LMFDB - Embedded newform 693.2.m.f.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.2
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.f.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43376 + 1.04169i) q^{2} +(0.352519 + 1.08494i) q^{4} +(0.477260 - 0.346750i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(0.470553 - 1.44821i) q^{8} +O(q^{10})$	\(q+(1.43376 + 1.04169i) q^{2} +(0.352519 + 1.08494i) q^{4} +(0.477260 - 0.346750i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(0.470553 - 1.44821i) q^{8} +1.04548 q^{10} +(2.19098 - 2.48990i) q^{11} +(1.24948 + 0.907802i) q^{13} +(0.547647 - 1.68548i) q^{14} +(4.02905 - 2.92728i) q^{16} +(5.78051 - 4.19979i) q^{17} +(-1.91300 + 5.88760i) q^{19} +(0.544446 + 0.395563i) q^{20} +(5.73503 - 1.28760i) q^{22} -3.76314 q^{23} +(-1.43754 + 4.42430i) q^{25} +(0.845811 + 2.60314i) q^{26} +(0.922906 - 0.670530i) q^{28} +(-0.187665 - 0.577574i) q^{29} +(5.55914 + 4.03895i) q^{31} +5.78051 q^{32} +12.6627 q^{34} +(-0.477260 - 0.346750i) q^{35} +(-2.38157 - 7.32972i) q^{37} +(-8.87581 + 6.44865i) q^{38} +(-0.277591 - 0.854338i) q^{40} +(-2.31233 + 7.11663i) q^{41} -10.9537 q^{43} +(3.47375 + 1.49935i) q^{44} +(-5.39544 - 3.92001i) q^{46} +(3.15419 - 9.70760i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-6.66983 + 4.84591i) q^{50} +(-0.544446 + 1.67563i) q^{52} +(5.69927 + 4.14076i) q^{53} +(0.182297 - 1.94805i) q^{55} -1.52274 q^{56} +(0.332585 - 1.02359i) q^{58} +(1.03640 + 3.18971i) q^{59} +(2.72674 - 1.98109i) q^{61} +(3.76314 + 11.5818i) q^{62} +(0.229756 + 0.166927i) q^{64} +0.911108 q^{65} -2.19138 q^{67} +(6.59426 + 4.79101i) q^{68} +(-0.323071 - 0.994311i) q^{70} +(-11.2801 + 8.19549i) q^{71} +(-0.800331 - 2.46317i) q^{73} +(4.22067 - 12.9899i) q^{74} -7.06206 q^{76} +(-3.04508 - 1.31433i) q^{77} +(3.77286 + 2.74114i) q^{79} +(0.907873 - 2.79415i) q^{80} +(-10.7286 + 7.79481i) q^{82} +(-2.83941 + 2.06295i) q^{83} +(1.30253 - 4.00878i) q^{85} +(-15.7050 - 11.4104i) q^{86} +(-2.57493 - 4.34464i) q^{88} -8.15095 q^{89} +(0.477260 - 1.46886i) q^{91} +(-1.32658 - 4.08279i) q^{92} +(14.6346 - 10.6327i) q^{94} +(1.12853 + 3.47325i) q^{95} +(3.88093 + 2.81966i) q^{97} -1.77222 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.43376	+	1.04169i	1.01382	+	0.736584i	0.965007	−	0.262224i	$-0.0844560\pi$
$2$	1.43376	+	1.04169i	1.01382	+	0.736584i	0.0488134	+	0.998808i	$0.484456\pi$
$3$		0			0
$3$		0			0
$4$	0.352519	+	1.08494i	0.176259	+	0.542470i
$5$	0.477260	−	0.346750i	0.213437	−	0.155071i	−0.475930	−	0.879483i	$-0.657889\pi$
$5$	0.477260	−	0.346750i	0.213437	−	0.155071i	0.689367	+	0.724412i	$0.257889\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.470553	−	1.44821i	0.166365	−	0.512020i
$9$		0			0
$10$	1.04548			0.330610
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$12$		0			0
$13$	1.24948	+	0.907802i	0.346544	+	0.251779i	0.747418	−	0.664354i	$-0.231293\pi$
$13$	1.24948	+	0.907802i	0.346544	+	0.251779i	−0.400874	+	0.916133i	$0.631293\pi$
$14$	0.547647	−	1.68548i	0.146365	−	0.450465i
$15$		0			0
$16$	4.02905	−	2.92728i	1.00726	−	0.731819i
$17$	5.78051	−	4.19979i	1.40198	−	1.01860i	0.407552	−	0.913182i	$-0.366382\pi$
$17$	5.78051	−	4.19979i	1.40198	−	1.01860i	0.994428	−	0.105417i	$-0.0336176\pi$
$18$		0			0
$19$	−1.91300	+	5.88760i	−0.438872	+	1.35071i	0.450195	+	0.892930i	$0.351354\pi$
$19$	−1.91300	+	5.88760i	−0.438872	+	1.35071i	−0.889067	+	0.457778i	$0.848646\pi$
$20$	0.544446	+	0.395563i	0.121742	+	0.0884506i
$21$		0			0
$22$	5.73503	−	1.28760i	1.22271	−	0.274516i
$23$	−3.76314			−0.784669			−0.392335	−	0.919823i	$-0.628332\pi$
$23$	−3.76314			−0.784669			−0.392335	+	0.919823i	$0.628332\pi$
$24$		0			0
$25$	−1.43754	+	4.42430i	−0.287509	+	0.884861i
$26$	0.845811	+	2.60314i	0.165877	+	0.510518i
$27$		0			0
$28$	0.922906	−	0.670530i	0.174413	−	0.126718i
$29$	−0.187665	−	0.577574i	−0.0348486	−	0.107253i	0.932119	−	0.362152i	$-0.117958\pi$
$29$	−0.187665	−	0.577574i	−0.0348486	−	0.107253i	−0.966968	+	0.254899i	$0.917958\pi$
$30$		0			0
$31$	5.55914	+	4.03895i	0.998451	+	0.725417i	0.961755	−	0.273909i	$-0.0883169\pi$
$31$	5.55914	+	4.03895i	0.998451	+	0.725417i	0.0366954	+	0.999326i	$0.488317\pi$
