0.997346	+	0.0728088i	$0.976804\pi$
$14$	1.15076	−	3.54167i	0.307553	−	0.946550i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.53693	−	2.56973i	0.857832	−	0.623251i	−0.0694626	−	0.997585i	$-0.522128\pi$
$17$	3.53693	−	2.56973i	0.857832	−	0.623251i	0.927294	+	0.374333i	$0.122128\pi$
$18$		0			0
$19$	1.35164	−	4.15992i	0.310087	−	0.954351i	−0.667642	−	0.744482i	$-0.732696\pi$
$19$	1.35164	−	4.15992i	0.310087	−	0.954351i	0.977730	−	0.209868i	$-0.0673036\pi$
$20$	−3.14677	−	2.28626i	−0.703640	−	0.511224i
$21$		0			0
$22$	2.51098	+	2.16679i	0.535342	+	0.461962i
$23$	0.169185			0.0352775			0.0176387	−	0.999844i	$-0.494385\pi$
$23$	0.169185			0.0352775			0.0176387	+	0.999844i	$0.494385\pi$
$24$		0			0
$25$	3.13009	−	9.63342i	0.626018	−	1.92668i
$26$	1.70263	+	5.24015i	0.333913	+	1.02768i
$27$		0			0
$28$	−3.01272	+	2.18887i	−0.569351	+	0.413658i
$29$	−2.59490	−	7.98629i	−0.481861	−	1.48302i	−0.836476	−	0.548004i	$-0.815388\pi$
$29$	−2.59490	−	7.98629i	−0.481861	−	1.48302i	0.354614	−	0.935013i	$-0.384612\pi$
$30$		0			0
$31$	0.272669	+	0.198105i	0.0489728	+	0.0355808i	0.612002	−	0.790856i	$-0.290364\pi$
$31$	0.272669	+	0.198105i	0.0489728	+	0.0355808i	−0.563030	+	0.826437i	$0.690364\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.37189			−0.749772
$35$	−11.7184	−	8.51388i	−1.98076	−	1.43911i
$36$		0			0
$37$	0.587055	+	1.80677i	0.0965112	+	0.297031i	0.987645	−	0.156710i	$-0.0500889\pi$
$37$	0.587055	+	1.80677i	0.0965112	+	0.297031i	−0.891133	+	0.453742i	$0.850089\pi$
$38$	−3.53864	+	2.57097i	−0.574043	+	0.417067i
$39$		0			0
$40$	1.20196	+	3.69925i	0.190047	+	0.584903i
$41$	−1.53799	+	4.73343i	−0.240193	+	0.739238i	0.756197	+	0.654344i	$0.227055\pi$
$41$	−1.53799	+	4.73343i	−0.240193	+	0.739238i	−0.996390	+	0.0848940i	$0.972945\pi$
$42$		0			0
$43$	−3.84121			−0.585779			−0.292889	−	0.956146i	$-0.594617\pi$
$43$	−3.84121			−0.585779			−0.292889	+	0.956146i	$0.594617\pi$
$44$	−0.757814	−	3.22889i	−0.114245	−	0.486773i
$45$		0			0
$46$	−0.136873	−	0.0994443i	−0.0201809	−	0.0146623i
$47$	−0.320660	+	0.986891i	−0.0467731	+	0.143953i	−0.971716	−	0.236154i	$-0.924113\pi$
$47$	−0.320660	+	0.986891i	−0.0467731	+	0.143953i	0.924942	+	0.380107i	$0.124113\pi$
$48$		0			0
$49$	−5.55604	+	4.03670i	−0.793720	+	0.576671i
$50$	−8.19468	+	5.95378i	−1.15890	+	0.841992i
$51$		0			0
$52$	1.70263	−	5.24015i	0.236112	−	0.726677i
$53$	5.59333	+	4.06379i	0.768303	+	0.558205i	0.901446	−	0.432892i	$-0.142507\pi$
$53$	5.59333	+	4.06379i	0.768303	+	0.558205i	−0.133143	+	0.991097i	$0.542507\pi$
$54$		0			0
$55$	11.0336	−	6.68434i	1.48777	−	0.901316i
$56$	3.72393			0.497631
$57$		0			0
$58$	−2.59490	+	7.98629i	−0.340728	+	1.04865i
$59$	−0.831841	−	2.56014i	−0.108296	−	0.333302i	0.882194	−	0.470887i	$-0.156066\pi$
$59$	−0.831841	−	2.56014i	−0.108296	−	0.333302i	−0.990490	+	0.137585i	$0.956066\pi$
$60$		0			0
$61$	−8.64453	+	6.28062i	−1.10682	+	0.804151i	−0.982160	−	0.188049i	$-0.939784\pi$
$61$	−8.64453	+	6.28062i	−1.10682	+	0.804151i	−0.124659	+	0.992200i	$0.539784\pi$
$62$	−0.104150	−	0.320541i	−0.0132271	−	0.0407088i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	21.4311			2.65820
$66$		0			0
$67$	−11.4875			−1.40342			−0.701708	−	0.712465i	$-0.747579\pi$
$67$	−11.4875			−1.40342			−0.701708	+	0.712465i	$0.747579\pi$
$68$	3.53693	+	2.56973i	0.428916	+	0.311626i
$69$		0			0
$70$	4.47601	+	13.7758i	0.534986	+	1.64652i
$71$	−10.3127	+	7.49261i	−1.22389	+	0.889209i	−0.996417	−	0.0845751i	$-0.973047\pi$
$71$	−10.3127	+	7.49261i	−1.22389	+	0.889209i	−0.227474	+	0.973784i	$0.573047\pi$
$72$		0			0
$73$	−1.62901	−	5.01358i	−0.190661	−	0.586795i	0.809339	−	0.587342i	$-0.199826\pi$
$73$	−1.62901	−	5.01358i	−0.190661	−	0.586795i	−1.00000		0.000547212i	$0.999826\pi$
$74$	0.587055	−	1.80677i	0.0682438	−	0.210033i
$75$		0			0
$76$	4.37400			0.501732
$77$	−2.82205	−	12.0241i	−0.321602	−	1.37028i
$78$		0			0
$79$	8.27471	+	6.01193i	0.930977	+	0.676394i	0.946232	−	0.323489i	$-0.104856\pi$
$79$	8.27471	+	6.01193i	0.930977	+	0.676394i	−0.0152547	+	0.999884i	$0.504856\pi$
$80$	1.20196	−	3.69925i	0.134383	−	0.413589i
$81$		0			0
$82$	4.02650	−	2.92542i	0.444652	−	0.323059i
$83$	5.38143	−	3.90984i	0.590689	−	0.429161i	−0.251873	−	0.967760i	$-0.581046\pi$
$83$	5.38143	−	3.90984i	0.590689	−	0.429161i	0.842562	+	0.538600i	$0.181046\pi$
$84$		0			0
$85$	−5.25483	+	16.1727i	−0.569967	+	1.75418i
$86$	3.10760	+	2.25781i	0.335101	+	0.243465i
$87$		0			0
$88$	−1.28481	+	3.05766i	−0.136961	+	0.325947i
$89$	−12.2110			−1.29436			−0.647181	−	0.762337i	$-0.724052\pi$
$89$	−12.2110			−1.29436			−0.647181	+	0.762337i	$0.724052\pi$
$90$		0			0
$91$	6.34046	−	19.5139i	0.664661	−	2.04562i
$92$	0.0522810	+	0.160904i	0.00545067	+	0.0167754i
$93$		0			0
$94$	0.839500	−	0.609932i	0.0865878	−	0.0629097i
$95$	5.25737	+	16.1805i	0.539395	+	1.66009i
$96$		0			0
$97$	−14.1868	−	10.3073i	−1.44045	−	1.04655i	−0.987948	−	0.154789i	$-0.950530\pi$
$97$	−14.1868	−	10.3073i	−1.44045	−	1.04655i	−0.452505	−	0.891762i	$-0.649470\pi$
$98$	6.86764			0.693737
$99$		0			0
$100$	10.1292			1.01292
$101$	5.45180	+	3.96097i	0.542475	+	0.394131i	0.825003	−	0.565128i	$-0.191173\pi$
$101$	5.45180	+	3.96097i	0.542475	+	0.394131i	−0.282528	+	0.959259i	$0.591173\pi$
$102$		0			0
$103$	−4.62012	−	14.2193i	−0.455233	−	1.40106i	−0.870861	−	0.491530i	$-0.836438\pi$
$103$	−4.62012	−	14.2193i	−0.455233	−	1.40106i	0.415627	−	0.909535i	$-0.363562\pi$
$104$	−4.45753	+	3.23859i	−0.437097	+	0.317570i
$105$		0			0
$106$	−2.13646	−	6.57535i	−0.207511	−	0.638655i
$107$	1.25563	−	3.86442i	0.121386	−	0.373587i	−0.871839	−	0.489792i	$-0.837073\pi$
$107$	1.25563	−	3.86442i	0.121386	−	0.373587i	0.993225	+	0.116204i	$0.0370728\pi$
$108$		0			0
$109$	−15.7612			−1.50965			−0.754825	−	0.655927i	$-0.772278\pi$
$109$	−15.7612			−1.50965			−0.754825	+	0.655927i	$0.772278\pi$
$110$	−12.8553	−	1.07765i	−1.22571	−	0.102750i
$111$		0			0
$112$	−3.01272	−	2.18887i	−0.284675	−	0.206829i
$113$	0.196023	−	0.603297i	0.0184403	−	0.0567534i	−0.941413	−	0.337256i	$-0.890501\pi$
$113$	0.196023	−	0.603297i	0.0184403	−	0.0567534i	0.959853	+	0.280503i	$0.0905012\pi$
$114$		0			0
$115$	−0.532386	+	0.386801i	−0.0496453	+	0.0360694i
$116$	6.79355	−	4.93580i	0.630765	−	0.458277i
$117$		0			0
$118$	−0.831841	+	2.56014i	−0.0765772	+	0.235680i
$119$	13.1713	+	9.56949i	1.20741	+	0.877234i
$120$		0			0
$121$	10.8465	+	1.83137i	0.986043	+	0.166488i
$122$	10.6852			0.967395
$123$		0			0
$124$	−0.104150	+	0.320541i	−0.00935297	+	0.0287855i
$125$	6.16507	+	18.9741i	0.551421	+	1.69710i
$126$		0			0
$127$	6.99219	−	5.08012i	0.620456	−	0.450788i	−0.232625	−	0.972567i	$-0.574731\pi$
$127$	6.99219	−	5.08012i	0.620456	−	0.450788i	0.853081	+	0.521779i	$0.174731\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−17.3381	−	12.5969i	−1.52065	−	1.10482i
$131$	0.692672			0.0605191			0.0302595	−	0.999542i	$-0.490367\pi$
$131$	0.692672			0.0605191			0.0302595	+	0.999542i	$0.490367\pi$
$132$		0			0
$133$	16.2885			1.41239
$134$	9.29355	+	6.75216i	0.802840	+	0.583297i
$135$		0			0
$136$	−1.35099	−	4.15791i	−0.115846	−	0.356538i
