LMFDB - Embedded newform 546.2.g.d.209.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (of order $2$, degree $1$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
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} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 $ x^12 - 2x^11 + 4x^10 - 8x^8 + 26x^7 - 50x^6 + 78x^5 - 72x^4 + 324x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.9
Root			$-1.73194 - 0.0198536i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.d.209.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.0198536 + 1.73194i) q^{3} -1.00000 q^{4} -1.44804 q^{5} +(-1.73194 + 0.0198536i) q^{6} +(-2.59654 + 0.507916i) q^{7} -1.00000i q^{8} +(-2.99921 + 0.0687703i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.0198536 + 1.73194i) q^{3} -1.00000 q^{4} -1.44804 q^{5} +(-1.73194 + 0.0198536i) q^{6} +(-2.59654 + 0.507916i) q^{7} -1.00000i q^{8} +(-2.99921 + 0.0687703i) q^{9} -1.44804i q^{10} -4.91192i q^{11} +(-0.0198536 - 1.73194i) q^{12} -1.00000i q^{13} +(-0.507916 - 2.59654i) q^{14} +(-0.0287488 - 2.50792i) q^{15} +1.00000 q^{16} +2.13894 q^{17} +(-0.0687703 - 2.99921i) q^{18} +2.79747i q^{19} +1.44804 q^{20} +(-0.931230 - 4.48696i) q^{21} +4.91192 q^{22} -2.25807i q^{23} +(1.73194 - 0.0198536i) q^{24} -2.90318 q^{25} +1.00000 q^{26} +(-0.178651 - 5.19308i) q^{27} +(2.59654 - 0.507916i) q^{28} -1.23419i q^{29} +(2.50792 - 0.0287488i) q^{30} +5.68792i q^{31} +1.00000i q^{32} +(8.50713 - 0.0975191i) q^{33} +2.13894i q^{34} +(3.75990 - 0.735484i) q^{35} +(2.99921 - 0.0687703i) q^{36} -10.3789 q^{37} -2.79747 q^{38} +(1.73194 - 0.0198536i) q^{39} +1.44804i q^{40} -7.01426 q^{41} +(4.48696 - 0.931230i) q^{42} -0.729206 q^{43} +4.91192i q^{44} +(4.34298 - 0.0995822i) q^{45} +2.25807 q^{46} -11.8184 q^{47} +(0.0198536 + 1.73194i) q^{48} +(6.48404 - 2.63765i) q^{49} -2.90318i q^{50} +(0.0424657 + 3.70452i) q^{51} +1.00000i q^{52} -12.9594i q^{53} +(5.19308 - 0.178651i) q^{54} +7.11266i q^{55} +(0.507916 + 2.59654i) q^{56} +(-4.84505 + 0.0555399i) q^{57} +1.23419 q^{58} +9.36446 q^{59} +(0.0287488 + 2.50792i) q^{60} +4.45255i q^{61} -5.68792 q^{62} +(7.75264 - 1.70191i) q^{63} -1.00000 q^{64} +1.44804i q^{65} +(0.0975191 + 8.50713i) q^{66} +1.73567 q^{67} -2.13894 q^{68} +(3.91083 - 0.0448307i) q^{69} +(0.735484 + 3.75990i) q^{70} +7.37313i q^{71} +(0.0687703 + 2.99921i) q^{72} -11.4637i q^{73} -10.3789i q^{74} +(-0.0576384 - 5.02812i) q^{75} -2.79747i q^{76} +(2.49484 + 12.7540i) q^{77} +(0.0198536 + 1.73194i) q^{78} +3.64979 q^{79} -1.44804 q^{80} +(8.99054 - 0.412513i) q^{81} -7.01426i q^{82} -15.0388 q^{83} +(0.931230 + 4.48696i) q^{84} -3.09728 q^{85} -0.729206i q^{86} +(2.13754 - 0.0245031i) q^{87} -4.91192 q^{88} -12.8229 q^{89} +(0.0995822 + 4.34298i) q^{90} +(0.507916 + 2.59654i) q^{91} +2.25807i q^{92} +(-9.85112 + 0.112926i) q^{93} -11.8184i q^{94} -4.05086i q^{95} +(-1.73194 + 0.0198536i) q^{96} -12.6157i q^{97} +(2.63765 + 6.48404i) q^{98} +(0.337794 + 14.7319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	$ 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.0198536	+	1.73194i	0.0114625	+	0.999934i
$3$	0.0198536	+	1.73194i	0.0114625	+	0.999934i
$4$	−1.00000			−0.500000
$5$	−1.44804			−0.647584			−0.323792	−	0.946128i	$-0.604958\pi$
$5$	−1.44804			−0.647584			−0.323792	+	0.946128i	$0.604958\pi$
$6$	−1.73194	+	0.0198536i	−0.707060	+	0.00810519i
$7$	−2.59654	+	0.507916i	−0.981400	+	0.191974i
$7$	−2.59654	+	0.507916i	−0.981400	+	0.191974i
$8$		−	1.00000i		−	0.353553i
$9$	−2.99921	+	0.0687703i	−0.999737	+	0.0229234i
$10$		−	1.44804i		−	0.457911i
$11$		−	4.91192i		−	1.48100i	−0.672057	−	0.740499i	$-0.734589\pi$
$11$		−	4.91192i		−	1.48100i	0.672057	−	0.740499i	$-0.265411\pi$
$12$	−0.0198536	−	1.73194i	−0.00573123	−	0.499967i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.507916	−	2.59654i	−0.135746	−	0.693955i
$15$	−0.0287488	−	2.50792i	−0.00742291	−	0.647541i
$16$	1.00000			0.250000
$17$	2.13894			0.518770			0.259385	−	0.965774i	$-0.416480\pi$
$17$	2.13894			0.518770			0.259385	+	0.965774i	$0.416480\pi$
$18$	−0.0687703	−	2.99921i	−0.0162093	−	0.706921i
$19$			2.79747i			0.641785i	0.947116	+	0.320892i	$0.103983\pi$
$19$			2.79747i			0.641785i	−0.947116	+	0.320892i	$0.896017\pi$
$20$	1.44804			0.323792
$21$	−0.931230	−	4.48696i	−0.203211	−	0.979135i
$22$	4.91192			1.04722
$23$		−	2.25807i		−	0.470839i	−0.971894	−	0.235420i	$-0.924354\pi$
$23$		−	2.25807i		−	0.470839i	0.971894	−	0.235420i	$-0.0756464\pi$
$24$	1.73194	−	0.0198536i	0.353530	−	0.00405259i
$25$	−2.90318			−0.580635
$26$	1.00000			0.196116
$27$	−0.178651	−	5.19308i	−0.0343814	−	0.999409i
$28$	2.59654	−	0.507916i	0.490700	−	0.0959872i
$29$		−	1.23419i		−	0.229183i	−0.993413	−	0.114592i	$-0.963444\pi$
$29$		−	1.23419i		−	0.229183i	0.993413	−	0.114592i	$-0.0365560\pi$
$30$	2.50792	−	0.0287488i	0.457881	−	0.00524879i
$31$			5.68792i			1.02158i	0.859705	+	0.510791i	$0.170647\pi$
$31$			5.68792i			1.02158i	−0.859705	+	0.510791i	$0.829353\pi$
$32$			1.00000i			0.176777i
$33$	8.50713	−	0.0975191i	1.48090	−	0.0169759i
$34$			2.13894i			0.366826i
$35$	3.75990	−	0.735484i	0.635539	−	0.124319i
$36$	2.99921	−	0.0687703i	0.499869	−	0.0114617i
$37$	−10.3789			−1.70628			−0.853140	−	0.521682i	$-0.825305\pi$
$37$	−10.3789			−1.70628			−0.853140	+	0.521682i	$0.825305\pi$
$38$	−2.79747			−0.453810
$39$	1.73194	−	0.0198536i	0.277332	−	0.00317912i
$40$			1.44804i			0.228955i
$41$	−7.01426			−1.09544			−0.547721	−	0.836661i	$-0.684505\pi$
$41$	−7.01426			−1.09544			−0.547721	+	0.836661i	$0.684505\pi$
$42$	4.48696	−	0.931230i	0.692353	−	0.143692i
$43$	−0.729206			−0.111203			−0.0556015	−	0.998453i	$-0.517708\pi$
$43$	−0.729206			−0.111203			−0.0556015	+	0.998453i	$0.517708\pi$
$44$			4.91192i			0.740499i
$45$	4.34298	−	0.0995822i	0.647414	−	0.0148448i
$46$	2.25807			0.332934
$47$	−11.8184			−1.72389			−0.861943	−	0.507005i	$-0.830753\pi$
$47$	−11.8184			−1.72389			−0.861943	+	0.507005i	$0.830753\pi$
$48$	0.0198536	+	1.73194i	0.00286562	+	0.249984i
$49$	6.48404	−	2.63765i	0.926292	−	0.376807i
$50$		−	2.90318i		−	0.410571i
$51$	0.0424657	+	3.70452i	0.00594638	+	0.518736i
$52$			1.00000i			0.138675i
$53$		−	12.9594i		−	1.78011i	−0.455851	−	0.890056i	$-0.650665\pi$
$53$		−	12.9594i		−	1.78011i	0.455851	−	0.890056i	$-0.349335\pi$
$54$	5.19308	−	0.178651i	0.706689	−	0.0243113i
$55$			7.11266i			0.959070i
$56$	0.507916	+	2.59654i	0.0678732	+	0.346977i
$57$	−4.84505	+	0.0555399i	−0.641743	+	0.00735643i
$58$	1.23419			0.162057
$59$	9.36446			1.21915			0.609575	−	0.792729i	$-0.291340\pi$
$59$	9.36446			1.21915			0.609575	+	0.792729i	$0.291340\pi$
$60$	0.0287488	+	2.50792i	0.00371145	+	0.323771i
$61$			4.45255i			0.570090i	0.958514	+	0.285045i	$0.0920086\pi$
$61$			4.45255i			0.570090i	−0.958514	+	0.285045i	$0.907991\pi$
$62$	−5.68792			−0.722367
$63$	7.75264	−	1.70191i	0.976741	−	0.214421i
$64$	−1.00000			−0.125000
$65$			1.44804i			0.179607i
$66$	0.0975191	+	8.50713i	0.0120038	+	1.04716i
$67$	1.73567			0.212046			0.106023	−	0.994364i	$-0.466188\pi$
$67$	1.73567			0.212046			0.106023	+	0.994364i	$0.466188\pi$
$68$	−2.13894			−0.259385
$69$	3.91083	−	0.0448307i	0.470808	−	0.00539698i
$70$	0.735484	+	3.75990i	0.0879071	+	0.449394i
$71$			7.37313i			0.875030i	0.899211	+	0.437515i	$0.144141\pi$
$71$			7.37313i			0.875030i	−0.899211	+	0.437515i	$0.855859\pi$
$72$	0.0687703	+	2.99921i	0.00810465	+	0.353460i
$73$		−	11.4637i		−	1.34172i	−0.741582	−	0.670862i	$-0.765924\pi$
$73$		−	11.4637i		−	1.34172i	0.741582	−	0.670862i	$-0.234076\pi$
$74$		−	10.3789i		−	1.20652i
$75$	−0.0576384	−	5.02812i	−0.00665551	−	0.580597i
$76$		−	2.79747i		−	0.320892i