$32$	5.78051			1.02186
$33$		0			0
$34$	12.6627			2.17164
$35$	−0.477260	−	0.346750i	−0.0806717	−	0.0586114i
$36$		0			0
$37$	−2.38157	−	7.32972i	−0.391528	−	1.20500i	−0.931633	−	0.363401i	$-0.881615\pi$
$37$	−2.38157	−	7.32972i	−0.391528	−	1.20500i	0.540105	−	0.841598i	$-0.318385\pi$
$38$	−8.87581	+	6.44865i	−1.43985	+	1.04611i
$39$		0			0
$40$	−0.277591	−	0.854338i	−0.0438910	−	0.135083i
$41$	−2.31233	+	7.11663i	−0.361126	+	1.11143i	0.591246	+	0.806492i	$0.298636\pi$
$41$	−2.31233	+	7.11663i	−0.361126	+	1.11143i	−0.952372	+	0.304940i	$0.901364\pi$
$42$		0			0
$43$	−10.9537			−1.67043			−0.835214	−	0.549925i	$-0.814656\pi$
$43$	−10.9537			−1.67043			−0.835214	+	0.549925i	$0.814656\pi$
$44$	3.47375	+	1.49935i	0.523688	+	0.226036i
$45$		0			0
$46$	−5.39544	−	3.92001i	−0.795514	−	0.577975i
$47$	3.15419	−	9.70760i	0.460086	−	1.41600i	−0.404973	−	0.914328i	$-0.632719\pi$
$47$	3.15419	−	9.70760i	0.460086	−	1.41600i	0.865059	−	0.501670i	$-0.167281\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−6.66983	+	4.84591i	−0.943256	+	0.685316i
$51$		0			0
$52$	−0.544446	+	1.67563i	−0.0755010	+	0.232368i
$53$	5.69927	+	4.14076i	0.782855	+	0.568778i	0.905835	−	0.423631i	$-0.139245\pi$
$53$	5.69927	+	4.14076i	0.782855	+	0.568778i	−0.122979	+	0.992409i	$0.539245\pi$
$54$		0			0
$55$	0.182297	−	1.94805i	0.0245809	−	0.262675i
$56$	−1.52274			−0.203485
$57$		0			0
$58$	0.332585	−	1.02359i	0.0436705	−	0.134404i
$59$	1.03640	+	3.18971i	0.134928	+	0.415265i	0.995579	−	0.0939305i	$-0.0299431\pi$
$59$	1.03640	+	3.18971i	0.134928	+	0.415265i	−0.860651	+	0.509195i	$0.829943\pi$
$60$		0			0
$61$	2.72674	−	1.98109i	0.349124	−	0.253653i	−0.399378	−	0.916787i	$-0.630774\pi$
$61$	2.72674	−	1.98109i	0.349124	−	0.253653i	0.748501	+	0.663133i	$0.230774\pi$
$62$	3.76314	+	11.5818i	0.477920	+	1.47088i
$63$		0			0
$64$	0.229756	+	0.166927i	0.0287194	+	0.0208659i
$65$	0.911108			0.113009
$66$		0			0
$67$	−2.19138			−0.267719			−0.133860	−	0.991000i	$-0.542737\pi$
$67$	−2.19138			−0.267719			−0.133860	+	0.991000i	$0.542737\pi$
$68$	6.59426	+	4.79101i	0.799671	+	0.580995i
$69$		0			0
$70$	−0.323071	−	0.994311i	−0.0386144	−	0.118843i
$71$	−11.2801	+	8.19549i	−1.33870	+	0.972625i	−0.339213	+	0.940710i	$0.610161\pi$
$71$	−11.2801	+	8.19549i	−1.33870	+	0.972625i	−0.999491	+	0.0319157i	$0.989839\pi$
$72$		0			0
$73$	−0.800331	−	2.46317i	−0.0936717	−	0.288292i	0.893234	−	0.449593i	$-0.148431\pi$
$73$	−0.800331	−	2.46317i	−0.0936717	−	0.288292i	−0.986905	+	0.161301i	$0.948431\pi$
$74$	4.22067	−	12.9899i	0.490643	−	1.51005i
$75$		0			0
$76$	−7.06206			−0.810074
$77$	−3.04508	−	1.31433i	−0.347020	−	0.149782i
$78$		0			0
$79$	3.77286	+	2.74114i	0.424480	+	0.308403i	0.779438	−	0.626479i	$-0.215505\pi$
$79$	3.77286	+	2.74114i	0.424480	+	0.308403i	−0.354958	+	0.934882i	$0.615505\pi$
$80$	0.907873	−	2.79415i	0.101503	−	0.312395i
$81$		0			0
$82$	−10.7286	+	7.79481i	−1.18478	+	0.860792i
$83$	−2.83941	+	2.06295i	−0.311666	+	0.226438i	−0.732611	−	0.680648i	$-0.761698\pi$
$83$	−2.83941	+	2.06295i	−0.311666	+	0.226438i	0.420945	+	0.907086i	$0.361698\pi$
$84$		0			0
$85$	1.30253	−	4.00878i	0.141279	−	0.434814i
$86$	−15.7050	−	11.4104i	−1.69351	−	1.23041i
$87$		0			0
$88$	−2.57493	−	4.34464i	−0.274488	−	0.463140i
$89$	−8.15095			−0.863999			−0.432000	−	0.901874i	$-0.642192\pi$
$89$	−8.15095			−0.863999			−0.432000	+	0.901874i	$0.642192\pi$
$90$		0			0
$91$	0.477260	−	1.46886i	0.0500304	−	0.153978i
$92$	−1.32658	−	4.08279i	−0.138305	−	0.425660i
$93$		0			0
$94$	14.6346	−	10.6327i	1.50945	−	1.09668i
$95$	1.12853	+	3.47325i	0.115784	+	0.356348i
$96$		0			0
$97$	3.88093	+	2.81966i	0.394049	+	0.286293i	0.767113	−	0.641512i	$-0.221693\pi$
$97$	3.88093	+	2.81966i	0.394049	+	0.286293i	−0.373064	+	0.927806i	$0.621693\pi$
$98$	−1.77222			−0.179022
$99$		0			0
$100$	−5.30687			−0.530687
$101$	−1.15419	−	0.838567i	−0.114846	−	0.0834406i	0.528880	−	0.848697i	$-0.322612\pi$
$101$	−1.15419	−	0.838567i	−0.114846	−	0.0834406i	−0.643726	+	0.765256i	$0.722612\pi$
$102$		0			0
$103$	5.44403	+	16.7550i	0.536416	+	1.65092i	0.740569	+	0.671980i	$0.234556\pi$
$103$	5.44403	+	16.7550i	0.536416	+	1.65092i	−0.204153	+	0.978939i	$0.565444\pi$