$137$	−7.90987	+	5.74686i	−0.675786	+	0.490987i	−0.871957	−	0.489582i	$-0.837149\pi$
$137$	−7.90987	+	5.74686i	−0.675786	+	0.490987i	0.196171	+	0.980570i	$0.437149\pi$
$138$		0			0
$139$	−0.929396	−	2.86039i	−0.0788304	−	0.242615i	0.903873	−	0.427800i	$-0.140711\pi$
$139$	−0.929396	−	2.86039i	−0.0788304	−	0.242615i	−0.982704	+	0.185185i	$0.940711\pi$
$140$	4.47601	−	13.7758i	0.378292	−	1.16426i
$141$		0			0
$142$	12.7472			1.06972
$143$	13.8350	+	11.9386i	1.15694	+	0.998358i
$144$		0			0
$145$	26.4243	+	19.1984i	2.19442	+	1.59434i
$146$	−1.62901	+	5.01358i	−0.134818	+	0.414927i
$147$		0			0
$148$	−1.53693	+	1.11664i	−0.126335	+	0.0917877i
$149$	7.41744	−	5.38909i	0.607661	−	0.441491i	−0.240929	−	0.970543i	$-0.577452\pi$
$149$	7.41744	−	5.38909i	0.607661	−	0.441491i	0.848590	+	0.529051i	$0.177452\pi$
$150$		0			0
$151$	−0.568765	+	1.75048i	−0.0462854	+	0.142452i	−0.971528	−	0.236923i	$-0.923861\pi$
$151$	−0.568765	+	1.75048i	−0.0462854	+	0.142452i	0.925243	+	0.379375i	$0.123861\pi$
$152$	−3.53864	−	2.57097i	−0.287021	−	0.208533i
$153$		0			0
$154$	−4.78453	+	11.3865i	−0.385549	+	0.917550i
$155$	−1.31095			−0.105298
$156$		0			0
$157$	−2.45819	+	7.56552i	−0.196185	+	0.603794i	0.803776	+	0.594932i	$0.202821\pi$
$157$	−2.45819	+	7.56552i	−0.196185	+	0.603794i	−0.999961	+	0.00886225i	$0.997179\pi$
$158$	−3.16066	−	9.72750i	−0.251448	−	0.773878i
$159$		0			0
$160$	−3.14677	+	2.28626i	−0.248774	+	0.180745i
$161$	0.194691	+	0.599196i	0.0153438	+	0.0472233i
$162$		0			0
$163$	0.897594	+	0.652140i	0.0703050	+	0.0510796i	0.622383	−	0.782713i	$-0.286165\pi$
$163$	0.897594	+	0.652140i	0.0703050	+	0.0510796i	−0.552078	+	0.833793i	$0.686165\pi$
$164$	−4.97703			−0.388640
$165$		0			0
$166$	−6.65182			−0.516281
$167$	4.07662	+	2.96184i	0.315459	+	0.229194i	0.734235	−	0.678895i	$-0.237541\pi$
$167$	4.07662	+	2.96184i	0.315459	+	0.229194i	−0.418777	+	0.908089i	$0.637541\pi$
$168$		0			0
$169$	5.36394	+	16.5085i	0.412610	+	1.26988i
$170$	13.7573	−	9.99529i	1.05514	−	0.766603i
$171$		0			0
$172$	−1.18700	−	3.65321i	−0.0905078	−	0.278554i
$173$	−0.683546	+	2.10374i	−0.0519691	+	0.159944i	−0.973673	−	0.227950i	$-0.926798\pi$
$173$	−0.683546	+	2.10374i	−0.0519691	+	0.159944i	0.921704	+	0.387895i	$0.126798\pi$
$174$		0			0
$175$	37.7203			2.85139
$176$	2.83668	−	1.71851i	0.213823	−	0.129537i
$177$		0			0
$178$	9.87889	+	7.17744i	0.740454	+	0.537972i
$179$	6.23737	−	19.1966i	0.466203	−	1.43482i	−0.391261	−	0.920280i	$-0.627961\pi$
$179$	6.23737	−	19.1966i	0.466203	−	1.43482i	0.857464	−	0.514545i	$-0.172039\pi$
$180$		0			0
$181$	−14.8130	+	10.7623i	−1.10104	+	0.799956i	−0.981230	−	0.192840i	$-0.938230\pi$
$181$	−14.8130	+	10.7623i	−1.10104	+	0.799956i	−0.119815	+	0.992796i	$0.538230\pi$
$182$	−16.5995	+	12.0603i	−1.23044	+	0.893967i
$183$		0			0
$184$	0.0522810	−	0.160904i	0.00385420	−	0.0118620i
$185$	−5.97808	−	4.34333i	−0.439517	−	0.319328i
$186$		0			0
$187$	−12.4016	+	7.51311i	−0.906897	+	0.549413i
$188$	−1.03768			−0.0756805
$189$		0			0
$190$	5.25737	−	16.1805i	0.381410	−	1.17386i
$191$	−1.82633	−	5.62088i	−0.132149	−	0.406713i	0.862987	−	0.505227i	$-0.168591\pi$
$191$	−1.82633	−	5.62088i	−0.132149	−	0.406713i	−0.995136	+	0.0985140i	$0.968591\pi$
$192$		0			0
$193$	−5.79555	+	4.21071i	−0.417173	+	0.303094i	−0.776499	−	0.630118i	$-0.783006\pi$
$193$	−5.79555	+	4.21071i	−0.417173	+	0.303094i	0.359327	+	0.933212i	$0.383006\pi$
$194$	5.41888	+	16.6776i	0.389053	+	1.19738i
$195$		0			0
$196$	−5.55604	−	4.03670i	−0.396860	−	0.288336i
$197$	−18.0381			−1.28516			−0.642581	−	0.766218i	$-0.722136\pi$
$197$	−18.0381			−1.28516			−0.642581	+	0.766218i	$0.722136\pi$
$198$		0			0
$199$	−12.5714			−0.891166			−0.445583	−	0.895241i	$-0.647004\pi$
$199$	−12.5714			−0.891166			−0.445583	+	0.895241i	$0.647004\pi$
$200$	−8.19468	−	5.95378i	−0.579451	−	0.420996i
$201$		0			0
$202$	−2.08240	−	6.40898i	−0.146517	−	0.450934i
$203$	25.2987	−	18.3806i	1.77562	−	1.29006i
$204$		0			0
$205$	−5.98219	−	18.4113i	−0.417814	−	1.28590i
$206$	−4.62012	+	14.2193i	−0.321899	+	0.990702i
$207$		0			0
$208$	5.50981			0.382037
$209$	−5.61975	+	13.3742i	−0.388726	+	0.925112i
$210$		0			0
$211$	18.2560	+	13.2637i	1.25679	+	0.913114i	0.998596	−	0.0529785i	$-0.0168715\pi$
$211$	18.2560	+	13.2637i	1.25679	+	0.913114i	0.258197	+	0.966092i	$0.416871\pi$
$212$	−2.13646	+	6.57535i	−0.146733	+	0.451597i
$213$		0			0
$214$	−3.28727	+	2.38834i	−0.224713	+	0.163264i
$215$	12.0874	−	8.78201i	0.824354	−	0.598928i
$216$		0			0
$217$	−0.387848	+	1.19367i	−0.0263288	+	0.0810318i
$218$	12.7511	+	9.26420i	0.863612	+	0.627451i
$219$		0			0
$220$	9.76676	+	8.42801i	0.658475	+	0.568217i
$221$	−24.0883			−1.62035
$222$		0			0
$223$	7.91662	−	24.3648i	0.530136	−	1.63159i	−0.223794	−	0.974636i	$-0.571844\pi$
$223$	7.91662	−	24.3648i	0.530136	−	1.63159i	0.753930	−	0.656955i	$-0.228156\pi$
$224$	1.15076	+	3.54167i	0.0768882	+	0.236638i
$225$		0			0
$226$	−0.513195	+	0.372858i	−0.0341372	+	0.0248021i
$227$	2.96983	+	9.14020i	0.197115	+	0.606656i	0.999945	+	0.0104493i	$0.00332617\pi$
$227$	2.96983	+	9.14020i	0.197115	+	0.606656i	−0.802831	+	0.596207i	$0.796674\pi$
$228$		0			0
$229$	2.54599	+	1.84977i	0.168244	+	0.122236i	0.668721	−	0.743513i	$-0.266842\pi$
$229$	2.54599	+	1.84977i	0.168244	+	0.122236i	−0.500477	+	0.865750i	$0.666842\pi$
$230$	0.658065			0.0433915
$231$		0			0
$232$	−8.39728			−0.551309
$233$	2.73361	+	1.98608i	0.179084	+	0.130112i	0.673716	−	0.738990i	$-0.264697\pi$
$233$	2.73361	+	1.98608i	0.179084	+	0.130112i	−0.494632	+	0.869103i	$0.664697\pi$
$234$		0			0
$235$	−1.24725	−	3.83864i	−0.0813615	−	0.250405i
$236$	2.17779	−	1.58226i	0.141762	−	0.102996i
$237$		0			0
$238$	−5.03098	−	15.4838i	−0.326110	−	1.00366i
$239$	0.916740	−	2.82144i	0.0592990	−	0.182504i	−0.917019	−	0.398843i	$-0.869412\pi$
$239$	0.916740	−	2.82144i	0.0592990	−	0.182504i	0.976318	+	0.216340i	$0.0694118\pi$
$240$		0			0
$241$	−22.0533			−1.42058			−0.710289	−	0.703910i	$-0.751436\pi$
$241$	−22.0533			−1.42058			−0.710289	+	0.703910i	$0.751436\pi$
$242$	−7.69853	−	7.85701i	−0.494881	−	0.505068i
$243$		0			0
$244$	−8.64453	−	6.28062i	−0.553409	−	0.402076i
$245$	8.25463	−	25.4051i	0.527369	−	1.62308i
$246$		0			0
$247$	−19.4972	+	14.1656i	−1.24058	+	0.901334i
$248$	0.272669	−	0.198105i	0.0173145	−	0.0125797i
$249$		0			0
$250$	6.16507	−	18.9741i	0.389913	−	1.20003i
$251$	−12.6939	−	9.22266i	−0.801232	−	0.582129i	0.110043	−	0.993927i	$-0.464901\pi$
$251$	−12.6939	−	9.22266i	−0.801232	−	0.582129i	−0.911275	+	0.411797i	$0.864901\pi$
$252$		0			0
$253$	−0.559161	−	0.0468739i	−0.0351542	−	0.00294694i
$254$	−8.64282			−0.542299
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.44847	−	13.6910i	−0.277488	−	0.854020i	−0.988550	−	0.150891i	$-0.951786\pi$
$257$	−4.44847	−	13.6910i	−0.277488	−	0.854020i	0.711063	−	0.703129i	$-0.248214\pi$
$258$		0			0
$259$	−5.72342	+	4.15831i	−0.355636	+	0.258385i
$260$	6.62258	+	20.3822i	0.410715	+	1.26405i
$261$		0			0
$262$	−0.560384	−	0.407143i	−0.0346206	−	0.0251534i
$263$	−19.2655			−1.18796			−0.593980	−	0.804480i	$-0.702444\pi$