$77$	2.49484	+	12.7540i	0.284314	+	1.45345i
$78$	0.0198536	+	1.73194i	0.00224797	+	0.196103i
$79$	3.64979			0.410634			0.205317	−	0.978696i	$-0.434178\pi$
$79$	3.64979			0.410634			0.205317	+	0.978696i	$0.434178\pi$
$80$	−1.44804			−0.161896
$81$	8.99054	−	0.412513i	0.998949	−	0.0458348i
$82$		−	7.01426i		−	0.774595i
$83$	−15.0388			−1.65073			−0.825363	−	0.564603i	$-0.809029\pi$
$83$	−15.0388			−1.65073			−0.825363	+	0.564603i	$0.809029\pi$
$84$	0.931230	+	4.48696i	0.101605	+	0.489567i
$85$	−3.09728			−0.335947
$86$		−	0.729206i		−	0.0786323i
$87$	2.13754	−	0.0245031i	0.229168	−	0.00262701i
$88$	−4.91192			−0.523612
$89$	−12.8229			−1.35922			−0.679611	−	0.733573i	$-0.737851\pi$
$89$	−12.8229			−1.35922			−0.679611	+	0.733573i	$0.737851\pi$
$90$	0.0995822	+	4.34298i	0.0104969	+	0.457791i
$91$	0.507916	+	2.59654i	0.0532441	+	0.272191i
$92$			2.25807i			0.235420i
$93$	−9.85112	+	0.112926i	−1.02151	+	0.0117098i
$94$		−	11.8184i		−	1.21897i
$95$		−	4.05086i		−	0.415609i
$96$	−1.73194	+	0.0198536i	−0.176765	+	0.00202630i
$97$		−	12.6157i		−	1.28093i	−0.767988	−	0.640464i	$-0.778742\pi$
$97$		−	12.6157i		−	1.28093i	0.767988	−	0.640464i	$-0.221258\pi$
$98$	2.63765	+	6.48404i	0.266443	+	0.654987i
$99$	0.337794	+	14.7319i	0.0339495	+	1.48061i
$100$	2.90318			0.290318
$101$	−8.12464			−0.808432			−0.404216	−	0.914664i	$-0.632456\pi$
$101$	−8.12464			−0.808432			−0.404216	+	0.914664i	$0.632456\pi$
$102$	−3.70452	+	0.0424657i	−0.366802	+	0.00420473i
$103$			12.0056i			1.18295i	0.806325	+	0.591473i	$0.201453\pi$
$103$			12.0056i			1.18295i	−0.806325	+	0.591473i	$0.798547\pi$
$104$	−1.00000			−0.0980581
$105$	1.34846	+	6.49730i	0.131596	+	0.634072i
$106$	12.9594			1.25873
$107$			15.6424i			1.51220i	0.654454	+	0.756102i	$0.272898\pi$
$107$			15.6424i			1.51220i	−0.654454	+	0.756102i	$0.727102\pi$
$108$	0.178651	+	5.19308i	0.0171907	+	0.499704i
$109$	−7.21227			−0.690811			−0.345405	−	0.938454i	$-0.612259\pi$
$109$	−7.21227			−0.690811			−0.345405	+	0.938454i	$0.612259\pi$
$110$	−7.11266			−0.678165
$111$	−0.206058	−	17.9756i	−0.0195582	−	1.70617i
$112$	−2.59654	+	0.507916i	−0.245350	+	0.0479936i
$113$		−	3.90703i		−	0.367542i	−0.982969	−	0.183771i	$-0.941169\pi$
$113$		−	3.90703i		−	0.367542i	0.982969	−	0.183771i	$-0.0588305\pi$
$114$	−0.0555399	−	4.84505i	−0.00520178	−	0.453781i
$115$			3.26977i			0.304908i
$116$			1.23419i			0.114592i
$117$	0.0687703	+	2.99921i	0.00635781	+	0.277277i
$118$			9.36446i			0.862069i
$119$	−5.55385	+	1.08640i	−0.509121	+	0.0995905i
$120$	−2.50792	+	0.0287488i	−0.228940	+	0.00262439i
$121$	−13.1269			−1.19336
$122$	−4.45255			−0.403115
$123$	−0.139258	−	12.1482i	−0.0125565	−	1.09537i
$124$		−	5.68792i		−	0.510791i
$125$	11.4441			1.02359
$126$	1.70191	+	7.75264i	0.151618	+	0.690660i
$127$	−0.381873			−0.0338858			−0.0169429	−	0.999856i	$-0.505393\pi$
$127$	−0.381873			−0.0338858			−0.0169429	+	0.999856i	$0.505393\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.0144773	−	1.26294i	−0.00127466	−	0.111196i
$130$	−1.44804			−0.127002
$131$	14.5078			1.26755			0.633775	−	0.773518i	$-0.281505\pi$
$131$	14.5078			1.26755			0.633775	+	0.773518i	$0.281505\pi$
$132$	−8.50713	+	0.0975191i	−0.740450	+	0.00848794i
$133$	−1.42088	−	7.26376i	−0.123206	−	0.629847i
$134$			1.73567i			0.149939i
$135$	0.258694	+	7.51979i	0.0222648	+	0.647201i
$136$		−	2.13894i		−	0.183413i
$137$			9.67855i			0.826895i	0.910528	+	0.413447i	$0.135675\pi$
$137$			9.67855i			0.826895i	−0.910528	+	0.413447i	$0.864325\pi$
$138$	0.0448307	+	3.91083i	0.00381624	+	0.332912i
$139$			16.3671i			1.38824i	0.719862	+	0.694118i	$0.244205\pi$
$139$			16.3671i			1.38824i	−0.719862	+	0.694118i	$0.755795\pi$
$140$	−3.75990	+	0.735484i	−0.317769	+	0.0621597i
$141$	−0.234637	−	20.4687i	−0.0197600	−	1.72377i
$142$	−7.37313			−0.618740
$143$	−4.91192			−0.410755
$144$	−2.99921	+	0.0687703i	−0.249934	+	0.00573086i
$145$			1.78716i			0.148415i
$146$	11.4637			0.948743
$147$	4.69698	+	11.1776i	0.387400	+	0.921912i
$148$	10.3789			0.853140
$149$			13.7804i			1.12893i	0.825456	+	0.564466i	$0.190918\pi$
$149$			13.7804i			1.12893i	−0.825456	+	0.564466i	$0.809082\pi$
$150$	5.02812	−	0.0576384i	0.410544	−	0.00470616i
$151$	−0.0637611			−0.00518880			−0.00259440	−	0.999997i	$-0.500826\pi$
$151$	−0.0637611			−0.00518880			−0.00259440	+	0.999997i	$0.500826\pi$
$152$	2.79747			0.226905
$153$	−6.41514	+	0.147096i	−0.518634	+	0.0118920i
$154$	−12.7540	+	2.49484i	−1.02775	+	0.201040i
$155$		−	8.23635i		−	0.661559i
$156$	−1.73194	+	0.0198536i	−0.138666	+	0.00158956i
$157$			1.41512i			0.112939i	0.998404	+	0.0564693i	$0.0179843\pi$
$157$			1.41512i			0.112939i	−0.998404	+	0.0564693i	$0.982016\pi$
$158$			3.64979i			0.290362i
$159$	22.4449	−	0.257291i	1.78000	−	0.0204045i
$160$		−	1.44804i		−	0.114478i
$161$	1.14691	+	5.86316i	0.0903890	+	0.462081i
$162$	0.412513	+	8.99054i	0.0324101	+	0.706364i
$163$	6.97550			0.546363			0.273182	−	0.961962i	$-0.411924\pi$
$163$	6.97550			0.546363			0.273182	+	0.961962i	$0.411924\pi$
$164$	7.01426			0.547721
$165$	−12.3187	+	0.141212i	−0.959007	+	0.0109933i
$166$		−	15.0388i		−	1.16724i
$167$	2.95102			0.228357			0.114178	−	0.993460i	$-0.463576\pi$
$167$	2.95102			0.228357			0.114178	+	0.993460i	$0.463576\pi$
$168$	−4.48696	+	0.931230i	−0.346176	+	0.0718459i
$169$	−1.00000			−0.0769231
$170$		−	3.09728i		−	0.237550i
$171$	−0.192383	−	8.39022i	−0.0147119	−	0.641616i
$172$	0.729206			0.0556015
$173$	−20.2590			−1.54026			−0.770132	−	0.637885i	$-0.779809\pi$
$173$	−20.2590			−1.54026			−0.770132	+	0.637885i	$0.779809\pi$
$174$	0.0245031	+	2.13754i	0.00185757	+	0.162047i
$175$	7.53821	−	1.47457i	0.569835	−	0.111467i
$176$		−	4.91192i		−	0.370250i
$177$	0.185918	+	16.2187i	0.0139745	+	1.21907i
$178$		−	12.8229i		−	0.961115i
$179$		−	13.6176i		−	1.01783i	−0.860817	−	0.508915i	$-0.830047\pi$
$179$		−	13.6176i		−	1.01783i	0.860817	−	0.508915i	$-0.169953\pi$
$180$	−4.34298	+	0.0995822i	−0.323707	+	0.00742242i
$181$			21.1609i			1.57288i	0.617668	+	0.786439i	$0.288078\pi$
$181$			21.1609i			1.57288i	−0.617668	+	0.786439i	$0.711922\pi$
$182$	−2.59654	+	0.507916i	−0.192468	+	0.0376493i
$183$	−7.71153	+	0.0883990i	−0.570053	+	0.00653464i
$184$	−2.25807			−0.166467
$185$	15.0291			1.10496
$186$	−0.112926	−	9.85112i	−0.00828010	−	0.722319i
$187$		−	10.5063i		−	0.768298i
$188$	11.8184			0.861943
$189$	3.10152	+	13.3933i	0.225603	+	0.974219i
$190$	4.05086			0.293880
$191$		−	0.502109i		−	0.0363314i	−0.999835	−	0.0181657i	$-0.994217\pi$
$191$		−	0.502109i		−	0.0363314i	0.999835	−	0.0181657i	$-0.00578263\pi$
$192$	−0.0198536	−	1.73194i	−0.00143281	−	0.124992i
$193$	13.5010			0.971823			0.485912	−	0.874008i	$-0.338488\pi$
$193$	13.5010			0.971823			0.485912	+	0.874008i	$0.338488\pi$
$194$	12.6157			0.905752
$195$	−2.50792	+	0.0287488i	−0.179596	+	0.00205874i
$196$	−6.48404	+	2.63765i	−0.463146	+	0.188404i
$197$			1.91620i			0.136524i	0.997667	+	0.0682619i	$0.0217453\pi$
$197$			1.91620i			0.136524i	−0.997667	+	0.0682619i	$0.978255\pi$
$198$	−14.7319	+	0.337794i	−1.04695	+	0.0240060i
$199$			9.74785i			0.691006i	0.938418	+	0.345503i	$0.112292\pi$
$199$			9.74785i			0.691006i	−0.938418	+	0.345503i	$0.887708\pi$
$200$			2.90318i			0.205286i
$201$	0.0344593	+	3.00607i	0.00243057	+	0.212032i
$202$		−	8.12464i		−	0.571648i
$203$	0.626866	+	3.20463i	0.0439973	+	0.224921i
$204$	−0.0424657	−	3.70452i	−0.00297319	−	0.259368i
$205$	10.1569			0.709391
$206$	−12.0056			−0.836469
$207$	0.155288	+	6.77242i	0.0107932	+	0.470715i
$208$		−	1.00000i		−	0.0693375i
$209$	13.7410			0.950482
$210$	−6.49730	+	1.34846i	−0.448357	+	0.0930525i
$211$	7.47422			0.514546			0.257273	−	0.966339i	$-0.417176\pi$