$104$	1.90264	−	1.38235i	0.186569	−	0.135550i
$105$		0			0
$106$	3.85800	+	11.8737i	0.374722	+	1.15328i
$107$	2.22494	−	6.84765i	0.215093	−	0.661987i	−0.784054	−	0.620692i	$-0.786852\pi$
$107$	2.22494	−	6.84765i	0.215093	−	0.661987i	0.999147	−	0.0412951i	$-0.0131484\pi$
$108$		0			0
$109$	−8.88678			−0.851199			−0.425599	−	0.904912i	$-0.639937\pi$
$109$	−8.88678			−0.851199			−0.425599	+	0.904912i	$0.639937\pi$
$110$	2.29063	−	2.60314i	0.218403	−	0.248200i
$111$		0			0
$112$	−4.02905	−	2.92728i	−0.380710	−	0.276602i
$113$	2.41300	−	7.42644i	0.226996	−	0.698621i	−0.771087	−	0.636730i	$-0.780287\pi$
$113$	2.41300	−	7.42644i	0.226996	−	0.698621i	0.998083	−	0.0618913i	$-0.0197132\pi$
$114$		0			0
$115$	−1.79600	+	1.30487i	−0.167478	+	0.121680i
$116$	0.560478	−	0.407211i	0.0520391	−	0.0378086i
$117$		0			0
$118$	−1.83673	+	5.65287i	−0.169085	+	0.520389i
$119$	−5.78051	−	4.19979i	−0.529899	−	0.384994i
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	5.97317			0.540785
$123$		0			0
$124$	−2.42232	+	7.45514i	−0.217531	+	0.669491i
$125$	1.75953	+	5.41527i	0.157377	+	0.484357i
$126$		0			0
$127$	−6.67589	+	4.85032i	−0.592390	+	0.430396i	−0.843170	−	0.537648i	$-0.819313\pi$
$127$	−6.67589	+	4.85032i	−0.592390	+	0.430396i	0.250780	+	0.968044i	$0.419313\pi$
$128$	−3.41703	−	10.5165i	−0.302025	−	0.929538i
$129$		0			0
$130$	1.30631	+	0.949089i	0.114571	+	0.0832406i
$131$	−12.1162			−1.05860			−0.529299	−	0.848435i	$-0.677545\pi$
$131$	−12.1162			−1.05860			−0.529299	+	0.848435i	$0.677545\pi$
$132$		0			0
$133$	6.19059			0.536792
$134$	−3.14191	−	2.28273i	−0.271419	−	0.197198i
$135$		0			0
$136$	−3.36215	−	10.3476i	−0.288302	−	0.887302i
$137$	−14.1212	+	10.2597i	−1.20646	+	0.876541i	−0.994904	−	0.100826i	$-0.967852\pi$
$137$	−14.1212	+	10.2597i	−1.20646	+	0.876541i	−0.211551	+	0.977367i	$0.567852\pi$
$138$		0			0
$139$	4.56182	+	14.0398i	0.386928	+	1.19084i	0.935072	+	0.354459i	$0.115335\pi$
$139$	4.56182	+	14.0398i	0.386928	+	1.19084i	−0.548143	+	0.836384i	$0.684665\pi$
$140$	0.207960	−	0.640034i	0.0175758	−	0.0540928i
$141$		0			0
$142$	−24.7101			−2.07362
$143$	4.99793	−	1.12211i	0.417948	−	0.0938352i
$144$		0			0
$145$	−0.289839	−	0.210580i	−0.0240698	−	0.0174877i
$146$	1.41837	−	4.36528i	0.117385	−	0.361273i
$147$		0			0
$148$	7.11276	−	5.16773i	0.584666	−	0.424784i
$149$	10.1336	−	7.36248i	0.830175	−	0.603158i	−0.0894336	−	0.995993i	$-0.528506\pi$
$149$	10.1336	−	7.36248i	0.830175	−	0.603158i	0.919609	+	0.392835i	$0.128506\pi$
$150$		0			0
$151$	0.101534	−	0.312491i	0.00826275	−	0.0254301i	−0.946840	−	0.321704i	$-0.895744\pi$
$151$	0.101534	−	0.312491i	0.00826275	−	0.0254301i	0.955103	+	0.296274i	$0.0957443\pi$
$152$	7.62632	+	5.54085i	0.618577	+	0.449422i
$153$		0			0
$154$	−2.99680	−	5.05645i	−0.241489	−	0.407461i
$155$	4.05366			0.325598
$156$		0			0
$157$	−0.828439	+	2.54967i	−0.0661167	+	0.203486i	−0.978657	−	0.205501i	$-0.934118\pi$
$157$	−0.828439	+	2.54967i	−0.0661167	+	0.203486i	0.912540	+	0.408987i	$0.134118\pi$
$158$	2.55396	+	7.86028i	0.203182	+	0.625330i
$159$		0			0
$160$	2.75881	−	2.00439i	0.218103	−	0.158461i
$161$	1.16287	+	3.57896i	0.0916474	+	0.282062i
$162$		0			0
$163$	0.721375	+	0.524109i	0.0565024	+	0.0410514i	0.615678	−	0.787998i	$-0.288882\pi$
$163$	0.721375	+	0.524109i	0.0565024	+	0.0410514i	−0.559176	+	0.829049i	$0.688882\pi$
$164$	−8.53627			−0.666570
$165$		0			0
$166$	−6.21997			−0.482764
$167$	9.35307	+	6.79540i	0.723762	+	0.525844i	0.887584	−	0.460646i	$-0.152382\pi$
$167$	9.35307	+	6.79540i	0.723762	+	0.525844i	−0.163822	+	0.986490i	$0.552382\pi$
$168$		0			0
$169$	−3.28012	−	10.0952i	−0.252317	−	0.776551i
$170$	6.04341	−	4.39080i	0.463509	−	0.336759i
$171$		0			0
$172$	−3.86139	−	11.8841i	−0.294428	−	0.906158i
$173$	−2.77784	+	8.54930i	−0.211195	+	0.649991i	0.788207	+	0.615410i	$0.211010\pi$
$173$	−2.77784	+	8.54930i	−0.211195	+	0.649991i	−0.999402	+	0.0345809i	$0.988990\pi$
$174$		0			0
$175$	4.65199			0.351657
$176$	1.53896	−	16.4455i	0.116004	−	1.23963i
$177$		0			0
$178$	−11.6865	−	8.49074i	−0.875940	−	0.636408i
$179$	1.89919	−	5.84510i	0.141952	−	0.436883i	−0.854655	−	0.519197i	$-0.826231\pi$