$263$	−19.2655			−1.18796			−0.593980	+	0.804480i	$0.702444\pi$
$264$		0			0
$265$	−26.8918			−1.65195
$266$	−13.1776	−	9.57411i	−0.807973	−	0.587026i
$267$		0			0
$268$	−3.54982	−	10.9252i	−0.216840	−	0.667364i
$269$	−23.4363	+	17.0274i	−1.42893	+	1.03818i	−0.438721	+	0.898623i	$0.644568\pi$
$269$	−23.4363	+	17.0274i	−1.42893	+	1.03818i	−0.990214	+	0.139559i	$0.955432\pi$
$270$		0			0
$271$	6.13856	+	18.8926i	0.372891	+	1.14764i	0.944890	+	0.327387i	$0.106168\pi$
$271$	6.13856	+	18.8926i	0.372891	+	1.14764i	−0.571999	+	0.820254i	$0.693832\pi$
$272$	−1.35099	+	4.15791i	−0.0819156	+	0.252110i
$273$		0			0
$274$	9.77714			0.590659
$275$	−13.0141	+	30.9716i	−0.784777	+	1.86766i
$276$		0			0
$277$	12.8969	+	9.37015i	0.774900	+	0.562998i	0.903444	−	0.428706i	$-0.141030\pi$
$277$	12.8969	+	9.37015i	0.774900	+	0.562998i	−0.128544	+	0.991704i	$0.541030\pi$
$278$	−0.929396	+	2.86039i	−0.0557415	+	0.171555i
$279$		0			0
$280$	−11.7184	+	8.51388i	−0.700306	+	0.508802i
$281$	−6.52961	+	4.74404i	−0.389524	+	0.283006i	−0.765260	−	0.643721i	$-0.777390\pi$
$281$	−6.52961	+	4.74404i	−0.389524	+	0.283006i	0.375736	+	0.926727i	$0.377390\pi$
$282$		0			0
$283$	6.49608	−	19.9929i	0.386152	−	1.18845i	−0.549490	−	0.835500i	$-0.685178\pi$
$283$	6.49608	−	19.9929i	0.386152	−	1.18845i	0.935641	−	0.352952i	$-0.114822\pi$
$284$	−10.3127	−	7.49261i	−0.611946	−	0.444605i
$285$		0			0
$286$	−4.17541	−	17.7906i	−0.246897	−	1.05198i
$287$	−18.5341			−1.09403
$288$		0			0
$289$	0.653072	−	2.00995i	0.0384160	−	0.118232i
$290$	−10.0932	−	31.0637i	−0.592693	−	1.82412i
$291$		0			0
$292$	4.26481	−	3.09856i	0.249579	−	0.181330i
$293$	−3.35493	−	10.3254i	−0.195997	−	0.603216i	−0.999964	−	0.00854190i	$-0.997281\pi$
$293$	−3.35493	−	10.3254i	−0.195997	−	0.603216i	0.803967	−	0.594674i	$-0.202719\pi$
$294$		0			0
$295$	8.47078	+	6.15438i	0.493188	+	0.358322i
$296$	1.89975			0.110421
$297$		0			0
$298$	−9.16847			−0.531115
$299$	−0.754147	−	0.547920i	−0.0436134	−	0.0316870i
$300$		0			0
$301$	−4.42030	−	13.6043i	−0.254782	−	0.784137i
$302$	1.48905	−	1.08185i	0.0856849	−	0.0622537i
$303$		0			0
$304$	1.35164	+	4.15992i	0.0775218	+	0.238588i
$305$	12.8432	−	39.5274i	0.735401	−	2.26333i
$306$		0			0
$307$	11.3580			0.648235			0.324118	−	0.946017i	$-0.394933\pi$
$307$	11.3580			0.648235			0.324118	+	0.946017i	$0.394933\pi$
$308$	10.5636	−	6.39959i	0.601916	−	0.364651i
$309$		0			0
$310$	1.06058	+	0.770556i	0.0602369	+	0.0437646i
$311$	−0.256690	+	0.790010i	−0.0145555	+	0.0447974i	−0.958070	−	0.286533i	$-0.907497\pi$
$311$	−0.256690	+	0.790010i	−0.0145555	+	0.0447974i	0.943515	+	0.331330i	$0.107497\pi$
$312$		0			0
$313$	−1.36259	+	0.989983i	−0.0770184	+	0.0559571i	−0.625628	−	0.780121i	$-0.715157\pi$
$313$	−1.36259	+	0.989983i	−0.0770184	+	0.0559571i	0.548610	+	0.836079i	$0.315157\pi$
$314$	6.43561	−	4.67575i	0.363183	−	0.263868i
$315$		0			0
$316$	−3.16066	+	9.72750i	−0.177801	+	0.547215i
$317$	14.6980	+	10.6787i	0.825520	+	0.599775i	0.918288	−	0.395912i	$-0.129572\pi$
$317$	14.6980	+	10.6787i	0.825520	+	0.599775i	−0.0927682	+	0.995688i	$0.529572\pi$
$318$		0			0
$319$	6.36358	+	27.1139i	0.356292	+	1.51809i
$320$	3.88962			0.217437
$321$		0			0
$322$	0.194691	−	0.599196i	0.0108497	−	0.0333919i
$323$	−5.90921	−	18.1867i	−0.328797	−	1.01193i
$324$		0			0
$325$	−45.1512	+	32.8042i	−2.50454	+	1.81965i
$326$	−0.342850	−	1.05519i	−0.0189887	−	0.0584413i
$327$		0			0
$328$	4.02650	+	2.92542i	0.222326	+	0.161529i
$329$	−3.86424			−0.213043
$330$		0			0
$331$	24.1155			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$331$	24.1155			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$332$	5.38143	+	3.90984i	0.295345	+	0.214580i
$333$		0			0
$334$	−1.55713	−	4.79236i	−0.0852024	−	0.262226i
$335$	36.1484	−	26.2634i	1.97500	−	1.43492i
$336$		0			0
$337$	−2.21240	−	6.80907i	−0.120517	−	0.370913i	0.872541	−	0.488542i	$-0.162471\pi$
$337$	−2.21240	−	6.80907i	−0.120517	−	0.370913i	−0.993058	+	0.117628i	$0.962471\pi$
$338$	5.36394	−	16.5085i	0.291760	−	0.897944i
$339$		0			0
$340$	−17.0050			−0.922225
$341$	−0.846293	−	0.730290i	−0.0458293	−	0.0395474i
$342$		0			0
$343$	0.398756	+	0.289713i	0.0215308	+	0.0156430i
$344$	−1.18700	+	3.65321i	−0.0639987	+	0.196968i
$345$		0			0
$346$	1.78955	−	1.30018i	0.0962067	−	0.0698982i
$347$	−1.60880	+	1.16886i	−0.0863650	+	0.0627478i	−0.630130	−	0.776490i	$-0.716998\pi$
$347$	−1.60880	+	1.16886i	−0.0863650	+	0.0627478i	0.543765	+	0.839238i	$0.316998\pi$
$348$		0			0
$349$	−4.13449	+	12.7246i	−0.221314	+	0.681134i	0.777331	+	0.629092i	$0.216573\pi$
$349$	−4.13449	+	12.7246i	−0.221314	+	0.681134i	−0.998645	+	0.0520424i	$0.983427\pi$
$350$	−30.5164	−	22.1715i	−1.63117	−	1.18511i
$351$		0			0
$352$	−3.30503	−	0.277057i	−0.176159	−	0.0147672i
$353$	−0.543932			−0.0289506			−0.0144753	−	0.999895i	$-0.504608\pi$
$353$	−0.543932			−0.0289506			−0.0144753	+	0.999895i	$0.504608\pi$
$354$		0			0
$355$	15.3216	−	47.1551i	0.813187	−	2.50273i
$356$	−3.77340	−	11.6133i	−0.199990	−	0.615505i
$357$		0			0
$358$	−16.3296	+	11.8642i	−0.863048	+	0.627041i
$359$	5.76702	+	17.7491i	0.304372	+	0.936759i	0.979911	+	0.199435i	$0.0639108\pi$
$359$	5.76702	+	17.7491i	0.304372	+	0.936759i	−0.675539	+	0.737324i	$0.736089\pi$
$360$		0			0
$361$	−0.106668	−	0.0774985i	−0.00561408	−	0.00407887i
$362$	18.3099			0.962348
$363$		0			0
$364$	20.5182			1.07544
$365$	16.5885	+	12.0522i	0.868282	+	0.630844i
$366$		0			0
$367$	1.76390	+	5.42873i	0.0920748	+	0.283377i	0.986480	−	0.163880i	$-0.0524009\pi$
$367$	1.76390	+	5.42873i	0.0920748	+	0.283377i	−0.894405	+	0.447257i	$0.852401\pi$
$368$	−0.136873	+	0.0994443i	−0.00713502	+	0.00518389i
$369$		0			0
$370$	2.28342	+	7.02766i	0.118710	+	0.365350i
$371$	−7.95603	+	24.4861i	−0.413057	+	1.27126i
$372$		0			0
$373$	37.6045			1.94709			0.973544	−	0.228498i	$-0.0733814\pi$
$373$	37.6045			1.94709			0.973544	+	0.228498i	$0.0733814\pi$
$374$	14.4492	+	1.21126i	0.747152	+	0.0626329i
$375$		0			0
$376$	0.839500	+	0.609932i	0.0432939	+	0.0314549i
$377$	−14.2974	+	44.0030i	−0.736355	+	2.26627i
$378$		0			0
$379$	−17.3210	+	12.5845i	−0.889722	+	0.646421i	−0.935805	−	0.352517i	$-0.885326\pi$
$379$	−17.3210	+	12.5845i	−0.889722	+	0.646421i	0.0460838	+	0.998938i	$0.485326\pi$
$380$	−13.7640	+	10.0001i	−0.706077	+	0.512995i
$381$		0			0
$382$	−1.82633	+	5.62088i	−0.0934434	+	0.287589i
$383$	−28.1088	−	20.4222i	−1.43629	−	1.04353i	−0.988801	−	0.149240i	$-0.952317\pi$
$383$	−28.1088	−	20.4222i	−1.43629	−	1.04353i	−0.447492	−	0.894288i	$-0.647683\pi$
$384$		0			0
$385$	36.3707	+	31.3853i	1.85362	+	1.59954i
$386$	7.16369			0.364622
$387$		0			0
$388$	5.41888	−	16.6776i	0.275102	−	0.846677i
$389$	2.67894	+	8.24493i	0.135828	+	0.418035i	0.995718	−	0.0924445i	$-0.0294681\pi$
$389$	2.67894	+	8.24493i	0.135828	+	0.418035i	−0.859890	+	0.510479i	$0.829468\pi$
$390$		0			0
$391$	0.598395	−	0.434759i	0.0302621	−	0.0219867i
$392$	2.12222	+	6.53152i	0.107188	+	0.329891i
$393$		0			0
$394$	14.5931	+	10.6025i	0.735191	+	0.534148i
$395$	−39.7835			−2.00172
$396$		0			0