$211$	7.47422			0.514546			0.257273	+	0.966339i	$0.417176\pi$
$212$			12.9594i			0.890056i
$213$	−12.7698	+	0.146383i	−0.874973	+	0.0100300i
$214$	−15.6424			−1.06929
$215$	1.05592			0.0720132
$216$	−5.19308	+	0.178651i	−0.353344	+	0.0121556i
$217$	−2.88899	−	14.7689i	−0.196117	−	1.00258i
$218$		−	7.21227i		−	0.488477i
$219$	19.8544	−	0.227595i	1.34164	−	0.0153795i
$220$		−	7.11266i		−	0.479535i
$221$		−	2.13894i		−	0.143881i
$222$	17.9756	−	0.206058i	1.20644	−	0.0138297i
$223$		−	19.5536i		−	1.30941i	−0.755885	−	0.654704i	$-0.772793\pi$
$223$		−	19.5536i		−	1.30941i	0.755885	−	0.654704i	$-0.227207\pi$
$224$	−0.507916	−	2.59654i	−0.0339366	−	0.173489i
$225$	8.70724	−	0.199652i	0.580483	−	0.0133101i
$226$	3.90703			0.259892
$227$	−8.93913			−0.593311			−0.296655	−	0.954985i	$-0.595871\pi$
$227$	−8.93913			−0.593311			−0.296655	+	0.954985i	$0.595871\pi$
$228$	4.84505	−	0.0555399i	0.320871	−	0.00367822i
$229$		−	8.03593i		−	0.531029i	−0.964107	−	0.265514i	$-0.914458\pi$
$229$		−	8.03593i		−	0.531029i	0.964107	−	0.265514i	$-0.0855418\pi$
$230$	−3.26977			−0.215602
$231$	−22.0396	+	4.57412i	−1.45010	+	0.300955i
$232$	−1.23419			−0.0810286
$233$		−	9.34192i		−	0.612009i	−0.952030	−	0.306005i	$-0.901008\pi$
$233$		−	9.34192i		−	0.612009i	0.952030	−	0.306005i	$-0.0989923\pi$
$234$	−2.99921	+	0.0687703i	−0.196065	+	0.00449565i
$235$	17.1135			1.11636
$236$	−9.36446			−0.609575
$237$	0.0724614	+	6.32121i	0.00470687	+	0.410607i
$238$	−1.08640	−	5.55385i	−0.0704211	−	0.360003i
$239$		−	14.3110i		−	0.925702i	−0.886436	−	0.462851i	$-0.846826\pi$
$239$		−	14.3110i		−	0.925702i	0.886436	−	0.462851i	$-0.153174\pi$
$240$	−0.0287488	−	2.50792i	−0.00185573	−	0.161885i
$241$			11.2737i			0.726201i	0.931750	+	0.363100i	$0.118282\pi$
$241$			11.2737i			0.726201i	−0.931750	+	0.363100i	$0.881718\pi$
$242$		−	13.1269i		−	0.843830i
$243$	0.892941	+	15.5629i	0.0572822	+	0.998358i
$244$		−	4.45255i		−	0.285045i
$245$	−9.38916	+	3.81943i	−0.599851	+	0.244014i
$246$	12.1482	−	0.139258i	0.774544	−	0.00887877i
$247$	2.79747			0.177999
$248$	5.68792			0.361183
$249$	−0.298574	−	26.0463i	−0.0189214	−	1.65062i
$250$			11.4441i			0.723790i
$251$	23.7489			1.49902			0.749509	−	0.661994i	$-0.230290\pi$
$251$	23.7489			1.49902			0.749509	+	0.661994i	$0.230290\pi$
$252$	−7.75264	+	1.70191i	−0.488371	+	0.107210i
$253$	−11.0914			−0.697312
$254$		−	0.381873i		−	0.0239609i
$255$	−0.0614920	−	5.36429i	−0.00385078	−	0.335925i
$256$	1.00000			0.0625000
$257$	−11.3496			−0.707968			−0.353984	−	0.935252i	$-0.615173\pi$
$257$	−11.3496			−0.707968			−0.353984	+	0.935252i	$0.615173\pi$
$258$	1.26294	−	0.0144773i	0.0786272	−	0.000901320i
$259$	26.9492	−	5.27161i	1.67454	−	0.327562i
$260$		−	1.44804i		−	0.0898037i
$261$	0.0848756	+	3.70160i	0.00525367	+	0.229123i
$262$			14.5078i			0.896293i
$263$		−	14.2128i		−	0.876399i	−0.898878	−	0.438199i	$-0.855616\pi$
$263$		−	14.2128i		−	0.876399i	0.898878	−	0.438199i	$-0.144384\pi$
$264$	−0.0975191	−	8.50713i	−0.00600188	−	0.523578i
$265$			18.7658i			1.15277i
$266$	7.26376	−	1.42088i	0.445369	−	0.0871199i
$267$	−0.254580	−	22.2084i	−0.0155800	−	1.35913i
$268$	−1.73567			−0.106023
$269$	−6.70104			−0.408570			−0.204285	−	0.978911i	$-0.565487\pi$
$269$	−6.70104			−0.408570			−0.204285	+	0.978911i	$0.565487\pi$
$270$	−7.51979	+	0.258694i	−0.457640	+	0.0157436i
$271$			7.56537i			0.459563i	0.973242	+	0.229782i	$0.0738012\pi$
$271$			7.56537i			0.459563i	−0.973242	+	0.229782i	$0.926199\pi$
$272$	2.13894			0.129693
$273$	−4.48696	+	0.931230i	−0.271563	+	0.0563606i
$274$	−9.67855			−0.584703
$275$			14.2602i			0.859920i
$276$	−3.91083	+	0.0448307i	−0.235404	+	0.00269849i
$277$	6.46838			0.388647			0.194324	−	0.980937i	$-0.437749\pi$
$277$	6.46838			0.388647			0.194324	+	0.980937i	$0.437749\pi$
$278$	−16.3671			−0.981630
$279$	−0.391160	−	17.0593i	−0.0234181	−	1.02131i
$280$	−0.735484	−	3.75990i	−0.0439536	−	0.224697i
$281$		−	20.7233i		−	1.23625i	−0.786080	−	0.618125i	$-0.787893\pi$
$281$		−	20.7233i		−	1.23625i	0.786080	−	0.618125i	$-0.212107\pi$
$282$	20.4687	−	0.234637i	1.21889	−	0.0139724i
$283$		−	0.0977777i		−	0.00581228i	−0.999996	−	0.00290614i	$-0.999075\pi$
$283$		−	0.0977777i		−	0.00581228i	0.999996	−	0.00290614i	$-0.000925054\pi$
$284$		−	7.37313i		−	0.437515i
$285$	7.01583	−	0.0804240i	0.415582	−	0.00476391i
$286$		−	4.91192i		−	0.290448i
$287$	18.2128	−	3.56266i	1.07507	−	0.210297i
$288$	−0.0687703	−	2.99921i	−0.00405233	−	0.176730i
$289$	−12.4249			−0.730878
$290$	−1.78716			−0.104946
$291$	21.8495	−	0.250466i	1.28084	−	0.0146826i
$292$			11.4637i			0.670862i
$293$	32.8772			1.92071			0.960354	−	0.278784i	$-0.0899313\pi$
$293$	32.8772			1.92071			0.960354	+	0.278784i	$0.0899313\pi$
$294$	−11.1776	+	4.69698i	−0.651890	+	0.273933i
$295$	−13.5601			−0.789501
$296$			10.3789i			0.603261i
$297$	−25.5080	+	0.877518i	−1.48012	+	0.0509187i
$298$	−13.7804			−0.798275
$299$	−2.25807			−0.130587
$300$	0.0576384	+	5.02812i	0.00332776	+	0.290299i
$301$	1.89341	−	0.370376i	0.109135	−	0.0213481i
$302$		−	0.0637611i		−	0.00366904i
$303$	−0.161303	−	14.0714i	−0.00926662	−	0.808379i
$304$			2.79747i			0.160446i
$305$		−	6.44747i		−	0.369181i
$306$	−0.147096	−	6.41514i	−0.00840890	−	0.366729i
$307$			11.8951i			0.678891i	0.940626	+	0.339445i	$0.110239\pi$
$307$			11.8951i			0.678891i	−0.940626	+	0.339445i	$0.889761\pi$
$308$	−2.49484	−	12.7540i	−0.142157	−	0.726726i
$309$	−20.7929	+	0.238354i	−1.18287	+	0.0135595i
$310$	8.23635			0.467793
$311$	−18.0050			−1.02097			−0.510484	−	0.859887i	$-0.670534\pi$
$311$	−18.0050			−1.02097			−0.510484	+	0.859887i	$0.670534\pi$
$312$	−0.0198536	−	1.73194i	−0.00112399	−	0.0980516i
$313$		−	16.5426i		−	0.935041i	−0.883982	−	0.467521i	$-0.845147\pi$
$313$		−	16.5426i		−	0.935041i	0.883982	−	0.467521i	$-0.154853\pi$
$314$	−1.41512			−0.0798596
$315$	−11.2261	+	2.46444i	−0.632522	+	0.138856i
$316$	−3.64979			−0.205317
$317$		−	13.7159i		−	0.770363i	−0.922841	−	0.385182i	$-0.874139\pi$
$317$		−	13.7159i		−	0.770363i	0.922841	−	0.385182i	$-0.125861\pi$
$318$	0.257291	+	22.4449i	0.0144281	+	1.25865i
$319$	−6.06224			−0.339420
$320$	1.44804			0.0809480
$321$	−27.0916	+	0.310557i	−1.51210	+	0.0173336i
$322$	−5.86316	+	1.14691i	−0.326741	+	0.0639147i
$323$			5.98364i			0.332939i
$324$	−8.99054	+	0.412513i	−0.499475	+	0.0229174i
$325$			2.90318i			0.161039i
$326$			6.97550i			0.386337i
$327$	−0.143189	−	12.4912i	−0.00791839	−	0.690765i
$328$			7.01426i			0.387298i
$329$	30.6869	−	6.00274i	1.69182	−	0.330942i
$330$	−0.141212	−	12.3187i	−0.00777344	−	0.678121i
$331$	19.5146			1.07262			0.536309	−	0.844022i	$-0.319818\pi$
$331$	19.5146			1.07262			0.536309	+	0.844022i	$0.319818\pi$
$332$	15.0388			0.825363
$333$	31.1285	−	0.713759i	1.70583	−	0.0391138i
$334$			2.95102i			0.161473i
$335$	−2.51332			−0.137318
$336$	−0.931230	−	4.48696i	−0.0508027	−	0.244784i
$337$	−6.95661			−0.378950			−0.189475	−	0.981885i	$-0.560679\pi$
$337$	−6.95661			−0.378950			−0.189475	+	0.981885i	$0.560679\pi$
$338$		−	1.00000i		−	0.0543928i
$339$	6.76672	−	0.0775684i	0.367518	−	0.00421294i
$340$	3.09728			0.167974
$341$	27.9386			1.51296
$342$	8.39022	−	0.192383i	0.453691	−	0.0104029i
$343$	−15.4964	+	10.1421i	−0.836725	+	0.547623i
$344$			0.729206i			0.0393162i
$345$	−5.66304	+	0.0649166i	−0.304888	+	0.00349499i
$346$		−	20.2590i		−	1.08913i
$347$		−	11.7554i		−	0.631063i	−0.948915	−	0.315532i	$-0.897817\pi$
$347$		−	11.7554i		−	0.631063i	0.948915	−	0.315532i	$-0.102183\pi$
$348$	−2.13754	+	0.0245031i	−0.114584	+	0.00131350i
$349$		−	4.59940i		−	0.246200i	−0.992394	−	0.123100i	$-0.960716\pi$
$349$		−	4.59940i		−	0.246200i	0.992394	−	0.123100i	$-0.0392836\pi$