$179$	1.89919	−	5.84510i	0.141952	−	0.436883i	0.996606	+	0.0823141i	$0.0262311\pi$
$180$		0			0
$181$	−12.1079	+	8.79692i	−0.899975	+	0.653870i	−0.938459	−	0.345389i	$-0.887747\pi$
$181$	−12.1079	+	8.79692i	−0.899975	+	0.653870i	0.0384849	+	0.999259i	$0.487747\pi$
$182$	2.21436	−	1.60883i	0.164139	−	0.119254i
$183$		0			0
$184$	−1.77076	+	5.44983i	−0.130542	+	0.401767i
$185$	−3.67821	−	2.67237i	−0.270427	−	0.196477i
$186$		0			0
$187$	2.20796	−	23.5946i	0.161462	−	1.72540i
$188$	11.6441			0.849231
$189$		0			0
$190$	−2.00000	+	6.15537i	−0.145095	+	0.446557i
$191$	−3.05108	−	9.39026i	−0.220768	−	0.679456i	−0.998694	−	0.0510986i	$-0.983728\pi$
$191$	−3.05108	−	9.39026i	−0.220768	−	0.679456i	0.777925	−	0.628357i	$-0.216272\pi$
$192$		0			0
$193$	5.00064	−	3.63318i	0.359954	−	0.261522i	−0.393079	−	0.919505i	$-0.628590\pi$
$193$	5.00064	−	3.63318i	0.359954	−	0.261522i	0.753033	+	0.657983i	$0.228590\pi$
$194$	2.62711	+	8.08543i	0.188616	+	0.580500i
$195$		0			0
$196$	−0.922906	−	0.670530i	−0.0659218	−	0.0478950i
$197$	19.0720			1.35882			0.679412	−	0.733757i	$-0.262235\pi$
$197$	19.0720			1.35882			0.679412	+	0.733757i	$0.262235\pi$
$198$		0			0
$199$	−11.8479			−0.839878			−0.419939	−	0.907552i	$-0.637948\pi$
$199$	−11.8479			−0.839878			−0.419939	+	0.907552i	$0.637948\pi$
$200$	5.73089	+	4.16373i	0.405235	+	0.294420i
$201$		0			0
$202$	−0.781304	−	2.40461i	−0.0549723	−	0.169187i
$203$	−0.491314	+	0.356961i	−0.0344835	+	0.0250537i
$204$		0			0
$205$	1.36411	+	4.19829i	0.0952733	+	0.293221i
$206$	−9.64803	+	29.6936i	−0.672210	+	2.06885i
$207$		0			0
$208$	7.69162			0.533318
$209$	10.4682	+	17.6628i	0.724099	+	1.22176i
$210$		0			0
$211$	16.9740	+	12.3324i	1.16854	+	0.848994i	0.990833	−	0.135089i	$-0.0431322\pi$
$211$	16.9740	+	12.3324i	1.16854	+	0.848994i	0.177707	+	0.984084i	$0.443132\pi$
$212$	−2.48338	+	7.64307i	−0.170560	+	0.524928i
$213$		0			0
$214$	10.3231	−	7.50019i	0.705674	−	0.512702i
$215$	−5.22778	+	3.79820i	−0.356531	+	0.259035i
$216$		0			0
$217$	2.12340	−	6.53516i	0.144146	−	0.443636i
$218$	−12.7415	−	9.25724i	−0.862963	−	0.626979i
$219$		0			0
$220$	2.17778	−	0.488943i	0.146826	−	0.0329645i
$221$	11.0352			0.742310
$222$		0			0
$223$	1.04714	−	3.22275i	0.0701214	−	0.215811i	−0.909855	−	0.414927i	$-0.863807\pi$
$223$	1.04714	−	3.22275i	0.0701214	−	0.215811i	0.979976	+	0.199116i	$0.0638070\pi$
$224$	−1.78628	−	5.49760i	−0.119351	−	0.367324i
$225$		0			0
$226$	11.1957	−	8.13414i	0.744725	−	0.541075i
$227$	−5.99409	−	18.4479i	−0.397841	−	1.22443i	−0.926726	−	0.375737i	$-0.877390\pi$
$227$	−5.99409	−	18.4479i	−0.397841	−	1.22443i	0.528885	−	0.848693i	$-0.322610\pi$
$228$		0			0
$229$	7.98018	+	5.79794i	0.527345	+	0.383139i	0.819364	−	0.573274i	$-0.194327\pi$
$229$	7.98018	+	5.79794i	0.527345	+	0.383139i	−0.292019	+	0.956413i	$0.594327\pi$
$230$	−3.93429			−0.259419
$231$		0			0
$232$	−0.924756			−0.0607132
$233$	5.76521	+	4.18867i	0.377691	+	0.274409i	0.760393	−	0.649463i	$-0.225006\pi$
$233$	5.76521	+	4.18867i	0.377691	+	0.274409i	−0.382702	+	0.923872i	$0.625006\pi$
$234$		0			0
$235$	−1.86074	−	5.72676i	−0.121381	−	0.373573i
$236$	−3.09529	+	2.24886i	−0.201486	+	0.146388i
$237$		0			0
$238$	−3.91300	−	12.0430i	−0.253642	−	0.780630i
$239$	−6.88781	+	21.1985i	−0.445535	+	1.37122i	0.436360	+	0.899772i	$0.356267\pi$
$239$	−6.88781	+	21.1985i	−0.445535	+	1.37122i	−0.881895	+	0.471445i	$0.843733\pi$
$240$		0			0
$241$	14.8753			0.958199			0.479100	−	0.877761i	$-0.340963\pi$
$241$	14.8753			0.958199			0.479100	+	0.877761i	$0.340963\pi$
$242$	9.35938	−	17.1008i	0.601644	−	1.09928i
$243$		0			0
$244$	3.11060	+	2.25998i	0.199136	+	0.144680i
$245$	−0.182297	+	0.561053i	−0.0116465	+	0.0358443i
$246$		0			0
$247$	−7.73503	+	5.61983i	−0.492168	+	0.357581i
$248$	8.46512	−	6.15027i	0.537536	−	0.390543i
$249$		0			0
$250$	−3.11828	+	9.59707i	−0.197217	+	0.606972i
$251$	−20.9724	−	15.2373i	−1.32376	−	0.961771i	−0.999877	−	0.0156760i	$-0.995010\pi$
$251$	−20.9724	−	15.2373i	−1.32376	−	0.961771i	−0.323888	−	0.946096i	$-0.604990\pi$
$252$		0			0
$253$	−8.24498	+	9.36984i	−0.518357	+	0.589077i
$254$	−14.6241			−0.917600
$255$		0			0
$256$	6.23125	−	19.1778i	0.389453	−	1.19861i