$397$	13.0635			0.655640			0.327820	−	0.944740i	$-0.393686\pi$
$397$	13.0635			0.655640			0.327820	+	0.944740i	$0.393686\pi$
$398$	10.1705	+	7.38931i	0.509801	+	0.370392i
$399$		0			0
$400$	3.13009	+	9.63342i	0.156504	+	0.481671i
$401$	−2.66861	+	1.93886i	−0.133264	+	0.0968219i	−0.652420	−	0.757857i	$-0.726246\pi$
$401$	−2.66861	+	1.93886i	−0.133264	+	0.0968219i	0.519156	+	0.854679i	$0.326246\pi$
$402$		0			0
$403$	−0.573848	−	1.76612i	−0.0285854	−	0.0879769i
$404$	−2.08240	+	6.40898i	−0.103603	+	0.318859i
$405$		0			0
$406$	−31.2709			−1.55195
$407$	−1.43966	−	6.13408i	−0.0713612	−	0.304055i
$408$		0			0
$409$	−21.0588	−	15.3001i	−1.04129	−	0.756541i	−0.0707522	−	0.997494i	$-0.522540\pi$
$409$	−21.0588	−	15.3001i	−1.04129	−	0.756541i	−0.970537	+	0.240953i	$0.922540\pi$
$410$	−5.98219	+	18.4113i	−0.295439	+	0.909268i
$411$		0			0
$412$	12.0956	−	8.78798i	0.595908	−	0.432953i
$413$	8.10993	−	5.89221i	0.399063	−	0.289937i
$414$		0			0
$415$	−7.99522	+	24.6068i	−0.392470	+	1.20790i
$416$	−4.45753	−	3.23859i	−0.218549	−	0.158785i
$417$		0			0
$418$	12.4076	−	7.51674i	0.606876	−	0.367656i
$419$	−22.7916			−1.11344			−0.556722	−	0.830699i	$-0.687941\pi$
$419$	−22.7916			−1.11344			−0.556722	+	0.830699i	$0.687941\pi$
$420$		0			0
$421$	−2.03658	+	6.26794i	−0.0992568	+	0.305481i	−0.988340	−	0.152265i	$-0.951343\pi$
$421$	−2.03658	+	6.26794i	−0.0992568	+	0.305481i	0.889083	+	0.457746i	$0.151343\pi$
$422$	−6.97316	−	21.4612i	−0.339448	−	1.04471i
$423$		0			0
$424$	5.59333	−	4.06379i	0.271636	−	0.197355i
$425$	−13.6844	−	42.1162i	−0.663791	−	2.04294i
$426$		0			0
$427$	−32.1916	−	23.3886i	−1.55786	−	1.13185i
$428$	4.06329			0.196407
$429$		0			0
$430$	−14.9409			−0.720512
$431$	−2.93648	−	2.13347i	−0.141445	−	0.102766i	0.514813	−	0.857303i	$-0.327862\pi$
$431$	−2.93648	−	2.13347i	−0.141445	−	0.102766i	−0.656258	+	0.754537i	$0.727862\pi$
$432$		0			0
$433$	0.324687	+	0.999283i	0.0156034	+	0.0480225i	0.958555	−	0.284907i	$-0.0919628\pi$
$433$	0.324687	+	0.999283i	0.0156034	+	0.0480225i	−0.942952	+	0.332930i	$0.891963\pi$
$434$	1.01540	−	0.737731i	0.0487407	−	0.0354122i
$435$		0			0
$436$	−4.87048	−	14.9898i	−0.233254	−	0.717881i
$437$	0.228677	−	0.703795i	0.0109391	−	0.0336671i
$438$		0			0
$439$	35.1100			1.67571			0.837854	−	0.545894i	$-0.183810\pi$
$439$	35.1100			1.67571			0.837854	+	0.545894i	$0.183810\pi$
$440$	−2.94761	−	12.5592i	−0.140522	−	0.598735i
$441$		0			0
$442$	19.4878	+	14.1587i	0.926941	+	0.673462i
$443$	7.60243	−	23.3979i	0.361202	−	1.11167i	−0.591123	−	0.806581i	$-0.701315\pi$
$443$	7.60243	−	23.3979i	0.361202	−	1.11167i	0.952325	−	0.305085i	$-0.0986848\pi$
$444$		0			0
$445$	38.4252	−	27.9175i	1.82153	−	1.32342i
$446$	−20.7260	+	15.0583i	−0.981404	+	0.713031i
$447$		0			0
$448$	1.15076	−	3.54167i	0.0543682	−	0.167328i
$449$	18.3082	+	13.3017i	0.864020	+	0.627747i	0.928976	−	0.370141i	$-0.120691\pi$
$449$	18.3082	+	13.3017i	0.864020	+	0.627747i	−0.0649560	+	0.997888i	$0.520691\pi$
$450$		0			0
$451$	6.39452	−	15.2180i	0.301106	−	0.716589i
$452$	0.634344			0.0298370
$453$		0			0
$454$	2.96983	−	9.14020i	0.139381	−	0.428971i
$455$	24.6620	+	75.9018i	1.15617	+	3.55833i
$456$		0			0
$457$	−1.18753	+	0.862792i	−0.0555504	+	0.0403597i	−0.615214	−	0.788360i	$-0.710930\pi$
$457$	−1.18753	+	0.862792i	−0.0555504	+	0.0403597i	0.559664	+	0.828720i	$0.310930\pi$
$458$	−0.972482	−	2.99299i	−0.0454411	−	0.139853i
$459$		0			0
$460$	−0.532386	−	0.386801i	−0.0248226	−	0.0180347i
$461$	−3.89222			−0.181279			−0.0906393	−	0.995884i	$-0.528891\pi$
$461$	−3.89222			−0.181279			−0.0906393	+	0.995884i	$0.528891\pi$
$462$		0			0
$463$	0.722010			0.0335547			0.0167773	−	0.999859i	$-0.494659\pi$
$463$	0.722010			0.0335547			0.0167773	+	0.999859i	$0.494659\pi$
$464$	6.79355	+	4.93580i	0.315382	+	0.229139i
$465$		0			0
$466$	−1.04414	−	3.21355i	−0.0483691	−	0.148865i
$467$	8.45676	−	6.14420i	0.391332	−	0.284319i	−0.374669	−	0.927159i	$-0.622244\pi$
$467$	8.45676	−	6.14420i	0.391332	−	0.284319i	0.766001	+	0.642839i	$0.222244\pi$
$468$		0			0
$469$	−13.2193	−	40.6847i	−0.610409	−	1.87865i
$470$	−1.24725	+	3.83864i	−0.0575313	+	0.177063i
$471$		0			0
$472$	−2.69189			−0.123904
$473$	12.6953	+	1.06423i	0.583731	+	0.0489336i
$474$		0			0
$475$	−35.8435	−	26.0418i	−1.64461	−	1.19488i
$476$	−5.03098	+	15.4838i	−0.230595	+	0.709697i
$477$		0			0
$478$	−2.40006	+	1.74374i	−0.109776	+	0.0797570i
$479$	−17.4310	+	12.6644i	−0.796444	+	0.578651i	−0.909869	−	0.414896i	$-0.863818\pi$
$479$	−17.4310	+	12.6644i	−0.796444	+	0.578651i	0.113425	+	0.993547i	$0.463818\pi$
$480$		0			0
$481$	3.23456	−	9.95497i	0.147483	−	0.453907i
$482$	17.8415	+	12.9626i	0.812658	+	0.590431i
$483$		0			0
$484$	1.61001	+	10.8815i	0.0731824	+	0.494615i
$485$	68.2080			3.09716
$486$		0			0
$487$	0.719442	−	2.21421i	0.0326010	−	0.100336i	−0.933432	−	0.358755i	$-0.883201\pi$
$487$	0.719442	−	2.21421i	0.0326010	−	0.100336i	0.966033	+	0.258419i	$0.0832015\pi$
$488$	3.30192	+	10.1623i	0.149471	+	0.460024i
$489$		0			0
$490$	−21.6109	+	15.7012i	−0.976281	+	0.709310i
$491$	−4.16636	−	12.8227i	−0.188025	−	0.578682i	0.811962	−	0.583710i	$-0.198399\pi$
$491$	−4.16636	−	12.8227i	−0.188025	−	0.578682i	−0.999987	+	0.00502816i	$0.998399\pi$
$492$		0			0
$493$	−29.7006	−	21.5788i	−1.33765	−	0.971858i
$494$	24.0999			1.08431
$495$		0			0
$496$	−0.337037			−0.0151334
$497$	−38.4037	−	27.9019i	−1.72264	−	1.25157i
$498$		0			0
$499$	13.1925	+	40.6024i	0.590578	+	1.81761i	0.575610	+	0.817724i	$0.304765\pi$
$499$	13.1925	+	40.6024i	0.590578	+	1.81761i	0.0149677	+	0.999888i	$0.495235\pi$
$500$	−16.1404	+	11.7267i	−0.721819	+	0.524432i
$501$		0			0
$502$	4.84864	+	14.9226i	0.216405	+	0.666028i
$503$	8.99549	−	27.6853i	0.401089	−	1.23443i	−0.523028	−	0.852316i	$-0.675198\pi$
$503$	8.99549	−	27.6853i	0.401089	−	1.23443i	0.924117	−	0.382110i	$-0.124802\pi$
$504$		0			0
$505$	−26.2114			−1.16639
$506$	0.424819	+	0.366589i	0.0188855	+	0.0162968i
$507$		0			0
$508$	6.99219	+	5.08012i	0.310228	+	0.225394i
$509$	5.95098	−	18.3152i	0.263773	−	0.811808i	−0.728201	−	0.685364i	$-0.759643\pi$
$509$	5.95098	−	18.3152i	0.263773	−	0.811808i	0.991974	−	0.126445i	$-0.0403567\pi$
$510$		0			0
$511$	15.8818	−	11.5388i	0.702571	−	0.510448i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−4.44847	+	13.6910i	−0.196214	+	0.603883i
$515$	47.0474	+	34.1820i	2.07316	+	1.50624i
$516$		0			0
$517$	1.33322	−	3.17287i	0.0586349	−	0.139542i
$518$	7.07453			0.310837
$519$		0			0
$520$	6.62258	−	20.3822i	0.290419	−	0.893819i
$521$	9.18913	+	28.2812i	0.402583	+	1.23902i	0.922897	+	0.385048i	$0.125815\pi$
$521$	9.18913	+	28.2812i	0.402583	+	1.23902i	−0.520314	+	0.853975i	$0.674185\pi$
$522$		0			0
$523$	−10.9172	+	7.93183i	−0.477377	+	0.346835i	−0.800309	−	0.599587i	$-0.795331\pi$
$523$	−10.9172	+	7.93183i	−0.477377	+	0.346835i	0.322932	+	0.946422i	$0.395331\pi$
$524$	0.214048	+	0.658771i	0.00935071	+	0.0287785i
$525$		0			0
$526$	15.5861	+	11.3240i	0.679586	+	0.493748i
$527$	1.47349			0.0641861
$528$		0			0
$529$	−22.9714			−0.998756
$530$	21.7560	+	15.8066i	0.945018	+	0.686596i