$350$	1.47457	+	7.53821i	0.0788191	+	0.402934i
$351$	−5.19308	+	0.178651i	−0.277186	+	0.00953568i
$352$	4.91192			0.261806
$353$	8.22304			0.437669			0.218834	−	0.975762i	$-0.429775\pi$
$353$	8.22304			0.437669			0.218834	+	0.975762i	$0.429775\pi$
$354$	−16.2187	+	0.185918i	−0.862012	+	0.00988143i
$355$		−	10.6766i		−	0.566655i
$356$	12.8229			0.679611
$357$	−1.99185	−	9.59736i	−0.105420	−	0.507946i
$358$	13.6176			0.719714
$359$		−	29.8313i		−	1.57444i	−0.616675	−	0.787218i	$-0.711521\pi$
$359$		−	29.8313i		−	1.57444i	0.616675	−	0.787218i	$-0.288479\pi$
$360$	−0.0995822	−	4.34298i	−0.00524844	−	0.228895i
$361$	11.1741			0.588112
$362$	−21.1609			−1.11219
$363$	−0.260616	−	22.7350i	−0.0136788	−	1.19328i
$364$	−0.507916	−	2.59654i	−0.0266221	−	0.136096i
$365$			16.5999i			0.868879i
$366$	−0.0883990	−	7.71153i	−0.00462069	−	0.403088i
$367$			9.85865i			0.514617i	0.966329	+	0.257309i	$0.0828357\pi$
$367$			9.85865i			0.514617i	−0.966329	+	0.257309i	$0.917164\pi$
$368$		−	2.25807i		−	0.117710i
$369$	21.0372	−	0.482372i	1.09515	−	0.0251113i
$370$			15.0291i			0.781324i
$371$	6.58230	+	33.6496i	0.341736	+	1.74700i
$372$	9.85112	−	0.112926i	0.510757	−	0.00585492i
$373$	−20.1463			−1.04314			−0.521568	−	0.853210i	$-0.674653\pi$
$373$	−20.1463			−1.04314			−0.521568	+	0.853210i	$0.674653\pi$
$374$	10.5063			0.543268
$375$	0.227207	+	19.8205i	0.0117329	+	1.02353i
$376$			11.8184i			0.609486i
$377$	−1.23419			−0.0635641
$378$	−13.3933	+	3.10152i	−0.688877	+	0.159525i
$379$	−5.34091			−0.274344			−0.137172	−	0.990547i	$-0.543801\pi$
$379$	−5.34091			−0.274344			−0.137172	+	0.990547i	$0.543801\pi$
$380$			4.05086i			0.207805i
$381$	−0.00758155	−	0.661381i	−0.000388415	−	0.0338836i
$382$	0.502109			0.0256902
$383$	−2.81834			−0.144011			−0.0720053	−	0.997404i	$-0.522940\pi$
$383$	−2.81834			−0.144011			−0.0720053	+	0.997404i	$0.522940\pi$
$384$	1.73194	−	0.0198536i	0.0883825	−	0.00101315i
$385$	−3.61263	−	18.4683i	−0.184117	−	0.941232i
$386$			13.5010i			0.687183i
$387$	2.18704	−	0.0501477i	0.111174	−	0.00254915i
$388$			12.6157i			0.640464i
$389$			4.05676i			0.205686i	0.994698	+	0.102843i	$0.0327939\pi$
$389$			4.05676i			0.205686i	−0.994698	+	0.102843i	$0.967206\pi$
$390$	−0.0287488	−	2.50792i	−0.00145575	−	0.126993i
$391$		−	4.82987i		−	0.244257i
$392$	−2.63765	−	6.48404i	−0.133221	−	0.327494i
$393$	0.288031	+	25.1265i	0.0145292	+	1.26747i
$394$	−1.91620			−0.0965369
$395$	−5.28505			−0.265920
$396$	−0.337794	−	14.7319i	−0.0169748	−	0.740305i
$397$			25.3537i			1.27247i	0.771497	+	0.636233i	$0.219508\pi$
$397$			25.3537i			1.27247i	−0.771497	+	0.636233i	$0.780492\pi$
$398$	−9.74785			−0.488615
$399$	12.5522	−	2.60509i	0.628394	−	0.130418i
$400$	−2.90318			−0.145159
$401$		−	8.32283i		−	0.415622i	−0.978169	−	0.207811i	$-0.933366\pi$
$401$		−	8.32283i		−	0.415622i	0.978169	−	0.207811i	$-0.0666339\pi$
$402$	−3.00607	+	0.0344593i	−0.149929	+	0.00171867i
$403$	5.68792			0.283336
$404$	8.12464			0.404216
$405$	−13.0187	+	0.597336i	−0.646903	+	0.0296819i
$406$	−3.20463	+	0.626866i	−0.159043	+	0.0311108i
$407$			50.9802i			2.52700i
$408$	3.70452	−	0.0424657i	0.183401	−	0.00210236i
$409$		−	25.8715i		−	1.27927i	−0.768681	−	0.639633i	$-0.779087\pi$
$409$		−	25.8715i		−	1.27927i	0.768681	−	0.639633i	$-0.220913\pi$
$410$			10.1569i			0.501615i
$411$	−16.7626	+	0.192154i	−0.826840	+	0.00947825i
$412$		−	12.0056i		−	0.591473i
$413$	−24.3152	+	4.75636i	−1.19647	+	0.234045i
$414$	−6.77242	+	0.155288i	−0.332846	+	0.00763198i
$415$	21.7768			1.06898
$416$	1.00000			0.0490290
$417$	−28.3467	+	0.324944i	−1.38814	+	0.0159126i
$418$			13.7410i			0.672092i
$419$	27.0326			1.32063			0.660315	−	0.750988i	$-0.270423\pi$
$419$	27.0326			1.32063			0.660315	+	0.750988i	$0.270423\pi$
$420$	−1.34846	−	6.49730i	−0.0657981	−	0.317036i
$421$	−34.0390			−1.65896			−0.829480	−	0.558536i	$-0.811363\pi$
$421$	−34.0390			−1.65896			−0.829480	+	0.558536i	$0.811363\pi$
$422$			7.47422i			0.363839i
$423$	35.4458	−	0.812752i	1.72343	−	0.0395174i
$424$	−12.9594			−0.629365
$425$	−6.20973			−0.301216
$426$	−0.146383	−	12.7698i	−0.00709228	−	0.618699i
$427$	−2.26152	−	11.5612i	−0.109443	−	0.559487i
$428$		−	15.6424i		−	0.756102i
$429$	−0.0975191	−	8.50713i	−0.00470826	−	0.410728i
$430$			1.05592i			0.0509210i
$431$			13.7707i			0.663310i	0.943401	+	0.331655i	$0.107607\pi$
$431$			13.7707i			0.663310i	−0.943401	+	0.331655i	$0.892393\pi$
$432$	−0.178651	−	5.19308i	−0.00859534	−	0.249852i
$433$		−	4.17996i		−	0.200876i	−0.994943	−	0.100438i	$-0.967976\pi$
$433$		−	4.17996i		−	0.200876i	0.994943	−	0.100438i	$-0.0320244\pi$
$434$	14.7689	−	2.88899i	0.708931	−	0.138676i
$435$	−3.09525	+	0.0354815i	−0.148406	+	0.00170121i
$436$	7.21227			0.345405
$437$	6.31688			0.302177
$438$	0.227595	+	19.8544i	0.0108749	+	0.948680i
$439$		−	0.677489i		−	0.0323348i	−0.999869	−	0.0161674i	$-0.994854\pi$
$439$		−	0.677489i		−	0.0323348i	0.999869	−	0.0161674i	$-0.00514647\pi$
$440$	7.11266			0.339083
$441$	−19.2656	+	8.35678i	−0.917411	+	0.397942i
$442$	2.13894			0.101739
$443$			9.94326i			0.472419i	0.971702	+	0.236209i	$0.0759051\pi$
$443$			9.94326i			0.472419i	−0.971702	+	0.236209i	$0.924095\pi$
$444$	0.206058	+	17.9756i	0.00977908	+	0.853084i
$445$	18.5681			0.880210
$446$	19.5536			0.925892
$447$	−23.8667	+	0.273590i	−1.12886	+	0.0129403i
$448$	2.59654	−	0.507916i	0.122675	−	0.0239968i
$449$		−	16.3281i		−	0.770569i	−0.922798	−	0.385285i	$-0.874103\pi$
$449$		−	16.3281i		−	0.770569i	0.922798	−	0.385285i	$-0.125897\pi$
$450$	0.199652	+	8.70724i	0.00941170	+	0.410463i
$451$			34.4534i			1.62235i
$452$			3.90703i			0.183771i
$453$	−0.00126589	−	0.110430i	−5.94765e−5	−	0.00518846i
$454$		−	8.93913i		−	0.419534i
$455$	−0.735484	−	3.75990i	−0.0344800	−	0.176267i
$456$	0.0555399	+	4.84505i	0.00260089	+	0.226890i
$457$	−29.0772			−1.36017			−0.680087	−	0.733131i	$-0.738058\pi$
$457$	−29.0772			−1.36017			−0.680087	+	0.733131i	$0.738058\pi$
$458$	8.03593			0.375494
$459$	−0.382124	−	11.1077i	−0.0178360	−	0.518463i
$460$		−	3.26977i		−	0.152454i
$461$	−2.61074			−0.121594			−0.0607972	−	0.998150i	$-0.519364\pi$
$461$	−2.61074			−0.121594			−0.0607972	+	0.998150i	$0.519364\pi$
$462$	−4.57412	−	22.0396i	−0.212807	−	1.02537i
$463$	−39.4237			−1.83217			−0.916087	−	0.400979i	$-0.868670\pi$
$463$	−39.4237			−1.83217			−0.916087	+	0.400979i	$0.868670\pi$
$464$		−	1.23419i		−	0.0572959i
$465$	14.2648	−	0.163521i	0.661516	−	0.00758310i
$466$	9.34192			0.432756
$467$	4.44514			0.205696			0.102848	−	0.994697i	$-0.467204\pi$
$467$	4.44514			0.205696			0.102848	+	0.994697i	$0.467204\pi$
$468$	−0.0687703	−	2.99921i	−0.00317891	−	0.138639i
$469$	−4.50674	+	0.881576i	−0.208102	+	0.0407074i
$470$			17.1135i			0.789386i
$471$	−2.45089	+	0.0280951i	−0.112931	+	0.00129455i
$472$		−	9.36446i		−	0.431034i
$473$			3.58180i			0.164691i
$474$	−6.32121	+	0.0724614i	−0.290343	+	0.00332826i
$475$		−	8.12156i		−	0.372643i
$476$	5.55385	−	1.08640i	0.254560	−	0.0497953i
$477$	0.891222	+	38.8680i	0.0408063	+	1.77964i
$478$	14.3110			0.654570
$479$	−26.2406			−1.19897			−0.599483	−	0.800388i	$-0.704627\pi$
$479$	−26.2406			−1.19897			−0.599483	+	0.800388i	$0.704627\pi$
$480$	2.50792	−	0.0287488i	0.114470	−	0.00131220i
$481$			10.3789i			0.473237i
$482$	−11.2737			−0.513502
$483$	−10.1318	+	2.10278i	−0.461015	+	0.0956797i
$484$	13.1269			0.596678
$485$			18.2680i			0.829508i
$486$	−15.5629	+	0.892941i	−0.705946	+	0.0405046i
$487$	−21.4582			−0.972364			−0.486182	−	0.873858i	$-0.661611\pi$
$487$	−21.4582			−0.972364			−0.486182	+	0.873858i	$0.661611\pi$
$488$	4.45255			0.201557
$489$	0.138489	+	12.0811i	0.00626267	+	0.546327i