$257$	−0.269300	−	0.828821i	−0.0167985	−	0.0517004i	0.942306	−	0.334753i	$-0.108653\pi$
$257$	−0.269300	−	0.828821i	−0.0167985	−	0.0517004i	−0.959104	+	0.283053i	$0.908653\pi$
$258$		0			0
$259$	−6.23503	+	4.53002i	−0.387426	+	0.281482i
$260$	0.321183	+	0.988498i	0.0199189	+	0.0613041i
$261$		0			0
$262$	−17.3717	−	12.6213i	−1.07323	−	0.779746i
$263$	−26.8873			−1.65794			−0.828970	−	0.559293i	$-0.811073\pi$
$263$	−26.8873			−1.65794			−0.828970	+	0.559293i	$0.811073\pi$
$264$		0			0
$265$	4.15584			0.255291
$266$	8.87581	+	6.44865i	0.544211	+	0.395392i
$267$		0			0
$268$	−0.772501	−	2.37751i	−0.0471880	−	0.145230i
$269$	−0.803010	+	0.583421i	−0.0489604	+	0.0355718i	−0.611996	−	0.790861i	$-0.709633\pi$
$269$	−0.803010	+	0.583421i	−0.0489604	+	0.0355718i	0.563036	+	0.826432i	$0.309633\pi$
$270$		0			0
$271$	8.30174	+	25.5501i	0.504295	+	1.55206i	0.801953	+	0.597388i	$0.203795\pi$
$271$	8.30174	+	25.5501i	0.504295	+	1.55206i	−0.297658	+	0.954673i	$0.596205\pi$
$272$	10.9960	−	33.8423i	0.666733	−	2.05199i
$273$		0			0
$274$	−30.9337			−1.86878
$275$	7.86643	+	13.2729i	0.474364	+	0.800387i
$276$		0			0
$277$	22.3533	+	16.2406i	1.34308	+	0.975805i	0.999325	+	0.0367459i	$0.0116992\pi$
$277$	22.3533	+	16.2406i	1.34308	+	0.975805i	0.343756	+	0.939059i	$0.388301\pi$
$278$	−8.08456	+	24.8817i	−0.484880	+	1.49231i
$279$		0			0
$280$	−0.726743	+	0.528010i	−0.0434312	+	0.0315546i
$281$	19.2884	−	14.0138i	1.15065	−	0.835996i	0.162083	−	0.986777i	$-0.448179\pi$
$281$	19.2884	−	14.0138i	1.15065	−	0.835996i	0.988567	+	0.150781i	$0.0481788\pi$
$282$		0			0
$283$	2.70308	−	8.31922i	0.160681	−	0.494527i	−0.838011	−	0.545654i	$-0.816281\pi$
$283$	2.70308	−	8.31922i	0.160681	−	0.494527i	0.998692	+	0.0511272i	$0.0162814\pi$
$284$	−12.8681	−	9.34920i	−0.763579	−	0.554773i
$285$		0			0
$286$	8.33471	+	3.59745i	0.492842	+	0.212722i
$287$	7.48287			0.441700
$288$		0			0
$289$	10.5228	−	32.3859i	0.618990	−	1.90505i
$290$	−0.196200	−	0.603842i	−0.0115213	−	0.0354588i
$291$		0			0
$292$	2.39026	−	1.73662i	0.139879	−	0.101628i
$293$	6.06451	+	18.6646i	0.354292	+	1.09040i	0.956419	+	0.291999i	$0.0943203\pi$
$293$	6.06451	+	18.6646i	0.354292	+	1.09040i	−0.602126	+	0.798401i	$0.705680\pi$
$294$		0			0
$295$	1.60066	+	1.16295i	0.0931942	+	0.0677095i
$296$	−11.7356			−0.682120
$297$		0			0
$298$	22.1985			1.28592
$299$	−4.70198	−	3.41619i	−0.271923	−	0.197563i
$300$		0			0
$301$	3.38489	+	10.4176i	0.195102	+	0.600461i
$302$	0.471093	−	0.342269i	0.0271084	−	0.0196954i
$303$		0			0
$304$	9.52707	+	29.3213i	0.546415	+	1.68169i
$305$	0.614421	−	1.89099i	0.0351817	−	0.108278i
$306$		0			0
$307$	−17.0835			−0.975009			−0.487504	−	0.873121i	$-0.662093\pi$
$307$	−17.0835			−0.975009			−0.487504	+	0.873121i	$0.662093\pi$
$308$	0.352519	−	3.76706i	0.0200866	−	0.214648i
$309$		0			0
$310$	5.81197	+	4.22264i	0.330098	+	0.239830i
$311$	2.23528	−	6.87948i	0.126751	−	0.390099i	−0.867465	−	0.497498i	$-0.834252\pi$
$311$	2.23528	−	6.87948i	0.126751	−	0.390099i	0.994216	+	0.107399i	$0.0342521\pi$
$312$		0			0
$313$	−11.1470	+	8.09877i	−0.630065	+	0.457769i	−0.856423	−	0.516275i	$-0.827318\pi$
$313$	−11.1470	+	8.09877i	−0.630065	+	0.457769i	0.226357	+	0.974044i	$0.427318\pi$
$314$	−3.84374	+	2.79264i	−0.216915	+	0.157598i
$315$		0			0
$316$	−1.64398	+	5.05964i	−0.0924808	+	0.284627i
$317$	−5.62775	−	4.08880i	−0.316086	−	0.229650i	0.418417	−	0.908255i	$-0.362585\pi$
$317$	−5.62775	−	4.08880i	−0.316086	−	0.229650i	−0.734504	+	0.678605i	$0.762585\pi$
$318$		0			0
$319$	−1.84927	−	0.798188i	−0.103539	−	0.0446900i
$320$	0.167535			0.00936550
$321$		0			0
$322$	−2.06087	+	6.34272i	−0.114848	+	0.353466i
$323$	13.6686	+	42.0675i	0.760540	+	2.34070i
$324$		0			0
$325$	−5.81258	+	4.22309i	−0.322424	+	0.234255i
$326$	0.488319	+	1.50289i	0.0270455	+	0.0832375i
$327$		0			0
$328$	9.21832	+	6.69750i	0.508997	+	0.369808i
$329$	−10.2072			−0.562739
$330$		0			0
$331$	−29.6698			−1.63080			−0.815401	−	0.578896i	$-0.803484\pi$
$331$	−29.6698			−1.63080			−0.815401	+	0.578896i	$0.803484\pi$
$332$	−3.23912	−	2.35336i	−0.177770	−	0.129157i
$333$		0			0
$334$	6.33136	+	19.4859i	0.346437	+	1.06622i