$531$		0			0
$532$	5.03341	+	15.4912i	0.218226	+	0.671630i
$533$	22.1853	−	16.1185i	0.960950	−	0.698171i
$534$		0			0
$535$	4.88391	+	15.0311i	0.211150	+	0.649853i
$536$	−3.54982	+	10.9252i	−0.153329	+	0.471898i
$537$		0			0
$538$	28.9688			1.24893
$539$	19.4813	−	11.8021i	0.839118	−	0.508352i
$540$		0			0
$541$	10.9342	+	7.94417i	0.470099	+	0.341547i	0.797480	−	0.603346i	$-0.206166\pi$
$541$	10.9342	+	7.94417i	0.470099	+	0.341547i	−0.327381	+	0.944892i	$0.606166\pi$
$542$	6.13856	−	18.8926i	0.263674	−	0.811505i
$543$		0			0
$544$	3.53693	−	2.56973i	0.151645	−	0.110176i
$545$	49.5969	−	36.0343i	2.12450	−	1.54354i
$546$		0			0
$547$	7.03356	−	21.6471i	0.300733	−	0.925561i	−0.680502	−	0.732746i	$-0.738238\pi$
$547$	7.03356	−	21.6471i	0.300733	−	0.925561i	0.981235	−	0.192815i	$-0.0617618\pi$
$548$	−7.90987	−	5.74686i	−0.337893	−	0.245494i
$549$		0			0
$550$	28.7332	−	17.4071i	1.22519	−	0.742239i
$551$	−36.7297			−1.56474
$552$		0			0
$553$	−11.7701	+	36.2245i	−0.500514	+	1.54042i
$554$	−4.92618	−	15.1612i	−0.209293	−	0.644139i
$555$		0			0
$556$	2.43319	−	1.76782i	0.103190	−	0.0749721i
$557$	1.98094	+	6.09671i	0.0839352	+	0.258326i	0.984212	−	0.176991i	$-0.0566363\pi$
$557$	1.98094	+	6.09671i	0.0839352	+	0.258326i	−0.900277	+	0.435317i	$0.856636\pi$
$558$		0			0
$559$	17.1223	+	12.4401i	0.724197	+	0.526160i
$560$	14.4847			0.612090
$561$		0			0
$562$	8.07105			0.340457
$563$	−5.28266	−	3.83807i	−0.222637	−	0.161756i	0.470876	−	0.882200i	$-0.343938\pi$
$563$	−5.28266	−	3.83807i	−0.222637	−	0.161756i	−0.693513	+	0.720444i	$0.743938\pi$
$564$		0			0
$565$	0.762456	+	2.34660i	0.0320768	+	0.0987222i
$566$	−17.0069	+	12.3563i	−0.714855	+	0.519373i
$567$		0			0
$568$	3.93910	+	12.1233i	0.165281	+	0.508682i
$569$	−9.92540	+	30.5472i	−0.416094	+	1.28061i	0.495174	+	0.868794i	$0.335104\pi$
$569$	−9.92540	+	30.5472i	−0.416094	+	1.28061i	−0.911268	+	0.411813i	$0.864896\pi$
$570$		0			0
$571$	−0.178273			−0.00746047			−0.00373024	−	0.999993i	$-0.501187\pi$
$571$	−0.178273			−0.00746047			−0.00373024	+	0.999993i	$0.501187\pi$
$572$	−7.07906	+	16.8471i	−0.295990	+	0.704414i
$573$		0			0
$574$	14.9944	+	10.8941i	0.625854	+	0.454709i
$575$	0.529564	−	1.62983i	0.0220843	−	0.0679686i
$576$		0			0
$577$	30.1514	−	21.9063i	1.25522	−	0.911971i	0.256708	−	0.966489i	$-0.417362\pi$
$577$	30.1514	−	21.9063i	1.25522	−	0.911971i	0.998513	+	0.0545181i	$0.0173623\pi$
$578$	−1.70977	+	1.24222i	−0.0711169	+	0.0516694i
$579$		0			0
$580$	−10.0932	+	31.0637i	−0.419097	+	1.28985i
$581$	20.0401	+	14.5600i	0.831402	+	0.604049i
$582$		0			0
$583$	−17.3602	−	14.9806i	−0.718987	−	0.620435i
$584$	−5.27159			−0.218140
$585$		0			0
$586$	−3.35493	+	10.3254i	−0.138591	+	0.426538i
$587$	5.39960	+	16.6183i	0.222865	+	0.685909i	0.998501	+	0.0547286i	$0.0174293\pi$
$587$	5.39960	+	16.6183i	0.222865	+	0.685909i	−0.775636	+	0.631181i	$0.782571\pi$
$588$		0			0
$589$	1.19265	−	0.866513i	0.0491424	−	0.0357040i
$590$	−3.23555	−	9.95800i	−0.133205	−	0.409964i
$591$		0			0
$592$	−1.53693	−	1.11664i	−0.0631674	−	0.0458938i
$593$	33.4398			1.37321			0.686603	−	0.727032i	$-0.259101\pi$
$593$	33.4398			1.37321			0.686603	+	0.727032i	$0.259101\pi$
$594$		0			0
$595$	−63.3254			−2.59609
$596$	7.41744	+	5.38909i	0.303830	+	0.220746i
$597$		0			0
$598$	0.288059	+	0.886553i	0.0117796	+	0.0362538i
$599$	−18.1595	+	13.1937i	−0.741979	+	0.539079i	−0.893330	−	0.449401i	$-0.851637\pi$
$599$	−18.1595	+	13.1937i	−0.741979	+	0.539079i	0.151351	+	0.988480i	$0.451637\pi$
$600$		0			0
$601$	−7.76499	−	23.8982i	−0.316741	−	0.974827i	−0.975032	−	0.222064i	$-0.928721\pi$
$601$	−7.76499	−	23.8982i	−0.316741	−	0.974827i	0.658291	−	0.752763i	$-0.271279\pi$
$602$	−4.42030	+	13.6043i	−0.180158	+	0.554469i
$603$		0			0
$604$	−1.84056			−0.0748914
$605$	−38.3184	+	19.0350i	−1.55786	+	0.773884i
$606$		0			0
$607$	9.50701	+	6.90724i	0.385877	+	0.280356i	0.763764	−	0.645495i	$-0.223349\pi$
$607$	9.50701	+	6.90724i	0.385877	+	0.280356i	−0.377887	+	0.925852i	$0.623349\pi$
$608$	1.35164	−	4.15992i	0.0548162	−	0.168707i
$609$		0			0
$610$	−33.6240	+	24.4293i	−1.36140	+	0.989112i
$611$	4.62549	−	3.36061i	0.187127	−	0.135956i
$612$		0			0
$613$	−5.20656	+	16.0242i	−0.210291	+	0.647210i	0.789163	+	0.614183i	$0.210514\pi$
$613$	−5.20656	+	16.0242i	−0.210291	+	0.647210i	−0.999454	+	0.0330263i	$0.989486\pi$
$614$	−9.18881	−	6.67606i	−0.370830	−	0.269424i
$615$		0			0
$616$	−12.3077	−	1.03174i	−0.495892	−	0.0415701i
$617$	29.4952			1.18743			0.593716	−	0.804675i	$-0.297660\pi$
$617$	29.4952			1.18743			0.593716	+	0.804675i	$0.297660\pi$
$618$		0			0
$619$	−5.88203	+	18.1030i	−0.236419	+	0.727623i	0.760511	+	0.649325i	$0.224948\pi$
$619$	−5.88203	+	18.1030i	−0.236419	+	0.727623i	−0.996930	+	0.0782977i	$0.975052\pi$
$620$	−0.405105	−	1.24679i	−0.0162694	−	0.0500721i
$621$		0			0
$622$	0.672023	−	0.488253i	0.0269457	−	0.0195772i
$623$	−14.0519	−	43.2472i	−0.562977	−	1.73266i
$624$		0			0
$625$	−21.8066	−	15.8434i	−0.872263	−	0.633736i
$626$	1.68426			0.0673165
$627$		0			0
$628$	−7.95486			−0.317433
$629$	6.71928	+	4.88184i	0.267915	+	0.194652i
$630$		0			0
$631$	0.143400	+	0.441339i	0.00570865	+	0.0175694i	0.953870	−	0.300219i	$-0.0970598\pi$
$631$	0.143400	+	0.441339i	0.00570865	+	0.0175694i	−0.948162	+	0.317789i	$0.897060\pi$
$632$	8.27471	−	6.01193i	0.329150	−	0.239142i
$633$		0			0
$634$	−5.61412	−	17.2785i	−0.222965	−	0.686217i
$635$	−10.3883	+	31.9720i	−0.412248	+	1.26877i
$636$		0			0
$637$	37.8394			1.49925
$638$	10.7889	−	25.6760i	0.427137	−	1.01652i
$639$		0			0
$640$	−3.14677	−	2.28626i	−0.124387	−	0.0903725i
$641$	−14.8630	+	45.7437i	−0.587054	+	1.80677i	0.00380416	+	0.999993i	$0.498789\pi$
$641$	−14.8630	+	45.7437i	−0.587054	+	1.80677i	−0.590859	+	0.806775i	$0.701211\pi$
$642$		0			0
$643$	−8.02188	+	5.82824i	−0.316352	+	0.229843i	−0.734617	−	0.678482i	$-0.762638\pi$
$643$	−8.02188	+	5.82824i	−0.316352	+	0.229843i	0.418265	+	0.908325i	$0.362638\pi$
$644$	−0.509707	+	0.370324i	−0.0200853	+	0.0145928i
$645$		0			0
$646$	−5.90921	+	18.1867i	−0.232495	+	0.715546i
$647$	−36.4740	−	26.4999i	−1.43394	−	1.04182i	−0.989266	−	0.146127i	$-0.953319\pi$
$647$	−36.4740	−	26.4999i	−1.43394	−	1.04182i	−0.444675	−	0.895692i	$-0.646681\pi$
$648$		0			0
$649$	2.03995	+	8.69182i	0.0800752	+	0.341184i
$650$	55.8099			2.18904
$651$		0			0
$652$	−0.342850	+	1.05519i	−0.0134271	+	0.0413242i
$653$	2.37151	+	7.29877i	0.0928046	+	0.285623i	0.986675	−	0.162702i	$-0.0520208\pi$
$653$	2.37151	+	7.29877i	0.0928046	+	0.285623i	−0.893871	+	0.448325i	$0.852021\pi$
$654$		0			0
$655$	−2.17968	+	1.58363i	−0.0851672	+	0.0618776i
$656$	−1.53799	−	4.73343i	−0.0600482	−	0.184809i
$657$		0			0
$658$	3.12624	+	2.27134i	0.121873	+	0.0885462i
$659$	21.4800			0.836743			0.418372	−	0.908276i	$-0.362601\pi$
$659$	21.4800			0.836743			0.418372	+	0.908276i	$0.362601\pi$
$660$		0			0
$661$	35.0869			1.36472			0.682362	−	0.731015i	$-0.260953\pi$
$661$	35.0869			1.36472			0.682362	+	0.731015i	$0.260953\pi$
$662$	−19.5099	−	14.1747i	−0.758272	−	0.550917i
$663$		0			0
$664$	−2.05552	−	6.32625i	−0.0797698	−	0.245506i