$490$	−3.81943	−	9.38916i	−0.172544	−	0.424159i
$491$		−	9.33758i		−	0.421399i	−0.977551	−	0.210700i	$-0.932426\pi$
$491$		−	9.33758i		−	0.421399i	0.977551	−	0.210700i	$-0.0675742\pi$
$492$	0.139258	+	12.1482i	0.00627824	+	0.547685i
$493$		−	2.63986i		−	0.118894i
$494$			2.79747i			0.125864i
$495$	−0.489139	−	21.3324i	−0.0219852	−	0.958818i
$496$			5.68792i			0.255395i
$497$	−3.74494	−	19.1446i	−0.167983	−	0.858754i
$498$	26.0463	−	0.298574i	1.16716	−	0.0133794i
$499$	32.2897			1.44548			0.722742	−	0.691117i	$-0.242881\pi$
$499$	32.2897			1.44548			0.722742	+	0.691117i	$0.242881\pi$
$500$	−11.4441			−0.511797
$501$	0.0585883	+	5.11098i	0.00261753	+	0.228342i
$502$			23.7489i			1.05997i
$503$	−0.722720			−0.0322245			−0.0161122	−	0.999870i	$-0.505129\pi$
$503$	−0.722720			−0.0322245			−0.0161122	+	0.999870i	$0.505129\pi$
$504$	−1.70191	−	7.75264i	−0.0758092	−	0.345330i
$505$	11.7648			0.523527
$506$		−	11.0914i		−	0.493074i
$507$	−0.0198536	−	1.73194i	−0.000881728	−	0.0769180i
$508$	0.381873			0.0169429
$509$	−27.6002			−1.22336			−0.611678	−	0.791107i	$-0.709505\pi$
$509$	−27.6002			−1.22336			−0.611678	+	0.791107i	$0.709505\pi$
$510$	5.36429	−	0.0614920i	0.237535	−	0.00272291i
$511$	5.82260	+	29.7660i	0.257577	+	1.31677i
$512$			1.00000i			0.0441942i
$513$	14.5275	−	0.499771i	0.641405	−	0.0220654i
$514$		−	11.3496i		−	0.500609i
$515$		−	17.3846i		−	0.766056i
$516$	0.0144773	+	1.26294i	0.000637330	+	0.0555978i
$517$			58.0508i			2.55307i
$518$	5.27161	+	26.9492i	0.231621	+	1.18408i
$519$	−0.402213	−	35.0873i	−0.0176552	−	1.54016i
$520$	1.44804			0.0635008
$521$	−9.28656			−0.406852			−0.203426	−	0.979090i	$-0.565208\pi$
$521$	−9.28656			−0.406852			−0.203426	+	0.979090i	$0.565208\pi$
$522$	−3.70160	+	0.0848756i	−0.162015	+	0.00371490i
$523$		−	27.3210i		−	1.19466i	−0.801994	−	0.597332i	$-0.796227\pi$
$523$		−	27.3210i		−	1.19466i	0.801994	−	0.597332i	$-0.203773\pi$
$524$	−14.5078			−0.633775
$525$	2.70352	+	13.0264i	0.117991	+	0.568520i
$526$	14.2128			0.619707
$527$			12.1661i			0.529966i
$528$	8.50713	−	0.0975191i	0.370225	−	0.00424397i
$529$	17.9011			0.778311
$530$	−18.7658			−0.815133
$531$	−28.0860	+	0.643997i	−1.21883	+	0.0279471i
$532$	1.42088	+	7.26376i	0.0616031	+	0.314924i
$533$			7.01426i			0.303821i
$534$	22.2084	−	0.254580i	0.961052	−	0.0110167i
$535$		−	22.6508i		−	0.979278i
$536$		−	1.73567i		−	0.0749696i
$537$	23.5849	−	0.270359i	1.01776	−	0.0116668i
$538$		−	6.70104i		−	0.288903i
$539$	−12.9559	−	31.8491i	−0.558051	−	1.37184i
$540$	−0.258694	−	7.51979i	−0.0111324	−	0.323600i
$541$	37.9607			1.63206			0.816029	−	0.578011i	$-0.196171\pi$
$541$	37.9607			1.63206			0.816029	+	0.578011i	$0.196171\pi$
$542$	−7.56537			−0.324960
$543$	−36.6494	+	0.420120i	−1.57278	+	0.0180291i
$544$			2.13894i			0.0917065i
$545$	10.4437			0.447358
$546$	−0.931230	−	4.48696i	−0.0398530	−	0.192024i
$547$	21.3007			0.910752			0.455376	−	0.890299i	$-0.349505\pi$
$547$	21.3007			0.910752			0.455376	+	0.890299i	$0.349505\pi$
$548$		−	9.67855i		−	0.413447i
$549$	−0.306203	−	13.3541i	−0.0130684	−	0.569941i
$550$	−14.2602			−0.608055
$551$	3.45262			0.147086
$552$	−0.0448307	−	3.91083i	−0.00190812	−	0.166456i
$553$	−9.47683	+	1.85379i	−0.402996	+	0.0788311i
$554$			6.46838i			0.274815i
$555$	0.298381	+	26.0294i	0.0126656	+	1.10489i
$556$		−	16.3671i		−	0.694118i
$557$			36.7401i			1.55673i	0.627813	+	0.778365i	$0.283950\pi$
$557$			36.7401i			1.55673i	−0.627813	+	0.778365i	$0.716050\pi$
$558$	17.0593	−	0.391160i	0.722177	−	0.0165591i
$559$			0.729206i			0.0308421i
$560$	3.75990	−	0.735484i	0.158885	−	0.0310799i
$561$	18.1963	−	0.208588i	0.768247	−	0.00880658i
$562$	20.7233			0.874160
$563$	−13.2058			−0.556556			−0.278278	−	0.960501i	$-0.589764\pi$
$563$	−13.2058			−0.556556			−0.278278	+	0.960501i	$0.589764\pi$
$564$	0.234637	+	20.4687i	0.00987999	+	0.861887i
$565$			5.65754i			0.238014i
$566$	0.0977777			0.00410990
$567$	−23.1348	+	5.63755i	−0.971569	+	0.236755i
$568$	7.37313			0.309370
$569$			22.2870i			0.934320i	0.884173	+	0.467160i	$0.154723\pi$
$569$			22.2870i			0.934320i	−0.884173	+	0.467160i	$0.845277\pi$
$570$	0.0804240	+	7.01583i	0.00336859	+	0.293861i
$571$	−15.1291			−0.633132			−0.316566	−	0.948571i	$-0.602530\pi$
$571$	−15.1291			−0.633132			−0.316566	+	0.948571i	$0.602530\pi$
$572$	4.91192			0.205377
$573$	0.869622	−	0.00996866i	0.0363290	−	0.000416447i
$574$	3.56266	+	18.2128i	0.148702	+	0.760187i
$575$			6.55556i			0.273386i
$576$	2.99921	−	0.0687703i	0.124967	−	0.00286543i
$577$		−	45.5962i		−	1.89820i	−0.314980	−	0.949098i	$-0.601998\pi$
$577$		−	45.5962i		−	1.89820i	0.314980	−	0.949098i	$-0.398002\pi$
$578$		−	12.4249i		−	0.516809i
$579$	0.268043	+	23.3829i	0.0111395	+	0.971759i
$580$		−	1.78716i		−	0.0742077i
$581$	39.0489	−	7.63847i	1.62002	−	0.316897i
$582$	0.250466	+	21.8495i	0.0103822	+	0.905693i
$583$	−63.6555			−2.63634
$584$	−11.4637			−0.474371
$585$	−0.0995822	−	4.34298i	−0.00411722	−	0.179560i
$586$			32.8772i			1.35815i
$587$	−25.7701			−1.06365			−0.531823	−	0.846855i	$-0.678493\pi$
$587$	−25.7701			−1.06365			−0.531823	+	0.846855i	$0.678493\pi$
$588$	−4.69698	−	11.1776i	−0.193700	−	0.460956i
$589$	−15.9118			−0.655635
$590$		−	13.5601i		−	0.558262i
$591$	−3.31874	+	0.0380435i	−0.136515	+	0.00156490i
$592$	−10.3789			−0.426570
$593$	−32.2574			−1.32465			−0.662326	−	0.749216i	$-0.730431\pi$
$593$	−32.2574			−1.32465			−0.662326	+	0.749216i	$0.730431\pi$
$594$	−0.877518	−	25.5080i	−0.0360050	−	1.04660i
$595$	8.04221	−	1.57316i	0.329698	−	0.0644932i
$596$		−	13.7804i		−	0.564466i
$597$	−16.8827	+	0.193530i	−0.690961	+	0.00792064i
$598$		−	2.25807i		−	0.0923391i
$599$			39.9386i			1.63185i	0.578158	+	0.815924i	$0.303772\pi$
$599$			39.9386i			1.63185i	−0.578158	+	0.815924i	$0.696228\pi$
$600$	−5.02812	+	0.0576384i	−0.205272	+	0.00235308i
$601$		−	29.0019i		−	1.18301i	−0.806300	−	0.591507i	$-0.798533\pi$
$601$		−	29.0019i		−	1.18301i	0.806300	−	0.591507i	$-0.201467\pi$
$602$	0.370376	+	1.89341i	0.0150954	+	0.0771698i
$603$	−5.20565	+	0.119363i	−0.211990	+	0.00486082i
$604$	0.0637611			0.00259440
$605$	19.0083			0.772798
$606$	14.0714	−	0.161303i	0.571610	−	0.00655249i
$607$			1.73581i			0.0704545i	0.999379	+	0.0352273i	$0.0112155\pi$
$607$			1.73581i			0.0704545i	−0.999379	+	0.0352273i	$0.988784\pi$
$608$	−2.79747			−0.113453
$609$	−5.53776	+	1.14932i	−0.224402	+	0.0465726i
$610$	6.44747			0.261051
$611$			11.8184i			0.478120i
$612$	6.41514	−	0.147096i	0.259317	−	0.00594599i
$613$	47.4153			1.91509			0.957543	−	0.288290i	$-0.0930869\pi$
$613$	47.4153			1.91509			0.957543	+	0.288290i	$0.0930869\pi$
$614$	−11.8951			−0.480048
$615$	0.201651	+	17.5912i	0.00813137	+	0.709344i
$616$	12.7540	−	2.49484i	0.513873	−	0.100520i
$617$			38.3327i			1.54322i	0.636097	+	0.771609i	$0.280548\pi$
$617$			38.3327i			1.54322i	−0.636097	+	0.771609i	$0.719452\pi$
$618$	−0.238354	−	20.7929i	−0.00958799	−	0.836414i
$619$			47.0915i			1.89277i	0.323046	+	0.946383i	$0.395293\pi$
$619$			47.0915i			1.89277i	−0.323046	+	0.946383i	$0.604707\pi$
$620$			8.23635i			0.330780i
$621$	−11.7263	+	0.403405i	−0.470561	+	0.0161881i
$622$		−	18.0050i		−	0.721933i
$623$	33.2951	−	6.51295i	1.33394	−	0.260936i
$624$	1.73194	−	0.0198536i	0.0693330	−	0.000794779i
$625$	−2.05569			−0.0822274
$626$	16.5426			0.661174
$627$	0.272807	+	23.7985i	0.0108949	+	0.950420i
$628$		−	1.41512i		−	0.0564693i
$629$	−22.1999			−0.885167
$630$	−2.46444	−	11.2261i	−0.0981857	−	0.447260i
$631$	−38.7782			−1.54373			−0.771867	−	0.635784i	$-0.780677\pi$
$631$	−38.7782			−1.54373			−0.771867	+	0.635784i	$0.780677\pi$
$632$		−	3.64979i		−	0.145181i