$335$	−1.04586	+	0.759860i	−0.0571413	+	0.0415156i
$336$		0			0
$337$	6.04791	+	18.6135i	0.329451	+	1.01394i	0.969391	+	0.245520i	$0.0789588\pi$
$337$	6.04791	+	18.6135i	0.329451	+	1.01394i	−0.639941	+	0.768424i	$0.721041\pi$
$338$	5.81310	−	17.8909i	0.316191	−	0.973136i
$339$		0			0
$340$	4.80846			0.260775
$341$	22.2366	−	4.99242i	1.20418	−	0.270355i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−5.15431	+	15.8633i	−0.277902	+	0.855293i
$345$		0			0
$346$	−12.8884	+	9.36399i	−0.692886	+	0.503411i
$347$	−5.25201	+	3.81581i	−0.281943	+	0.204843i	−0.719764	−	0.694218i	$-0.755750\pi$
$347$	−5.25201	+	3.81581i	−0.281943	+	0.204843i	0.437822	+	0.899062i	$0.355750\pi$
$348$		0			0
$349$	2.43495	−	7.49400i	0.130340	−	0.401144i	−0.864496	−	0.502639i	$-0.832362\pi$
$349$	2.43495	−	7.49400i	0.130340	−	0.401144i	0.994836	+	0.101495i	$0.0323625\pi$
$350$	6.66983	+	4.84591i	0.356517	+	0.259025i
$351$		0			0
$352$	12.6650	−	14.3929i	0.675047	−	0.767144i
$353$	5.34594			0.284536			0.142268	−	0.989828i	$-0.454561\pi$
$353$	5.34594			0.284536			0.142268	+	0.989828i	$0.454561\pi$
$354$		0			0
$355$	−2.54177	+	7.82276i	−0.134903	+	0.415189i
$356$	−2.87336	−	8.84330i	−0.152288	−	0.468694i
$357$		0			0
$358$	8.81173	−	6.40210i	0.465715	−	0.338361i
$359$	5.51643	+	16.9778i	0.291146	+	0.896056i	0.984489	+	0.175448i	$0.0561372\pi$
$359$	5.51643	+	16.9778i	0.291146	+	0.896056i	−0.693343	+	0.720608i	$0.743863\pi$
$360$		0			0
$361$	−15.6329	−	11.3580i	−0.822786	−	0.597789i
$362$	−26.5235			−1.39404
$363$		0			0
$364$	1.76186			0.0923467
$365$	−1.23607	−	0.898056i	−0.0646988	−	0.0470064i
$366$		0			0
$367$	−9.25065	−	28.4706i	−0.482880	−	1.48615i	−0.835028	−	0.550207i	$-0.814549\pi$
$367$	−9.25065	−	28.4706i	−0.482880	−	1.48615i	0.352148	−	0.935944i	$-0.385451\pi$
$368$	−15.1619	+	11.0158i	−0.790368	+	0.574236i
$369$		0			0
$370$	−2.48988	−	7.66308i	−0.129443	−	0.398384i
$371$	2.17693	−	6.69990i	0.113021	−	0.347841i
$372$		0			0
$373$	23.4915			1.21635			0.608173	−	0.793805i	$-0.291903\pi$
$373$	23.4915			1.21635			0.608173	+	0.793805i	$0.291903\pi$
$374$	27.7438	−	31.5289i	1.43460	−	1.63032i
$375$		0			0
$376$	−12.5744	−	9.13587i	−0.648477	−	0.471146i
$377$	0.289839	−	0.892032i	0.0149275	−	0.0459420i
$378$		0			0
$379$	25.4462	−	18.4877i	1.30708	−	0.949650i	0.307084	−	0.951683i	$-0.400647\pi$
$379$	25.4462	−	18.4877i	1.30708	−	0.949650i	0.999998	+	0.00203230i	$0.000646901\pi$
$380$	−3.37044	+	2.44877i	−0.172900	+	0.125619i
$381$		0			0
$382$	5.40720	−	16.6416i	0.276656	−	0.851460i
$383$	−4.55274	−	3.30776i	−0.232634	−	0.169018i	0.465361	−	0.885121i	$-0.345924\pi$
$383$	−4.55274	−	3.30776i	−0.232634	−	0.169018i	−0.697995	+	0.716102i	$0.745924\pi$
$384$		0			0
$385$	−1.90904	+	0.428606i	−0.0972937	+	0.0218438i
$386$	10.9543			0.557561
$387$		0			0
$388$	−1.69107	+	5.20456i	−0.0858508	+	0.264222i
$389$	−8.06758	−	24.8295i	−0.409043	−	1.25890i	−0.917472	−	0.397800i	$-0.869774\pi$
$389$	−8.06758	−	24.8295i	−0.409043	−	1.25890i	0.508430	−	0.861104i	$-0.330226\pi$
$390$		0			0
$391$	−21.7529	+	15.8044i	−1.10009	+	0.799263i
$392$	0.470553	+	1.44821i	0.0237665	+	0.0731457i
$393$		0			0
$394$	27.3447	+	19.8671i	1.37760	+	1.00089i
$395$	2.75113			0.138424
$396$		0			0
$397$	10.3828			0.521096			0.260548	−	0.965461i	$-0.416097\pi$
$397$	10.3828			0.521096			0.260548	+	0.965461i	$0.416097\pi$
$398$	−16.9871	−	12.3418i	−0.851485	−	0.618640i
$399$		0			0
$400$	7.15923	+	22.0338i	0.357961	+	1.10169i
$401$	2.98427	−	2.16820i	0.149027	−	0.108275i	−0.510773	−	0.859716i	$-0.670641\pi$
$401$	2.98427	−	2.16820i	0.149027	−	0.108275i	0.659801	+	0.751441i	$0.270641\pi$
$402$		0			0
$403$	3.27948	+	10.0932i	0.163363	+	0.502778i
$404$	0.502923	−	1.54784i	0.0250213	−	0.0770078i
$405$		0			0
$406$	−1.07627			−0.0534142
$407$	−23.4682	−	10.1294i	−1.16328	−	0.502097i
$408$		0			0
$409$	−0.873919	−	0.634940i	−0.0432125	−	0.0313957i	0.565969	−	0.824426i	$-0.308502\pi$
$409$	−0.873919	−	0.634940i	−0.0432125	−	0.0313957i	−0.609182	+	0.793031i	$0.708502\pi$
$410$	−2.41750	+	7.44030i	−0.119392	+	0.367450i
$411$		0			0
$412$	−16.2591	+	11.8129i	−0.801026	+	0.581979i
$413$	2.71333	−	1.97135i	0.133514	−	0.0970037i
$414$		0			0