$665$	−51.2561	+	37.2397i	−1.98762	+	1.44409i
$666$		0			0
$667$	−0.439018	−	1.35116i	−0.0169989	−	0.0523171i
$668$	−1.55713	+	4.79236i	−0.0602472	+	0.185422i
$669$		0			0
$670$	−44.6819			−1.72621
$671$	30.3106	−	18.3626i	1.17013	−	0.708881i
$672$		0			0
$673$	−6.82002	−	4.95503i	−0.262892	−	0.191003i	0.448529	−	0.893768i	$-0.351948\pi$
$673$	−6.82002	−	4.95503i	−0.262892	−	0.191003i	−0.711421	+	0.702766i	$0.751948\pi$
$674$	−2.21240	+	6.80907i	−0.0852185	+	0.262275i
$675$		0			0
$676$	−14.0430	+	10.2028i	−0.540114	+	0.392416i
$677$	11.6866	−	8.49082i	0.449153	−	0.326329i	−0.340108	−	0.940386i	$-0.610464\pi$
$677$	11.6866	−	8.49082i	0.449153	−	0.326329i	0.789261	+	0.614058i	$0.210464\pi$
$678$		0			0
$679$	20.1795	−	62.1062i	0.774419	−	2.38342i
$680$	13.7573	+	9.99529i	0.527570	+	0.383302i
$681$		0			0
$682$	0.255411	+	1.08826i	0.00978021	+	0.0416714i
$683$	36.5728			1.39942			0.699710	−	0.714427i	$-0.253312\pi$
$683$	36.5728			1.39942			0.699710	+	0.714427i	$0.253312\pi$
$684$		0			0
$685$	11.7517	−	36.1681i	0.449011	−	1.38191i
$686$	−0.152311	−	0.468765i	−0.00581527	−	0.0178975i
$687$		0			0
$688$	3.10760	−	2.25781i	0.118476	−	0.0860780i
$689$	−11.7715	−	36.2290i	−0.448459	−	1.38021i
$690$		0			0
$691$	−15.4846	−	11.2502i	−0.589061	−	0.427978i	0.252918	−	0.967488i	$-0.418610\pi$
$691$	−15.4846	−	11.2502i	−0.589061	−	0.427978i	−0.841979	+	0.539510i	$0.818610\pi$
$692$	−2.21200			−0.0840877
$693$		0			0
$694$	1.98859			0.0754857
$695$	9.46420	+	6.87615i	0.358998	+	0.260827i
$696$		0			0
$697$	6.72390	+	20.6940i	0.254686	+	0.783842i
$698$	10.8242	−	7.86426i	0.409703	−	0.297667i
$699$		0			0
$700$	11.6562	+	35.8742i	0.440564	+	1.35592i
$701$	−7.16339	+	22.0467i	−0.270558	+	0.832691i	0.719803	+	0.694178i	$0.244232\pi$
$701$	−7.16339	+	22.0467i	−0.270558	+	0.832691i	−0.990361	+	0.138512i	$0.955768\pi$
$702$		0			0
$703$	8.30950			0.313399
$704$	2.51098	+	2.16679i	0.0946360	+	0.0816641i
$705$		0			0
$706$	0.440051	+	0.319715i	0.0165615	+	0.0120326i
$707$	−7.75472	+	23.8666i	−0.291646	+	0.897595i
$708$		0			0
$709$	−36.7011	+	26.6649i	−1.37834	+	1.00142i	−0.381306	+	0.924449i	$0.624525\pi$
$709$	−36.7011	+	26.6649i	−1.37834	+	1.00142i	−0.997033	+	0.0769728i	$0.975475\pi$
$710$	−40.1125	+	29.1434i	−1.50540	+	1.09373i
$711$		0			0
$712$	−3.77340	+	11.6133i	−0.141414	+	0.435228i
$713$	0.0461314	+	0.0335164i	0.00172764	+	0.00125520i
$714$		0			0
$715$	−70.8305	−	5.93765i	−2.64891	−	0.222055i
$716$	20.1845			0.754332
$717$		0			0
$718$	5.76702	−	17.7491i	0.215223	−	0.662389i
$719$	0.172985	+	0.532395i	0.00645127	+	0.0198550i	0.954230	−	0.299073i	$-0.0966773\pi$
$719$	0.172985	+	0.532395i	0.00645127	+	0.0198550i	−0.947779	+	0.318928i	$0.896677\pi$
$720$		0			0
$721$	45.0432	−	32.7258i	1.67750	−	1.21877i
$722$	0.0407434	+	0.125395i	0.00151631	+	0.00466673i
$723$		0			0
$724$	−14.8130	−	10.7623i	−0.550522	−	0.399978i
$725$	−85.0576			−3.15896
$726$		0			0
$727$	−21.5446			−0.799045			−0.399523	−	0.916723i	$-0.630824\pi$
$727$	−21.5446			−0.799045			−0.399523	+	0.916723i	$0.630824\pi$
$728$	−16.5995	−	12.0603i	−0.615220	−	0.446983i
$729$		0			0
$730$	−6.33624	−	19.5009i	−0.234515	−	0.721762i
$731$	−13.5861	+	9.87087i	−0.502499	+	0.365087i
$732$		0			0
$733$	9.95778	+	30.6469i	0.367799	+	1.13197i	0.948210	+	0.317645i	$0.102892\pi$
$733$	9.95778	+	30.6469i	0.367799	+	1.13197i	−0.580411	+	0.814324i	$0.697108\pi$
$734$	1.76390	−	5.42873i	0.0651067	−	0.200378i
$735$		0			0
$736$	0.169185			0.00623623
$737$	37.9664	+	3.18268i	1.39851	+	0.117236i
$738$		0			0
$739$	−1.45229	−	1.05515i	−0.0534234	−	0.0388144i	0.560753	−	0.827983i	$-0.310512\pi$
$739$	−1.45229	−	1.05515i	−0.0534234	−	0.0388144i	−0.614176	+	0.789169i	$0.710512\pi$
$740$	2.28342	−	7.02766i	0.0839403	−	0.258342i
$741$		0			0
$742$	20.8292	−	15.1333i	0.764662	−	0.555560i
$743$	34.2685	−	24.8975i	1.25719	−	0.913402i	0.258574	−	0.965992i	$-0.416747\pi$
$743$	34.2685	−	24.8975i	1.25719	−	0.913402i	0.998616	+	0.0525895i	$0.0167475\pi$
$744$		0			0
$745$	−11.0201	+	33.9165i	−0.403746	+	1.24260i
$746$	−30.4227	−	22.1034i	−1.11385	−	0.809263i
$747$		0			0
$748$	−10.9777	−	9.47297i	−0.401385	−	0.346366i
$749$	15.1314			0.552889
$750$		0			0
$751$	9.02861	−	27.7872i	0.329459	−	1.01397i	−0.639929	−	0.768434i	$-0.721036\pi$
$751$	9.02861	−	27.7872i	0.329459	−	1.01397i	0.969388	−	0.245535i	$-0.0789637\pi$
$752$	−0.320660	−	0.986891i	−0.0116933	−	0.0359882i
$753$		0			0
$754$	37.4312	−	27.1953i	1.36316	−	0.990396i
$755$	−2.21228	−	6.80870i	−0.0805132	−	0.247794i
$756$		0			0
$757$	−24.0513	−	17.4743i	−0.874158	−	0.635113i	0.0575416	−	0.998343i	$-0.481674\pi$
$757$	−24.0513	−	17.4743i	−0.874158	−	0.635113i	−0.931699	+	0.363230i	$0.881674\pi$
$758$	21.4100			0.777645
$759$		0			0
$760$	17.0132			0.617134
$761$	−12.8332	−	9.32389i	−0.465205	−	0.337991i	0.330365	−	0.943853i	$-0.392828\pi$
$761$	−12.8332	−	9.32389i	−0.465205	−	0.337991i	−0.795569	+	0.605862i	$0.792828\pi$
$762$		0			0
$763$	−18.1373	−	55.8209i	−0.656615	−	2.02085i
$764$	4.78141	−	3.47389i	0.172985	−	0.125681i
$765$		0			0
$766$	10.7366	+	33.0439i	0.387929	+	1.19392i
$767$	−4.58329	+	14.1059i	−0.165493	+	0.509335i
$768$		0			0
$769$	−20.0451			−0.722845			−0.361423	−	0.932402i	$-0.617709\pi$
$769$	−20.0451			−0.722845			−0.361423	+	0.932402i	$0.617709\pi$
$770$	−10.9767	−	46.7694i	−0.395573	−	1.68545i
$771$		0			0
$772$	−5.79555	−	4.21071i	−0.208586	−	0.151547i
$773$	3.72846	−	11.4750i	0.134103	−	0.412727i	−0.861346	−	0.508018i	$-0.830378\pi$
$773$	3.72846	−	11.4750i	0.134103	−	0.412727i	0.995449	+	0.0952910i	$0.0303782\pi$
$774$		0			0
$775$	2.76191	−	2.00665i	0.0992108	−	0.0720809i
$776$	−14.1868	+	10.3073i	−0.509277	+	0.370011i
$777$		0			0
$778$	2.67894	−	8.24493i	0.0960446	−	0.295595i
$779$	17.6119	+	12.7958i	0.631011	+	0.458457i
$780$		0			0
$781$	36.1597	−	21.9061i	1.29389	−	0.783862i
$782$	−0.739657			−0.0264501
$783$		0			0
$784$	2.12222	−	6.53152i	0.0757935	−	0.233268i
$785$	−9.56142	−	29.4270i	−0.341262	−	1.05030i
$786$		0			0
$787$	−19.3353	+	14.0479i	−0.689229	+	0.500754i	−0.876406	−	0.481572i	$-0.840066\pi$
$787$	−19.3353	+	14.0479i	−0.689229	+	0.500754i	0.187178	+	0.982326i	$0.440066\pi$
$788$	−5.57408	−	17.1552i	−0.198568	−	0.611130i
$789$		0			0
$790$	32.1855	+	23.3841i	1.14511	+	0.831970i
$791$	2.36225			0.0839920
$792$		0			0
$793$	58.8736			2.09066
$794$	−10.5686	−	7.67856i	−0.375066	−	0.272502i
$795$		0			0
$796$	−3.88479	−	11.9561i	−0.137693	−	0.423774i
$797$	−31.9508	+	23.2136i	−1.13176	+	0.822268i	−0.985949	−	0.167045i	$-0.946578\pi$
$797$	−31.9508	+	23.2136i	−1.13176	+	0.822268i	−0.145806	+	0.989313i	$0.546578\pi$
$798$		0			0
$799$	1.40189	+	4.31458i	0.0495953	+	0.152639i
$800$	3.13009	−	9.63342i	0.110665	−	0.340593i
$801$		0			0
$802$	3.29858			0.116477
$803$	3.99489	+	17.0214i	0.140976	+	0.600671i
$804$		0			0
$805$	−1.98257	−	1.44042i	−0.0698763	−	0.0507681i
$806$	−0.573848	+	1.76612i	−0.0202129	+	0.0622091i
$807$		0			0
$808$	5.45180	−	3.96097i	0.191794	−	0.139346i
$809$	12.8540	−	9.33900i	0.451924	−	0.328342i	−0.338431	−	0.940991i	$-0.609896\pi$