$633$	0.148390	+	12.9449i	0.00589797	+	0.514513i
$634$	13.7159			0.544729
$635$	0.552968			0.0219439
$636$	−22.4449	+	0.257291i	−0.889998	+	0.0102022i
$637$	−2.63765	−	6.48404i	−0.104508	−	0.256907i
$638$		−	6.06224i		−	0.240006i
$639$	−0.507052	−	22.1136i	−0.0200587	−	0.874800i
$640$			1.44804i			0.0572389i
$641$			12.7936i			0.505316i	0.967556	+	0.252658i	$0.0813048\pi$
$641$			12.7936i			0.505316i	−0.967556	+	0.252658i	$0.918695\pi$
$642$	−0.310557	−	27.0916i	−0.0122567	−	1.06922i
$643$		−	7.89152i		−	0.311211i	−0.987819	−	0.155606i	$-0.950267\pi$
$643$		−	7.89152i		−	0.311211i	0.987819	−	0.155606i	$-0.0497329\pi$
$644$	−1.14691	−	5.86316i	−0.0451945	−	0.231041i
$645$	0.0209638	+	1.82879i	0.000825449	+	0.0720085i
$646$	−5.98364			−0.235423
$647$	36.8884			1.45023			0.725116	−	0.688627i	$-0.241786\pi$
$647$	36.8884			1.45023			0.725116	+	0.688627i	$0.241786\pi$
$648$	−0.412513	−	8.99054i	−0.0162050	−	0.353182i
$649$		−	45.9975i		−	1.80556i
$650$	−2.90318			−0.113872
$651$	25.5215	−	5.29676i	1.00027	−	0.207596i
$652$	−6.97550			−0.273182
$653$		−	29.6715i		−	1.16114i	−0.814212	−	0.580568i	$-0.802831\pi$
$653$		−	29.6715i		−	1.16114i	0.814212	−	0.580568i	$-0.197169\pi$
$654$	12.4912	−	0.143189i	0.488445	−	0.00559915i
$655$	−21.0078			−0.820844
$656$	−7.01426			−0.273861
$657$	0.788362	+	34.3821i	0.0307569	+	1.34137i
$658$	6.00274	+	30.6869i	0.234011	+	1.19630i
$659$		−	21.9700i		−	0.855829i	−0.903819	−	0.427914i	$-0.859248\pi$
$659$		−	21.9700i		−	0.855829i	0.903819	−	0.427914i	$-0.140752\pi$
$660$	12.3187	−	0.141212i	0.479504	−	0.00549665i
$661$		−	17.3095i		−	0.673261i	−0.941637	−	0.336631i	$-0.890713\pi$
$661$		−	17.3095i		−	0.673261i	0.941637	−	0.336631i	$-0.109287\pi$
$662$			19.5146i			0.758455i
$663$	3.70452	−	0.0424657i	0.143871	−	0.00164923i
$664$			15.0388i			0.583620i
$665$	2.05750	+	10.5182i	0.0797863	+	0.407879i
$666$	0.713759	+	31.1285i	0.0276576	+	1.20620i
$667$	−2.78688			−0.107909
$668$	−2.95102			−0.114178
$669$	33.8657	−	0.388210i	1.30932	−	0.0150090i
$670$		−	2.51332i		−	0.0970982i
$671$	21.8705			0.844303
$672$	4.48696	−	0.931230i	0.173088	−	0.0359230i
$673$	40.2644			1.55208			0.776039	−	0.630685i	$-0.217226\pi$
$673$	40.2644			1.55208			0.776039	+	0.630685i	$0.217226\pi$
$674$		−	6.95661i		−	0.267958i
$675$	0.518655	+	15.0764i	0.0199630	+	0.580292i
$676$	1.00000			0.0384615
$677$	−8.37867			−0.322019			−0.161009	−	0.986953i	$-0.551475\pi$
$677$	−8.37867			−0.322019			−0.161009	+	0.986953i	$0.551475\pi$
$678$	0.0775684	+	6.76672i	0.00297900	+	0.259874i
$679$	6.40771	+	32.7571i	0.245905	+	1.25710i
$680$			3.09728i			0.118775i
$681$	−0.177474	−	15.4820i	−0.00680080	−	0.593272i
$682$			27.9386i			1.06982i
$683$			31.4732i			1.20429i	0.798387	+	0.602145i	$0.205687\pi$
$683$			31.4732i			1.20429i	−0.798387	+	0.602145i	$0.794313\pi$
$684$	0.192383	+	8.39022i	0.00735595	+	0.320808i
$685$		−	14.0149i		−	0.535484i
$686$	−10.1421	−	15.4964i	−0.387228	−	0.591654i
$687$	13.9177	−	0.159542i	0.530994	−	0.00608690i
$688$	−0.729206			−0.0278007
$689$	−12.9594			−0.493714
$690$	−0.0649166	−	5.66304i	−0.00247133	−	0.215588i
$691$		−	13.6971i		−	0.521061i	−0.965466	−	0.260531i	$-0.916103\pi$
$691$		−	13.6971i		−	0.521061i	0.965466	−	0.260531i	$-0.0838975\pi$
$692$	20.2590			0.770132
$693$	−8.35965	−	38.0803i	−0.317557	−	1.44655i
$694$	11.7554			0.446229
$695$		−	23.7002i		−	0.898999i
$696$	−0.0245031	−	2.13754i	−0.000928787	−	0.0810233i
$697$	−15.0031			−0.568283
$698$	4.59940			0.174090
$699$	16.1796	−	0.185470i	0.611969	−	0.00701514i
$700$	−7.53821	+	1.47457i	−0.284918	+	0.0557335i
$701$		−	36.3624i		−	1.37339i	−0.726947	−	0.686694i	$-0.759061\pi$
$701$		−	36.3624i		−	1.37339i	0.726947	−	0.686694i	$-0.240939\pi$
$702$	−0.178651	−	5.19308i	−0.00674274	−	0.196000i
$703$		−	29.0347i		−	1.09506i
$704$			4.91192i			0.185125i
$705$	0.339764	+	29.6395i	0.0127962	+	1.11629i
$706$			8.22304i			0.309478i
$707$	21.0960	−	4.12664i	0.793395	−	0.155198i
$708$	−0.185918	−	16.2187i	−0.00698723	−	0.609535i
$709$	23.1477			0.869331			0.434666	−	0.900592i	$-0.356867\pi$
$709$	23.1477			0.869331			0.434666	+	0.900592i	$0.356867\pi$
$710$	10.6766			0.400686
$711$	−10.9465	+	0.250997i	−0.410526	+	0.00941313i
$712$			12.8229i			0.480558i
$713$	12.8437			0.481000
$714$	9.59736	−	1.99185i	0.359172	−	0.0745430i
$715$	7.11266			0.265998
$716$			13.6176i			0.508915i
$717$	24.7858	−	0.284125i	0.925641	−	0.0106108i
$718$	29.8313			1.11329
$719$	4.85565			0.181085			0.0905426	−	0.995893i	$-0.471140\pi$
$719$	4.85565			0.181085			0.0905426	+	0.995893i	$0.471140\pi$
$720$	4.34298	−	0.0995822i	0.161853	−	0.00371121i
$721$	−6.09783	−	31.1730i	−0.227095	−	1.16094i
$722$			11.1741i			0.415858i
$723$	−19.5253	+	0.223823i	−0.726153	+	0.00832405i
$724$		−	21.1609i		−	0.786439i
$725$			3.58307i			0.133072i
$726$	22.7350	−	0.260616i	0.843774	−	0.00967237i
$727$		−	19.8979i		−	0.737973i	−0.929435	−	0.368986i	$-0.879705\pi$
$727$		−	19.8979i		−	0.737973i	0.929435	−	0.368986i	$-0.120295\pi$
$728$	2.59654	−	0.507916i	0.0962342	−	0.0188246i
$729$	−26.9362	+	1.85550i	−0.997636	+	0.0687221i
$730$	−16.5999			−0.614390
$731$	−1.55973			−0.0576887
$732$	7.71153	−	0.0883990i	0.285026	−	0.00326732i
$733$		−	27.6167i		−	1.02005i	−0.860161	−	0.510023i	$-0.829637\pi$
$733$		−	27.6167i		−	1.02005i	0.860161	−	0.510023i	$-0.170363\pi$
$734$	−9.85865			−0.363889
$735$	−6.80142	−	16.1856i	−0.250874	−	0.597015i
$736$	2.25807			0.0832334
$737$		−	8.52547i		−	0.314040i
$738$	0.482372	+	21.0372i	0.0177564	+	0.774391i
$739$	−13.5322			−0.497791			−0.248895	−	0.968530i	$-0.580067\pi$
$739$	−13.5322			−0.497791			−0.248895	+	0.968530i	$0.580067\pi$
$740$	−15.0291			−0.552479
$741$	0.0555399	+	4.84505i	0.00204031	+	0.177987i
$742$	−33.6496	+	6.58230i	−1.23532	+	0.241644i
$743$		−	18.1815i		−	0.667014i	−0.942748	−	0.333507i	$-0.891768\pi$
$743$		−	18.1815i		−	0.667014i	0.942748	−	0.333507i	$-0.108232\pi$
$744$	0.112926	+	9.85112i	0.00414005	+	0.361160i
$745$		−	19.9545i		−	0.731078i
$746$		−	20.1463i		−	0.737609i
$747$	45.1046	−	1.03422i	1.65029	−	0.0378403i
$748$			10.5063i			0.384149i
$749$	−7.94501	−	40.6160i	−0.290304	−	1.48408i
$750$	−19.8205	+	0.227207i	−0.723743	+	0.00829642i
$751$	−36.8001			−1.34286			−0.671428	−	0.741070i	$-0.734319\pi$
$751$	−36.8001			−1.34286			−0.671428	+	0.741070i	$0.734319\pi$
$752$	−11.8184			−0.430972
$753$	0.471501	+	41.1316i	0.0171824	+	1.49892i
$754$		−	1.23419i		−	0.0449466i
$755$	0.0923287			0.00336019
$756$	−3.10152	−	13.3933i	−0.112801	−	0.487110i
$757$	−33.0255			−1.20033			−0.600166	−	0.799875i	$-0.704899\pi$
$757$	−33.0255			−1.20033			−0.600166	+	0.799875i	$0.704899\pi$
$758$		−	5.34091i		−	0.193991i
$759$	−0.220204	−	19.2096i	−0.00799291	−	0.697266i
$760$	−4.05086			−0.146940
$761$	−16.2865			−0.590386			−0.295193	−	0.955438i	$-0.595384\pi$
$761$	−16.2865			−0.590386			−0.295193	+	0.955438i	$0.595384\pi$
$762$	0.661381	−	0.00758155i	0.0239593	−	0.000274651i
$763$	18.7270	−	3.66323i	0.677961	−	0.132618i
$764$			0.502109i			0.0181657i
$765$	9.28939	−	0.213001i	0.335859	−	0.00770106i
$766$		−	2.81834i		−	0.101831i
$767$		−	9.36446i		−	0.338131i
$768$	0.0198536	+	1.73194i	0.000716404	+	0.0624959i
$769$			12.4178i			0.447797i	0.974612	+	0.223899i	$0.0718785\pi$
$769$			12.4178i			0.447797i	−0.974612	+	0.223899i	$0.928122\pi$
$770$	18.4683	−	3.61263i	0.665551	−	0.130190i
$771$	−0.225330	−	19.6568i	−0.00811505	−	0.707921i
$772$	−13.5010			−0.485912
$773$	34.0996			1.22648			0.613238	−	0.789898i	$-0.289867\pi$
$773$	34.0996			1.22648			0.613238	+	0.789898i	$0.289867\pi$
$774$	0.0501477	+	2.18704i	0.00180252	+	0.0786117i
$775$		−	16.5130i		−	0.593166i
$776$	−12.6157			−0.452876