$415$	−0.639809	+	1.96913i	−0.0314070	+	0.0966607i
$416$	7.22265	+	5.24756i	0.354120	+	0.257283i
$417$		0			0
$418$	−3.39026	+	36.2287i	−0.165823	+	1.77201i
$419$	−10.0766			−0.492273			−0.246136	−	0.969235i	$-0.579161\pi$
$419$	−10.0766			−0.492273			−0.246136	+	0.969235i	$0.579161\pi$
$420$		0			0
$421$	3.70069	−	11.3895i	0.180360	−	0.555092i	−0.819477	−	0.573112i	$-0.805736\pi$
$421$	3.70069	−	11.3895i	0.180360	−	0.555092i	0.999838	+	0.0180196i	$0.00573612\pi$
$422$	11.4902	+	35.3632i	0.559335	+	1.72145i
$423$		0			0
$424$	8.67851	−	6.30531i	0.421466	−	0.306213i
$425$	10.2714	+	31.6121i	0.498236	+	1.53341i
$426$		0			0
$427$	−2.72674	−	1.98109i	−0.131956	−	0.0958719i
$428$	8.21363			0.397021
$429$		0			0
$430$	−11.4519			−0.552260
$431$	−0.443784	−	0.322428i	−0.0213763	−	0.0155308i	0.577046	−	0.816712i	$-0.304205\pi$
$431$	−0.443784	−	0.322428i	−0.0213763	−	0.0155308i	−0.598422	+	0.801181i	$0.704205\pi$
$432$		0			0
$433$	6.05298	+	18.6292i	0.290888	+	0.895260i	0.984572	+	0.174981i	$0.0559864\pi$
$433$	6.05298	+	18.6292i	0.290888	+	0.895260i	−0.693684	+	0.720279i	$0.744014\pi$
$434$	9.85203	−	7.15792i	0.472913	−	0.343591i
$435$		0			0
$436$	−3.13275	−	9.64162i	−0.150032	−	0.461750i
$437$	7.19888	−	22.1559i	0.344369	−	1.05986i
$438$		0			0
$439$	37.4069			1.78533			0.892667	−	0.450716i	$-0.148831\pi$
$439$	37.4069			1.78533			0.892667	+	0.450716i	$0.148831\pi$
$440$	−2.73541	−	1.18067i	−0.130406	−	0.0562860i
$441$		0			0
$442$	15.8219	+	11.4953i	0.752569	+	0.546773i
$443$	−6.62774	+	20.3981i	−0.314893	+	0.969142i	0.660905	+	0.750469i	$0.270173\pi$
$443$	−6.62774	+	20.3981i	−0.314893	+	0.969142i	−0.975798	+	0.218672i	$0.929827\pi$
$444$		0			0
$445$	−3.89012	+	2.82634i	−0.184410	+	0.133981i
$446$	4.85844	−	3.52986i	0.230054	−	0.167144i
$447$		0			0
$448$	0.0877588	−	0.270094i	0.00414621	−	0.0127607i
$449$	5.17693	+	3.76126i	0.244314	+	0.177505i	0.703203	−	0.710989i	$-0.251752\pi$
$449$	5.17693	+	3.76126i	0.244314	+	0.177505i	−0.458889	+	0.888494i	$0.651752\pi$
$450$		0			0
$451$	12.6534	+	21.3499i	0.595826	+	1.00533i
$452$	8.90787			0.418991
$453$		0			0
$454$	10.6229	−	32.6938i	0.498555	−	1.53440i
$455$	−0.281548	−	0.866516i	−0.0131992	−	0.0406229i
$456$		0			0
$457$	29.8875	−	21.7145i	1.39808	−	1.01576i	0.403155	−	0.915132i	$-0.367914\pi$
$457$	29.8875	−	21.7145i	1.39808	−	1.01576i	0.994924	−	0.100632i	$-0.0320865\pi$
$458$	5.40202	+	16.6257i	0.252420	+	0.776868i
$459$		0			0
$460$	−2.04883	−	1.48856i	−0.0955270	−	0.0694045i
$461$	−7.39825			−0.344571			−0.172285	−	0.985047i	$-0.555115\pi$
$461$	−7.39825			−0.344571			−0.172285	+	0.985047i	$0.555115\pi$
$462$		0			0
$463$	−14.3717			−0.667910			−0.333955	−	0.942589i	$-0.608383\pi$
$463$	−14.3717			−0.667910			−0.333955	+	0.942589i	$0.608383\pi$
$464$	−2.44683	−	1.77773i	−0.113591	−	0.0825290i
$465$		0			0
$466$	3.90264	+	12.0111i	0.180786	+	0.556403i
$467$	29.2562	−	21.2559i	1.35382	−	0.983604i	0.355004	−	0.934865i	$-0.384480\pi$
$467$	29.2562	−	21.2559i	1.35382	−	0.983604i	0.998812	−	0.0487394i	$-0.0155204\pi$
$468$		0			0
$469$	0.677173	+	2.08412i	0.0312689	+	0.0962359i
$470$	3.29764	−	10.1491i	0.152109	−	0.468143i
$471$		0			0
$472$	5.10705			0.235071
$473$	−23.9994	+	27.2737i	−1.10350	+	1.25404i
$474$		0			0
$475$	−23.2985	−	16.9274i	−1.06901	−	0.776680i
$476$	2.51878	−	7.75202i	0.115448	−	0.355313i
$477$		0			0
$478$	−31.9577	+	23.2186i	−1.46171	+	1.06199i
$479$	12.9647	−	9.41941i	0.592372	−	0.430384i	−0.250791	−	0.968041i	$-0.580691\pi$
$479$	12.9647	−	9.41941i	0.592372	−	0.430384i	0.843163	+	0.537658i	$0.180691\pi$
$480$		0			0
$481$	3.67821	−	11.3204i	0.167712	−	0.516164i
$482$	21.3275	+	15.4953i	0.971442	+	0.705794i
$483$		0			0
$484$	11.3442	−	5.36424i	0.515644	−	0.243829i
$485$	2.82993			0.128501
$486$		0			0
$487$	0.479160	−	1.47470i	0.0217128	−	0.0668251i	−0.939613	−	0.342239i	$-0.888815\pi$
$487$	0.479160	−	1.47470i	0.0217128	−	0.0668251i	0.961326	+	0.275414i	$0.0888148\pi$
$488$	−1.58597	−	4.88111i	−0.0717934	−	0.220957i
$489$		0			0
$490$	−0.845811	+	0.614518i	−0.0382099	+	0.0277611i
$491$	0.0102481	+	0.0315404i	0.000462490	+	0.00142340i	0.951287	−	0.308305i	$-0.0997618\pi$