$809$	12.8540	−	9.33900i	0.451924	−	0.328342i	0.790355	+	0.612649i	$0.209896\pi$
$810$		0			0
$811$	3.09560	−	9.52728i	0.108701	−	0.334548i	−0.881880	−	0.471474i	$-0.843722\pi$
$811$	3.09560	−	9.52728i	0.108701	−	0.334548i	0.990581	+	0.136926i	$0.0437222\pi$
$812$	25.2987	+	18.3806i	0.887809	+	0.645031i
$813$		0			0
$814$	−2.44081	+	5.80878i	−0.0855505	+	0.203598i
$815$	−4.31549			−0.151165
$816$		0			0
$817$	−5.19193	+	15.9791i	−0.181643	+	0.559038i
$818$	8.04373	+	24.7561i	0.281243	+	0.865576i
$819$		0			0
$820$	15.6616	−	11.3788i	0.546926	−	0.397365i
$821$	−13.4978	−	41.5419i	−0.471076	−	1.44982i	−0.851178	−	0.524878i	$-0.824111\pi$
$821$	−13.4978	−	41.5419i	−0.471076	−	1.44982i	0.380102	−	0.924945i	$-0.375889\pi$
$822$		0			0
$823$	26.3539	+	19.1473i	0.918641	+	0.667431i	0.943185	−	0.332267i	$-0.107814\pi$
$823$	26.3539	+	19.1473i	0.918641	+	0.667431i	−0.0245446	+	0.999699i	$0.507814\pi$
$824$	−14.9510			−0.520843
$825$		0			0
$826$	−10.0244			−0.348794
$827$	−20.8995	−	15.1844i	−0.726746	−	0.528012i	0.161786	−	0.986826i	$-0.448275\pi$
$827$	−20.8995	−	15.1844i	−0.726746	−	0.528012i	−0.888532	+	0.458814i	$0.848275\pi$
$828$		0			0
$829$	−7.86781	−	24.2146i	−0.273260	−	0.841009i	−0.989674	−	0.143334i	$-0.954218\pi$
$829$	−7.86781	−	24.2146i	−0.273260	−	0.841009i	0.716414	−	0.697675i	$-0.245782\pi$
$830$	20.9318	−	15.2078i	0.726552	−	0.527871i
$831$		0			0
$832$	1.70263	+	5.24015i	0.0590279	+	0.181669i
$833$	−9.27810	+	28.5550i	−0.321467	+	0.989374i
$834$		0			0
$835$	−19.5998			−0.678277
$836$	−14.4562	−	1.21185i	−0.499978	−	0.0419126i
$837$		0			0
$838$	18.4388	+	13.3966i	0.636958	+	0.462777i
$839$	5.30001	−	16.3118i	0.182977	−	0.563145i	−0.816931	−	0.576736i	$-0.804326\pi$
$839$	5.30001	−	16.3118i	0.182977	−	0.563145i	0.999908	+	0.0135909i	$0.00432626\pi$
$840$		0			0
$841$	−33.5858	+	24.4015i	−1.15813	+	0.841432i
$842$	5.33183	−	3.87380i	0.183747	−	0.133500i
$843$		0			0
$844$	−6.97316	+	21.4612i	−0.240026	+	0.738724i
$845$	−54.6219	−	39.6851i	−1.87905	−	1.36521i
$846$		0			0
$847$	5.99557	+	40.5221i	0.206010	+	1.39235i
$848$	−6.91374			−0.237419
$849$		0			0
$850$	−13.6844	+	42.1162i	−0.469371	+	1.44457i
$851$	0.0993208	+	0.305678i	0.00340467	+	0.0104785i
$852$		0			0
$853$	4.62528	−	3.36047i	0.158367	−	0.115060i	−0.505780	−	0.862663i	$-0.668795\pi$
$853$	4.62528	−	3.36047i	0.158367	−	0.115060i	0.664146	+	0.747603i	$0.268795\pi$
$854$	12.2961	+	37.8435i	0.420764	+	1.29498i
$855$		0			0
$856$	−3.28727	−	2.38834i	−0.112357	−	0.0816319i
$857$	13.0129			0.444511			0.222256	−	0.974988i	$-0.428658\pi$
$857$	13.0129			0.444511			0.222256	+	0.974988i	$0.428658\pi$
$858$		0			0
$859$	−36.5028			−1.24546			−0.622729	−	0.782437i	$-0.713976\pi$
$859$	−36.5028			−1.24546			−0.622729	+	0.782437i	$0.713976\pi$
$860$	12.0874	+	8.78201i	0.412177	+	0.299464i
$861$		0			0
$862$	1.12163	+	3.45203i	0.0382030	+	0.117577i
$863$	6.25299	−	4.54306i	0.212854	−	0.154648i	−0.476250	−	0.879310i	$-0.658004\pi$
$863$	6.25299	−	4.54306i	0.212854	−	0.154648i	0.689104	+	0.724662i	$0.258004\pi$
$864$		0			0
$865$	−2.65874	−	8.18276i	−0.0903998	−	0.278222i
$866$	0.324687	−	0.999283i	0.0110333	−	0.0339570i
$867$		0			0
$868$	−1.25510			−0.0426009
$869$	−25.6825	−	22.1622i	−0.871220	−	0.751800i
$870$		0			0
$871$	51.2057	+	37.2031i	1.73504	+	1.26058i
$872$	−4.87048	+	14.9898i	−0.164935	+	0.507618i
$873$		0			0
$874$	−0.598684	+	0.434969i	−0.0202508	+	0.0147131i
$875$	−60.1056	+	43.6693i	−2.03194	+	1.47629i
$876$		0			0
$877$	14.6884	−	45.2063i	0.495993	−	1.52651i	−0.319411	−	0.947616i	$-0.603485\pi$
$877$	14.6884	−	45.2063i	0.495993	−	1.52651i	0.815404	−	0.578893i	$-0.196515\pi$
$878$	−28.4046	−	20.6371i	−0.958608	−	0.696470i
$879$		0			0
$880$	−4.99742	+	11.8931i	−0.168463	+	0.400918i
$881$	−45.3262			−1.52708			−0.763539	−	0.645761i	$-0.776540\pi$
$881$	−45.3262			−1.52708			−0.763539	+	0.645761i	$0.776540\pi$
$882$		0			0
$883$	−13.8524	+	42.6334i	−0.466171	+	1.43473i	0.391332	+	0.920250i	$0.372014\pi$
$883$	−13.8524	+	42.6334i	−0.466171	+	1.43473i	−0.857503	+	0.514478i	$0.827986\pi$
$884$	−7.44369	−	22.9093i	−0.250358	−	0.770524i
$885$		0			0
$886$	−19.9034	+	14.4607i	−0.668668	+	0.485816i
$887$	−3.93466	−	12.1096i	−0.132113	−	0.406602i	0.863017	−	0.505175i	$-0.168572\pi$
$887$	−3.93466	−	12.1096i	−0.132113	−	0.406602i	−0.995130	+	0.0985734i	$0.968572\pi$
$888$		0			0
$889$	26.0384	+	18.9180i	0.873300	+	0.634490i
$890$	−47.4961			−1.59207
$891$		0			0
$892$	25.6187			0.857778
$893$	3.67197	+	2.66784i	0.122878	+	0.0892759i
$894$		0			0
$895$	24.2610	+	74.6677i	0.810957	+	2.49587i
$896$	−3.01272	+	2.18887i	−0.100648	+	0.0731250i
$897$		0			0
$898$	−6.99313	−	21.5226i	−0.233364	−	0.718220i
$899$	0.874579	−	2.69168i	0.0291688	−	0.0897725i
$900$		0			0
$901$	30.2261			1.00698
$902$	−14.1182	+	8.55304i	−0.470085	+	0.284785i
$903$		0			0
$904$	−0.513195	−	0.372858i	−0.0170686	−	0.0124011i
$905$	22.0078	−	67.7331i	0.731564	−	2.25152i
$906$		0			0
$907$	−6.34157	+	4.60742i	−0.210568	+	0.152987i	−0.688071	−	0.725644i	$-0.741542\pi$
$907$	−6.34157	+	4.60742i	−0.210568	+	0.152987i	0.477502	+	0.878630i	$0.341542\pi$
$908$	−7.77511	+	5.64895i	−0.258026	+	0.187467i
$909$		0			0
$910$	24.6620	−	75.9018i	0.817538	−	2.51612i
$911$	19.1134	+	13.8867i	0.633255	+	0.460086i	0.857526	−	0.514440i	$-0.172000\pi$
$911$	19.1134	+	13.8867i	0.633255	+	0.460086i	−0.224272	+	0.974527i	$0.572000\pi$
$912$		0			0
$913$	−18.8691	+	11.4312i	−0.624475	+	0.378317i
$914$	1.46787			0.0485528
$915$		0			0
$916$	−0.972482	+	2.99299i	−0.0321317	+	0.0988912i
$917$	0.797098	+	2.45321i	0.0263225	+	0.0810123i
$918$		0			0
$919$	45.8848	−	33.3373i	1.51360	−	1.09969i	0.549052	−	0.835788i	$-0.314989\pi$
$919$	45.8848	−	33.3373i	1.51360	−	1.09969i	0.964548	−	0.263907i	$-0.0850110\pi$
$920$	0.203353	+	0.625857i	0.00670436	+	0.0206339i
$921$		0			0
$922$	3.14887	+	2.28779i	0.103702	+	0.0753442i
$923$	70.2346			2.31180
$924$		0			0
$925$	19.2429			0.632703
$926$	−0.584119	−	0.424387i	−0.0191953	−	0.0139462i
$927$		0			0
$928$	−2.59490	−	7.98629i	−0.0851819	−	0.262163i
$929$	5.95967	−	4.32995i	0.195530	−	0.142061i	−0.485712	−	0.874119i	$-0.661440\pi$
$929$	5.95967	−	4.32995i	0.195530	−	0.142061i	0.681243	+	0.732058i	$0.261440\pi$
$930$		0			0
$931$	9.28258	+	28.5688i	0.304224	+	0.936306i
$932$	−1.04414	+	3.21355i	−0.0342021	+	0.105263i
$933$		0			0
$934$	−10.4531			−0.342037
$935$	21.8482	−	51.9954i	0.714511	−	1.70043i
$936$		0			0
$937$	−22.2928	−	16.1966i	−0.728272	−	0.529121i	0.160744	−	0.986996i	$-0.448611\pi$
$937$	−22.2928	−	16.1966i	−0.728272	−	0.529121i	−0.889016	+	0.457875i	$0.848611\pi$
$938$	−13.2193	+	40.6847i	−0.431624	+	1.32840i
$939$		0			0
$940$	3.26534	−	2.37241i	0.106504	−	0.0773794i
$941$	−20.9421	+	15.2153i	−0.682693	+	0.496006i	−0.874250	−	0.485476i	$-0.838646\pi$
$941$	−20.9421	+	15.2153i	−0.682693	+	0.496006i	0.191557	+	0.981482i	$0.438646\pi$
$942$		0			0
$943$	−0.260204	+	0.800825i	−0.00847340	+	0.0260784i
$944$	2.17779	+	1.58226i	0.0708810	+	0.0514980i
$945$		0			0