$777$	9.66513	+	46.5697i	0.346735	+	1.67068i
$778$	−4.05676			−0.145442
$779$		−	19.6222i		−	0.703038i
$780$	2.50792	−	0.0287488i	0.0897978	−	0.00102937i
$781$	36.2162			1.29592
$782$	4.82987			0.172716
$783$	−6.40925	+	0.220489i	−0.229048	+	0.00787964i
$784$	6.48404	−	2.63765i	0.231573	−	0.0942018i
$785$		−	2.04915i		−	0.0731371i
$786$	−25.1265	+	0.288031i	−0.896234	+	0.0102737i
$787$			31.0152i			1.10557i	0.833323	+	0.552787i	$0.186436\pi$
$787$			31.0152i			1.10557i	−0.833323	+	0.552787i	$0.813564\pi$
$788$		−	1.91620i		−	0.0682619i
$789$	24.6157	−	0.282175i	0.876341	−	0.0100457i
$790$		−	5.28505i		−	0.188034i
$791$	1.98444	+	10.1448i	0.0705587	+	0.360706i
$792$	14.7319	−	0.337794i	0.523474	−	0.0120030i
$793$	4.45255			0.158115
$794$	−25.3537			−0.899769
$795$	−32.5011	+	0.372567i	−1.15270	+	0.0132136i
$796$		−	9.74785i		−	0.345503i
$797$	−41.7871			−1.48017			−0.740087	−	0.672511i	$-0.765216\pi$
$797$	−41.7871			−1.48017			−0.740087	+	0.672511i	$0.765216\pi$
$798$	2.60509	+	12.5522i	0.0922192	+	0.444342i
$799$	−25.2788			−0.894301
$800$		−	2.90318i		−	0.102643i
$801$	38.4585	−	0.881833i	1.35887	−	0.0311580i
$802$	8.32283			0.293889
$803$	−56.3087			−1.98709
$804$	−0.0344593	−	3.00607i	−0.00121528	−	0.106016i
$805$	−1.66077	−	8.49009i	−0.0585345	−	0.299236i
$806$			5.68792i			0.200349i
$807$	−0.133040	−	11.6058i	−0.00468322	−	0.408543i
$808$			8.12464i			0.285824i
$809$		−	50.9042i		−	1.78970i	−0.446371	−	0.894848i	$-0.647284\pi$
$809$		−	50.9042i		−	1.78970i	0.446371	−	0.894848i	$-0.352716\pi$
$810$	−0.597336	−	13.0187i	−0.0209883	−	0.457430i
$811$			25.7349i			0.903676i	0.892100	+	0.451838i	$0.149232\pi$
$811$			25.7349i			0.903676i	−0.892100	+	0.451838i	$0.850768\pi$
$812$	−0.626866	−	3.20463i	−0.0219987	−	0.112460i
$813$	−13.1027	+	0.150200i	−0.459533	+	0.00526773i
$814$	−50.9802			−1.78686
$815$	−10.1008			−0.353816
$816$	0.0424657	+	3.70452i	0.00148660	+	0.129684i
$817$		−	2.03994i		−	0.0713683i
$818$	25.8715			0.904577
$819$	−1.70191	−	7.75264i	−0.0594697	−	0.270899i
$820$	−10.1569			−0.354695
$821$		−	8.06899i		−	0.281610i	−0.990037	−	0.140805i	$-0.955031\pi$
$821$		−	8.06899i		−	0.281610i	0.990037	−	0.140805i	$-0.0449690\pi$
$822$	−0.192154	−	16.7626i	−0.00670214	−	0.584664i
$823$	−19.4372			−0.677538			−0.338769	−	0.940870i	$-0.610011\pi$
$823$	−19.4372			−0.677538			−0.338769	+	0.940870i	$0.610011\pi$
$824$	12.0056			0.418234
$825$	−24.6977	+	0.283115i	−0.859863	+	0.00985680i
$826$	−4.75636	−	24.3152i	−0.165495	−	0.846034i
$827$			10.6246i			0.369452i	0.982790	+	0.184726i	$0.0591398\pi$
$827$			10.6246i			0.369452i	−0.982790	+	0.184726i	$0.940860\pi$
$828$	−0.155288	−	6.77242i	−0.00539662	−	0.235358i
$829$			17.9116i			0.622096i	0.950394	+	0.311048i	$0.100680\pi$
$829$			17.9116i			0.622096i	−0.950394	+	0.311048i	$0.899320\pi$
$830$			21.7768i			0.755885i
$831$	0.128420	+	11.2028i	0.00445486	+	0.388622i
$832$			1.00000i			0.0346688i
$833$	13.8690	−	5.64179i	0.480532	−	0.195476i
$834$	−0.324944	−	28.3467i	−0.0112519	−	0.981566i
$835$	−4.27320			−0.147880
$836$	−13.7410			−0.475241
$837$	29.5378	−	1.01615i	1.02098	−	0.0351234i
$838$			27.0326i			0.933827i
$839$	−38.8098			−1.33986			−0.669932	−	0.742422i	$-0.733677\pi$
$839$	−38.8098			−1.33986			−0.669932	+	0.742422i	$0.733677\pi$
$840$	6.49730	−	1.34846i	0.224178	−	0.0465263i
$841$	27.4768			0.947475
$842$		−	34.0390i		−	1.17306i
$843$	35.8915	−	0.411432i	1.23617	−	0.0141705i
$844$	−7.47422			−0.257273
$845$	1.44804			0.0498141
$846$	0.812752	+	35.4458i	0.0279430	+	1.21865i
$847$	34.0846	−	6.66737i	1.17116	−	0.229094i
$848$		−	12.9594i		−	0.445028i
$849$	0.169345	−	0.00194124i	0.00581190	−	6.66230e-5i
$850$		−	6.20973i		−	0.212992i
$851$			23.4362i			0.803383i
$852$	12.7698	−	0.146383i	0.437486	−	0.00501500i
$853$		−	49.9088i		−	1.70884i	−0.519580	−	0.854422i	$-0.673912\pi$
$853$		−	49.9088i		−	1.70884i	0.519580	−	0.854422i	$-0.326088\pi$
$854$	11.5612	−	2.26152i	0.395617	−	0.0773877i
$855$	0.278579	+	12.1494i	0.00952719	+	0.415500i
$856$	15.6424			0.534645
$857$	−56.3897			−1.92624			−0.963118	−	0.269080i	$-0.913281\pi$
$857$	−56.3897			−1.92624			−0.963118	+	0.269080i	$0.913281\pi$
$858$	8.50713	−	0.0975191i	0.290429	−	0.00332925i
$859$		−	40.6014i		−	1.38530i	−0.721273	−	0.692651i	$-0.756443\pi$
$859$		−	40.6014i		−	1.38530i	0.721273	−	0.692651i	$-0.243557\pi$
$860$	−1.05592			−0.0360066
$861$	6.53188	+	31.4727i	0.222606	+	1.07259i
$862$	−13.7707			−0.469031
$863$		−	0.934052i		−	0.0317955i	−0.999874	−	0.0158977i	$-0.994939\pi$
$863$		−	0.934052i		−	0.0317955i	0.999874	−	0.0158977i	$-0.00506062\pi$
$864$	5.19308	−	0.178651i	0.176672	−	0.00607782i
$865$	29.3359			0.997449
$866$	4.17996			0.142041
$867$	−0.246679	−	21.5192i	−0.00837766	−	0.730830i
$868$	2.88899	+	14.7689i	0.0980587	+	0.501290i
$869$		−	17.9275i		−	0.608148i
$870$	−0.0354815	−	3.09525i	−0.00120294	−	0.104939i
$871$		−	1.73567i		−	0.0588110i
$872$			7.21227i			0.244238i
$873$	0.867583	+	37.8371i	0.0293632	+	1.28059i
$874$			6.31688i			0.213672i
$875$	−29.7151	+	5.81266i	−1.00455	+	0.196504i
$876$	−19.8544	+	0.227595i	−0.670818	+	0.00768974i
$877$	1.75990			0.0594276			0.0297138	−	0.999558i	$-0.490540\pi$
$877$	1.75990			0.0594276			0.0297138	+	0.999558i	$0.490540\pi$
$878$	0.677489			0.0228642
$879$	0.652730	+	56.9413i	0.0220160	+	1.92058i
$880$			7.11266i			0.239768i
$881$	29.0153			0.977552			0.488776	−	0.872409i	$-0.337444\pi$
$881$	29.0153			0.977552			0.488776	+	0.872409i	$0.337444\pi$
$882$	−8.35678	−	19.2656i	−0.281387	−	0.648707i
$883$	−2.19513			−0.0738719			−0.0369360	−	0.999318i	$-0.511760\pi$
$883$	−2.19513			−0.0738719			−0.0369360	+	0.999318i	$0.511760\pi$
$884$			2.13894i			0.0719405i
$885$	−0.269217	−	23.4853i	−0.00904963	−	0.789449i
$886$	−9.94326			−0.334051
$887$	−26.2772			−0.882303			−0.441152	−	0.897433i	$-0.645430\pi$
$887$	−26.2772			−0.882303			−0.441152	+	0.897433i	$0.645430\pi$
$888$	−17.9756	+	0.206058i	−0.603221	+	0.00691486i
$889$	0.991550	−	0.193960i	0.0332555	−	0.00650520i
$890$			18.5681i			0.622403i
$891$	−2.02623	−	44.1608i	−0.0678812	−	1.47944i
$892$			19.5536i			0.654704i
$893$		−	33.0616i		−	1.10636i
$894$	−0.273590	−	23.8667i	−0.00915020	−	0.798223i
$895$			19.7189i			0.659130i
$896$	0.507916	+	2.59654i	0.0169683	+	0.0867443i
$897$	−0.0448307	−	3.91083i	−0.00149685	−	0.130579i
$898$	16.3281			0.544875
$899$	7.01998			0.234129
$900$	−8.70724	+	0.199652i	−0.290241	+	0.00665507i
$901$		−	27.7195i		−	0.923469i
$902$	−34.4534			−1.14717
$903$	0.679059	+	3.27192i	0.0225977	+	0.108883i
$904$	−3.90703			−0.129946
$905$		−	30.6419i		−	1.01857i
$906$	0.110430	−	0.00126589i	0.00366880	−	4.20562e-5i
$907$	−24.2378			−0.804804			−0.402402	−	0.915463i	$-0.631825\pi$
$907$	−24.2378			−0.804804			−0.402402	+	0.915463i	$0.631825\pi$
$908$	8.93913			0.296655
$909$	24.3675	−	0.558734i	0.808219	−	0.0185320i
$910$	3.75990	−	0.735484i	0.124639	−	0.0243811i
$911$		−	19.3671i		−	0.641661i	−0.947137	−	0.320830i	$-0.896038\pi$
$911$		−	19.3671i		−	0.641661i	0.947137	−	0.320830i	$-0.103962\pi$
$912$	−4.84505	+	0.0555399i	−0.160436	+	0.00183911i
$913$			73.8694i			2.44472i
$914$		−	29.0772i		−	0.961789i
$915$	11.1666	−	0.128005i	0.369157	−	0.00423173i
$916$			8.03593i			0.265514i
$917$	−37.6700	+	7.36873i	−1.24397	+	0.243337i
$918$	11.1077	−	0.382124i	0.366609	−	0.0126120i
$919$	19.8735			0.655566			0.327783	−	0.944753i	$-0.393698\pi$
$919$	19.8735			0.655566			0.327783	+	0.944753i	$0.393698\pi$
$920$	3.26977			0.107801
$921$	−20.6016	+	0.236161i	−0.678846	+	0.00778176i
$922$		−	2.61074i		−	0.0859802i
$923$	7.37313			0.242690
$924$	22.0396	−	4.57412i	0.725049	−	0.150478i
$925$	30.1318			0.990726
$926$		−	39.4237i		−	1.29554i
$927$	−0.825627	−	36.0073i	−0.0271172	−	1.18263i
$928$	1.23419			0.0405143
$929$	−22.6067			−0.741703			−0.370852	−	0.928692i	$-0.620934\pi$
$929$	−22.6067			−0.741703			−0.370852	+	0.928692i	$0.620934\pi$
$930$	0.163521	+	14.2648i	0.00536206	+	0.467762i
$931$	7.37876	+	18.1389i	0.241829	+	0.594480i
$932$			9.34192i			0.306005i
$933$	−0.357463	−	31.1835i	−0.0117028	−	1.02090i
$934$			4.44514i			0.145449i
$935$			15.2136i			0.497537i
$936$	2.99921	−	0.0687703i	0.0980323	−	0.00224783i
$937$		−	32.1007i		−	1.04868i	−0.851508	−	0.524341i	$-0.824312\pi$
$937$		−	32.1007i		−	1.04868i	0.851508	−	0.524341i	$-0.175688\pi$
$938$	−0.881576	−	4.50674i	−0.0287845	−	0.147150i
$939$	28.6507	−	0.328429i	0.934980	−	0.0107179i
$940$	−17.1135			−0.558180
$941$	−48.2085			−1.57155			−0.785776	−	0.618511i	$-0.787736\pi$
$941$	−48.2085			−1.57155			−0.785776	+	0.618511i	$0.787736\pi$
$942$	−0.0280951	−	2.45089i	−0.000915388	−	0.0798543i
$943$			15.8386i			0.515777i
$944$	9.36446			0.304787
$945$	−4.49114	−	19.3941i	−0.146097	−	0.630889i
$946$	−3.58180			−0.116454
$947$		−	49.8678i		−	1.62048i	−0.586095	−	0.810242i	$-0.699336\pi$
$947$		−	49.8678i		−	1.62048i	0.586095	−	0.810242i	$-0.300664\pi$
$948$	−0.0724614	−	6.32121i	−0.00235344	−	0.205303i
$949$	−11.4637			−0.372127
$950$	8.12156			0.263498
$951$	23.7551	−	0.272310i	0.770313	−	0.00883026i
$952$	1.08640	+	5.55385i	0.0352106	+	0.180001i
$953$			33.0259i			1.06981i	0.844911	+	0.534907i	$0.179653\pi$
$953$			33.0259i			1.06981i	−0.844911	+	0.534907i	$0.820347\pi$
$954$	−38.8680	+	0.891222i	−1.25840	+	0.0288544i
$955$			0.727075i			0.0235276i
$956$			14.3110i			0.462851i
$957$	−0.120357	−	10.4994i	−0.00389059	−	0.339398i
$958$		−	26.2406i		−	0.847797i
$959$	−4.91590	−	25.1308i	−0.158743	−	0.811514i
$960$	0.0287488	+	2.50792i	0.000927863	+	0.0809427i
$961$	−1.35246			−0.0436278
$962$	−10.3789			−0.334629
$963$	−1.07573	−	46.9147i	−0.0346649	−	1.51181i
$964$		−	11.2737i		−	0.363100i
$965$	−19.5500			−0.629337
$966$	−2.10278	−	10.1318i	−0.0676558	−	0.325987i
$967$	55.9802			1.80020			0.900101	−	0.435682i	$-0.143493\pi$
$967$	55.9802			1.80020			0.900101	+	0.435682i	$0.143493\pi$
$968$			13.1269i			0.421915i
$969$	−10.3633	+	0.118797i	−0.332917	+	0.00381630i
$970$	−18.2680			−0.586551
$971$	9.10244			0.292111			0.146056	−	0.989276i	$-0.453342\pi$
$971$	9.10244			0.292111			0.146056	+	0.989276i	$0.453342\pi$
$972$	−0.892941	−	15.5629i	−0.0286411	−	0.499179i
$973$	−8.31309	−	42.4977i	−0.266506	−	1.36241i
$974$		−	21.4582i		−	0.687565i
$975$	−5.02812	+	0.0576384i	−0.161029	+	0.00184591i
$976$			4.45255i			0.142523i
$977$			57.8867i			1.85196i	0.377574	+	0.925979i	$0.376758\pi$
$977$			57.8867i			1.85196i	−0.377574	+	0.925979i	$0.623242\pi$
$978$	−12.0811	+	0.138489i	−0.386312	+	0.00442837i
$979$			62.9849i			2.01301i
$980$	9.38916	−	3.81943i	0.299926	−	0.122007i
$981$	21.6311	−	0.495990i	0.690629	−	0.0158357i
$982$	9.33758			0.297974
$983$	43.4963			1.38732			0.693659	−	0.720304i	$-0.255998\pi$
$983$	43.4963			1.38732			0.693659	+	0.720304i	$0.255998\pi$
$984$	−12.1482	+	0.139258i	−0.387272	+	0.00443938i
$985$		−	2.77474i		−	0.0884106i
$986$	2.63986			0.0840704
$987$	11.0056	+	53.0286i	0.350313	+	1.68792i
$988$	−2.79747			−0.0889995
$989$			1.64660i			0.0523587i
$990$	21.3324	−	0.489139i	0.677987	−	0.0155459i
$991$	−51.1240			−1.62401			−0.812004	−	0.583652i	$-0.801623\pi$
$991$	−51.1240			−1.62401			−0.812004	+	0.583652i	$0.801623\pi$
$992$	−5.68792			−0.180592
$993$	0.387434	+	33.7980i	0.0122948	+	1.07255i
$994$	19.1446	−	3.74494i	0.607231	−	0.118782i
$995$		−	14.1153i		−	0.447485i
$996$	0.298574	+	26.0463i	0.00946069	+	0.825309i
$997$			30.0800i			0.952642i	0.879272	+	0.476321i	$0.158030\pi$
$997$			30.0800i			0.952642i	−0.879272	+	0.476321i	$0.841970\pi$
$998$			32.2897i			1.02211i
$999$	1.85420	+	53.8984i	0.0586642	+	1.70527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.d.209.9	yes	12
3.2	odd	2		546.2.g.c.209.4	✓	12
7.6	odd	2		546.2.g.c.209.10	yes	12
21.20	even	2	inner	546.2.g.d.209.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.c.209.4	✓	12	3.2	odd	2
546.2.g.c.209.10	yes	12	7.6	odd	2
546.2.g.d.209.3	yes	12	21.20	even	2	inner
546.2.g.d.209.9	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.0198536 + 1.73194i) q^{3} -1.00000 q^{4} -1.44804 q^{5} +(-1.73194 + 0.0198536i) q^{6} +(-2.59654 + 0.507916i) q^{7} -1.00000i q^{8} +(-2.99921 + 0.0687703i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.0198536 + 1.73194i) q^{3} -1.00000 q^{4} -1.44804 q^{5} +(-1.73194 + 0.0198536i) q^{6} +(-2.59654 + 0.507916i) q^{7} -1.00000i q^{8} +(-2.99921 + 0.0687703i) q^{9} -1.44804i q^{10} -4.91192i q^{11} +(-0.0198536 - 1.73194i) q^{12} -1.00000i q^{13} +(-0.507916 - 2.59654i) q^{14} +(-0.0287488 - 2.50792i) q^{15} +1.00000 q^{16} +2.13894 q^{17} +(-0.0687703 - 2.99921i) q^{18} +2.79747i q^{19} +1.44804 q^{20} +(-0.931230 - 4.48696i) q^{21} +4.91192 q^{22} -2.25807i q^{23} +(1.73194 - 0.0198536i) q^{24} -2.90318 q^{25} +1.00000 q^{26} +(-0.178651 - 5.19308i) q^{27} +(2.59654 - 0.507916i) q^{28} -1.23419i q^{29} +(2.50792 - 0.0287488i) q^{30} +5.68792i q^{31} +1.00000i q^{32} +(8.50713 - 0.0975191i) q^{33} +2.13894i q^{34} +(3.75990 - 0.735484i) q^{35} +(2.99921 - 0.0687703i) q^{36} -10.3789 q^{37} -2.79747 q^{38} +(1.73194 - 0.0198536i) q^{39} +1.44804i q^{40} -7.01426 q^{41} +(4.48696 - 0.931230i) q^{42} -0.729206 q^{43} +4.91192i q^{44} +(4.34298 - 0.0995822i) q^{45} +2.25807 q^{46} -11.8184 q^{47} +(0.0198536 + 1.73194i) q^{48} +(6.48404 - 2.63765i) q^{49} -2.90318i q^{50} +(0.0424657 + 3.70452i) q^{51} +1.00000i q^{52} -12.9594i q^{53} +(5.19308 - 0.178651i) q^{54} +7.11266i q^{55} +(0.507916 + 2.59654i) q^{56} +(-4.84505 + 0.0555399i) q^{57} +1.23419 q^{58} +9.36446 q^{59} +(0.0287488 + 2.50792i) q^{60} +4.45255i q^{61} -5.68792 q^{62} +(7.75264 - 1.70191i) q^{63} -1.00000 q^{64} +1.44804i q^{65} +(0.0975191 + 8.50713i) q^{66} +1.73567 q^{67} -2.13894 q^{68} +(3.91083 - 0.0448307i) q^{69} +(0.735484 + 3.75990i) q^{70} +7.37313i q^{71} +(0.0687703 + 2.99921i) q^{72} -11.4637i q^{73} -10.3789i q^{74} +(-0.0576384 - 5.02812i) q^{75} -2.79747i q^{76} +(2.49484 + 12.7540i) q^{77} +(0.0198536 + 1.73194i) q^{78} +3.64979 q^{79} -1.44804 q^{80} +(8.99054 - 0.412513i) q^{81} -7.01426i q^{82} -15.0388 q^{83} +(0.931230 + 4.48696i) q^{84} -3.09728 q^{85} -0.729206i q^{86} +(2.13754 - 0.0245031i) q^{87} -4.91192 q^{88} -12.8229 q^{89} +(0.0995822 + 4.34298i) q^{90} +(0.507916 + 2.59654i) q^{91} +2.25807i q^{92} +(-9.85112 + 0.112926i) q^{93} -11.8184i q^{94} -4.05086i q^{95} +(-1.73194 + 0.0198536i) q^{96} -12.6157i q^{97} +(2.63765 + 6.48404i) q^{98} +(0.337794 + 14.7319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	\( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^4 - 4 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 - 2 * q^12 + 10 * q^14 + 4 * q^15 + 12 * q^16 + 12 * q^17 + 8 * q^18 + 4 * q^20 - 20 * q^21 - 2 * q^24 + 20 * q^25 + 12 * q^26 + 8 * q^27 + 8 * q^28 + 14 * q^30 + 46 * q^33 - 22 * q^35 - 4 * q^36 + 16 * q^37 - 8 * q^38 - 2 * q^39 + 28 * q^41 + 4 * q^42 - 8 * q^43 + 24 * q^46 - 68 * q^47 + 2 * q^48 + 26 * q^49 - 50 * q^51 + 16 * q^54 - 10 * q^56 - 28 * q^57 - 24 * q^58 + 8 * q^59 - 4 * q^60 + 16 * q^62 - 2 * q^63 - 12 * q^64 - 12 * q^66 + 8 * q^67 - 12 * q^68 - 24 * q^69 - 28 * q^70 - 8 * q^72 + 92 * q^75 - 8 * q^77 + 2 * q^78 + 36 * q^79 - 4 * q^80 + 16 * q^81 - 32 * q^83 + 20 * q^84 + 8 * q^87 - 48 * q^89 + 2 * q^90 - 10 * q^91 + 8 * q^93 + 2 * q^96 + 16 * q^98

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