$946$	−9.64518	−	8.32310i	−0.313592	−	0.270607i
$947$	−40.0180			−1.30041			−0.650206	−	0.759758i	$-0.725317\pi$
$947$	−40.0180			−1.30041			−0.650206	+	0.759758i	$0.725317\pi$
$948$		0			0
$949$	−8.97555	+	27.6239i	−0.291359	+	0.896710i
$950$	13.6910	+	42.1366i	0.444195	+	1.36709i
$951$		0			0
$952$	13.1713	−	9.56949i	0.426883	−	0.310149i
$953$	4.58346	+	14.1064i	0.148473	+	0.456953i	0.997441	−	0.0714911i	$-0.0227758\pi$
$953$	4.58346	+	14.1064i	0.148473	+	0.456953i	−0.848968	+	0.528444i	$0.822776\pi$
$954$		0			0
$955$	18.5979	+	13.5121i	0.601813	+	0.437243i
$956$	2.96663			0.0959478
$957$		0			0
$958$	21.5459			0.696118
$959$	−29.4558	−	21.4009i	−0.951177	−	0.691071i
$960$		0			0
$961$	−9.54442	−	29.3747i	−0.307885	−	0.947572i
$962$	−8.46820	+	6.15251i	−0.273026	+	0.198365i
$963$		0			0
$964$	−6.81485	−	20.9739i	−0.219491	−	0.675525i
$965$	8.61047	−	26.5003i	0.277181	−	0.853075i
$966$		0			0
$967$	−53.6333			−1.72473			−0.862366	−	0.506286i	$-0.831018\pi$
$967$	−53.6333			−1.72473			−0.862366	+	0.506286i	$0.831018\pi$
$968$	5.09348	−	9.74969i	0.163711	−	0.313367i
$969$		0			0
$970$	−55.1814	−	40.0916i	−1.77177	−	1.28726i
$971$	−2.56649	+	7.89885i	−0.0823626	+	0.253486i	−0.983755	−	0.179518i	$-0.942546\pi$
$971$	−2.56649	+	7.89885i	−0.0823626	+	0.253486i	0.901392	+	0.433004i	$0.142546\pi$
$972$		0			0
$973$	9.06103	−	6.58322i	0.290483	−	0.211048i
$974$	−1.88352	+	1.36846i	−0.0603520	+	0.0438483i
$975$		0			0
$976$	3.30192	−	10.1623i	0.105692	−	0.325286i
$977$	0.898246	+	0.652614i	0.0287374	+	0.0208790i	0.602061	−	0.798450i	$-0.294346\pi$
$977$	0.898246	+	0.652614i	0.0287374	+	0.0208790i	−0.573324	+	0.819329i	$0.694346\pi$
$978$		0			0
$979$	40.3577	+	3.38314i	1.28984	+	0.108126i
$980$	26.7126			0.853301
$981$		0			0
$982$	−4.16636	+	12.8227i	−0.132954	+	0.409190i
$983$	−12.9159	−	39.7511i	−0.411954	−	1.26786i	−0.914947	−	0.403574i	$-0.867768\pi$
$983$	−12.9159	−	39.7511i	−0.411954	−	1.26786i	0.502993	−	0.864290i	$-0.332232\pi$
$984$		0			0
$985$	56.7618	−	41.2399i	1.80858	−	1.31401i
$986$	11.3446	+	34.9152i	0.361286	+	1.11193i
$987$		0			0
$988$	−19.4972	−	14.1656i	−0.620290	−	0.450667i
$989$	−0.649874			−0.0206648
$990$		0			0
$991$	45.5023			1.44543			0.722715	−	0.691147i	$-0.242894\pi$
$991$	45.5023			1.44543			0.722715	+	0.691147i	$0.242894\pi$
$992$	0.272669	+	0.198105i	0.00865724	+	0.00628986i
$993$		0			0
$994$	14.6689	+	45.1463i	0.465270	+	1.43195i
$995$	39.5595	−	28.7416i	1.25412	−	0.911171i
$996$		0			0
$997$	−4.41447	−	13.5863i	−0.139808	−	0.430283i	0.856499	−	0.516148i	$-0.172635\pi$
$997$	−4.41447	−	13.5863i	−0.139808	−	0.430283i	−0.996307	+	0.0858649i	$0.972635\pi$
$998$	13.1925	−	40.6024i	0.417602	−	1.28525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	594.2.f.k.433.1	✓	12
3.2	odd	2		594.2.f.l.433.3	yes	12
11.3	even	5	inner	594.2.f.k.487.1	yes	12
11.5	even	5		6534.2.a.cx.1.5		6
11.6	odd	10		6534.2.a.cv.1.5		6
33.5	odd	10		6534.2.a.cu.1.2		6
33.14	odd	10		594.2.f.l.487.3	yes	12
33.17	even	10		6534.2.a.cw.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
594.2.f.k.433.1	✓	12	1.1	even	1	trivial
594.2.f.k.487.1	yes	12	11.3	even	5	inner
594.2.f.l.433.3	yes	12	3.2	odd	2
594.2.f.l.487.3	yes	12	33.14	odd	10
6534.2.a.cu.1.2		6	33.5	odd	10
6534.2.a.cv.1.5		6	11.6	odd	10
6534.2.a.cw.1.2		6	33.17	even	10
6534.2.a.cx.1.5		6	11.5	even	5

Overview	Random
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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:	\( N \)	\(=\)	\( 594 = 2 \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	594.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-3.14677 + 2.28626i) q^{5} +(1.15076 + 3.54167i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-3.14677 + 2.28626i) q^{5} +(1.15076 + 3.54167i) q^{7} +(0.309017 - 0.951057i) q^{8} +3.88962 q^{10} +(-3.30503 - 0.277057i) q^{11} +(-4.45753 - 3.23859i) q^{13} +(1.15076 - 3.54167i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.53693 - 2.56973i) q^{17} +(1.35164 - 4.15992i) q^{19} +(-3.14677 - 2.28626i) q^{20} +(2.51098 + 2.16679i) q^{22} +0.169185 q^{23} +(3.13009 - 9.63342i) q^{25} +(1.70263 + 5.24015i) q^{26} +(-3.01272 + 2.18887i) q^{28} +(-2.59490 - 7.98629i) q^{29} +(0.272669 + 0.198105i) q^{31} +1.00000 q^{32} -4.37189 q^{34} +(-11.7184 - 8.51388i) q^{35} +(0.587055 + 1.80677i) q^{37} +(-3.53864 + 2.57097i) q^{38} +(1.20196 + 3.69925i) q^{40} +(-1.53799 + 4.73343i) q^{41} -3.84121 q^{43} +(-0.757814 - 3.22889i) q^{44} +(-0.136873 - 0.0994443i) q^{46} +(-0.320660 + 0.986891i) q^{47} +(-5.55604 + 4.03670i) q^{49} +(-8.19468 + 5.95378i) q^{50} +(1.70263 - 5.24015i) q^{52} +(5.59333 + 4.06379i) q^{53} +(11.0336 - 6.68434i) q^{55} +3.72393 q^{56} +(-2.59490 + 7.98629i) q^{58} +(-0.831841 - 2.56014i) q^{59} +(-8.64453 + 6.28062i) q^{61} +(-0.104150 - 0.320541i) q^{62} +(-0.809017 - 0.587785i) q^{64} +21.4311 q^{65} -11.4875 q^{67} +(3.53693 + 2.56973i) q^{68} +(4.47601 + 13.7758i) q^{70} +(-10.3127 + 7.49261i) q^{71} +(-1.62901 - 5.01358i) q^{73} +(0.587055 - 1.80677i) q^{74} +4.37400 q^{76} +(-2.82205 - 12.0241i) q^{77} +(8.27471 + 6.01193i) q^{79} +(1.20196 - 3.69925i) q^{80} +(4.02650 - 2.92542i) q^{82} +(5.38143 - 3.90984i) q^{83} +(-5.25483 + 16.1727i) q^{85} +(3.10760 + 2.25781i) q^{86} +(-1.28481 + 3.05766i) q^{88} -12.2110 q^{89} +(6.34046 - 19.5139i) q^{91} +(0.0522810 + 0.160904i) q^{92} +(0.839500 - 0.609932i) q^{94} +(5.25737 + 16.1805i) q^{95} +(-14.1868 - 10.3073i) q^{97} +6.86764 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 - 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - q^{5} + 3 q^{7} - 3 q^{8} + 4 q^{10} - 7 q^{11} + 2 q^{13} + 3 q^{14} - 3 q^{16} + 15 q^{17} - 6 q^{19} - q^{20} + 8 q^{22} - 18 q^{23} - 2 q^{25} - 3 q^{26} - 2 q^{28} - 7 q^{29} - 30 q^{31} + 12 q^{32} - 9 q^{35} - 21 q^{37} - q^{38} - q^{40} + 2 q^{41} + 10 q^{43} - 7 q^{44} + 17 q^{46} + 33 q^{47} - 22 q^{49} - 12 q^{50} - 3 q^{52} - 3 q^{53} + 71 q^{55} - 2 q^{56} - 7 q^{58} - 24 q^{59} - 29 q^{61} + 20 q^{62} - 3 q^{64} + 4 q^{65} + 28 q^{67} + 15 q^{68} - 9 q^{70} - 35 q^{71} + 16 q^{73} - 21 q^{74} + 14 q^{76} + 17 q^{77} + 31 q^{79} - q^{80} - 13 q^{82} + 26 q^{83} - 40 q^{85} - 10 q^{86} - 2 q^{88} - 24 q^{89} + 3 q^{91} - 8 q^{92} - 32 q^{94} + 13 q^{95} - 67 q^{97} + 58 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - q^5 + 3 * q^7 - 3 * q^8 + 4 * q^10 - 7 * q^11 + 2 * q^13 + 3 * q^14 - 3 * q^16 + 15 * q^17 - 6 * q^19 - q^20 + 8 * q^22 - 18 * q^23 - 2 * q^25 - 3 * q^26 - 2 * q^28 - 7 * q^29 - 30 * q^31 + 12 * q^32 - 9 * q^35 - 21 * q^37 - q^38 - q^40 + 2 * q^41 + 10 * q^43 - 7 * q^44 + 17 * q^46 + 33 * q^47 - 22 * q^49 - 12 * q^50 - 3 * q^52 - 3 * q^53 + 71 * q^55 - 2 * q^56 - 7 * q^58 - 24 * q^59 - 29 * q^61 + 20 * q^62 - 3 * q^64 + 4 * q^65 + 28 * q^67 + 15 * q^68 - 9 * q^70 - 35 * q^71 + 16 * q^73 - 21 * q^74 + 14 * q^76 + 17 * q^77 + 31 * q^79 - q^80 - 13 * q^82 + 26 * q^83 - 40 * q^85 - 10 * q^86 - 2 * q^88 - 24 * q^89 + 3 * q^91 - 8 * q^92 - 32 * q^94 + 13 * q^95 - 67 * q^97 + 58 * q^98

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