$491$	0.0102481	+	0.0315404i	0.000462490	+	0.00142340i	−0.950825	+	0.309729i	$0.899762\pi$
$492$		0			0
$493$	−3.51049	−	2.55052i	−0.158105	−	0.114870i
$494$	−16.9443			−0.762359
$495$		0			0
$496$	34.2212			1.53658
$497$	11.2801	+	8.19549i	0.505982	+	0.367618i
$498$		0			0
$499$	−8.35317	−	25.7084i	−0.373939	−	1.15087i	−0.944192	−	0.329397i	$-0.893155\pi$
$499$	−8.35317	−	25.7084i	−0.373939	−	1.15087i	0.570252	−	0.821470i	$-0.306845\pi$
$500$	−5.25498	+	3.81797i	−0.235010	+	0.170745i
$501$		0			0
$502$	−14.1968	−	43.6933i	−0.633635	−	1.95013i
$503$	9.06474	−	27.8984i	0.404177	−	1.24393i	−0.517404	−	0.855741i	$-0.673101\pi$
$503$	9.06474	−	27.8984i	0.404177	−	1.24393i	0.921581	−	0.388187i	$-0.126899\pi$
$504$		0			0
$505$	−0.841621			−0.0374516
$506$	−21.5817	+	4.84540i	−0.959426	+	0.215404i
$507$		0			0
$508$	−7.61569	−	5.53312i	−0.337891	−	0.245493i
$509$	5.13984	−	15.8188i	0.227819	−	0.701156i	−0.770174	−	0.637834i	$-0.779831\pi$
$509$	5.13984	−	15.8188i	0.227819	−	0.701156i	0.997993	−	0.0633219i	$-0.0201695\pi$
$510$		0			0
$511$	−2.09529	+	1.52232i	−0.0926903	+	0.0673435i
$512$	11.0196	−	8.00620i	0.487002	−	0.353828i
$513$		0			0
$514$	0.477260	−	1.46886i	0.0210510	−	0.0647884i
$515$	8.40801	+	6.10877i	0.370501	+	0.269185i
$516$		0			0
$517$	−17.2602	−	29.1228i	−0.759101	−	1.28082i
$518$	−13.6584			−0.600115
$519$		0			0
$520$	0.428724	−	1.31948i	0.0188008	−	0.0578629i
$521$	−11.0913	−	34.1356i	−0.485920	−	1.49551i	−0.830644	−	0.556805i	$-0.812027\pi$
$521$	−11.0913	−	34.1356i	−0.485920	−	1.49551i	0.344723	−	0.938704i	$-0.387973\pi$
$522$		0			0
$523$	−5.88861	+	4.27833i	−0.257491	+	0.187078i	−0.709040	−	0.705168i	$-0.750872\pi$
$523$	−5.88861	+	4.27833i	−0.257491	+	0.187078i	0.451549	+	0.892246i	$0.350872\pi$
$524$	−4.27119	−	13.1454i	−0.186588	−	0.574258i
$525$		0			0
$526$	−38.5498	−	28.0081i	−1.68085	−	1.22121i
$527$	49.0974			2.13872
$528$		0			0
$529$	−8.83876			−0.384294
$530$	5.95848	+	4.32909i	0.258820	+	0.188044i
$531$		0			0
$532$	2.18230	+	6.71642i	0.0946146	+	0.291194i
$533$	−9.34972	+	6.79297i	−0.404981	+	0.294236i
$534$		0			0
$535$	−1.31255	−	4.03961i	−0.0567464	−	0.174647i
$536$	−1.03116	+	3.17358i	−0.0445393	+	0.137078i
$537$		0			0
$538$	−1.75906			−0.0758386
$539$	−0.309017	+	3.30220i	−0.0133103	+	0.142236i
$540$		0			0
$541$	8.47110	+	6.15462i	0.364201	+	0.264608i	0.754802	−	0.655952i	$-0.227733\pi$
$541$	8.47110	+	6.15462i	0.364201	+	0.264608i	−0.390601	+	0.920560i	$0.627733\pi$
$542$	−14.7125	+	45.2805i	−0.631958	+	1.94497i
$543$		0			0
$544$	33.4143	−	24.2769i	1.43263	−	1.04087i
$545$	−4.24130	+	3.08149i	−0.181677	+	0.131996i
$546$		0			0
$547$	2.52346	−	7.76642i	0.107895	−	0.332068i	−0.882504	−	0.470305i	$-0.844144\pi$
$547$	2.52346	−	7.76642i	0.107895	−	0.332068i	0.990399	+	0.138238i	$0.0441437\pi$
$548$	−16.1091	−	11.7039i	−0.688147	−	0.499968i
$549$		0			0
$550$	−2.54765	+	27.2245i	−0.108632	+	1.16086i
$551$	3.75953			0.160161
$552$		0			0
$553$	1.44111	−	4.43527i	0.0612820	−	0.188607i
$554$	15.1316	+	46.5703i	0.642880	+	1.97858i
$555$		0			0
$556$	−13.6243	+	9.89860i	−0.577797	+	0.419794i
$557$	−3.67005	−	11.2953i	−0.155505	−	0.478595i	0.842707	−	0.538373i	$-0.180961\pi$
$557$	−3.67005	−	11.2953i	−0.155505	−	0.478595i	−0.998212	+	0.0597778i	$0.980961\pi$
$558$		0			0
$559$	−13.6865	−	9.94382i	−0.578877	−	0.420579i
$560$	−2.93794			−0.124151
$561$		0			0
$562$	42.2530			1.78233
$563$	3.91507	+	2.84446i	0.165000	+	0.119880i	0.667221	−	0.744860i	$-0.267484\pi$
$563$	3.91507	+	2.84446i	0.165000	+	0.119880i	−0.502221	+	0.864739i	$0.667484\pi$
$564$		0			0
$565$	−1.42349	−	4.38105i	−0.0598866	−	0.184312i
$566$	12.5416	−	9.11200i	0.527162	−	0.383006i
$567$		0			0
$568$	6.56091	+	20.1924i	0.275290	+	0.847255i
$569$	−2.01786	+	6.21033i	−0.0845931	+	0.260351i	−0.984402	−	0.175933i	$-0.943706\pi$
$569$	−2.01786	+	6.21033i	−0.0845931	+	0.260351i	0.899809	+	0.436284i	$0.143706\pi$
$570$		0			0
$571$	−33.8691			−1.41738			−0.708689	−	0.705521i	$-0.750713\pi$
$571$	−33.8691			−1.41738			−0.708689	+	0.705521i	$0.750713\pi$
$572$	2.97928	+	5.02690i	0.124570	+	0.210185i
$573$		0			0
$574$	10.7286	+	7.79481i	0.447804	+	0.325349i
$575$	5.40968	−	16.6493i	0.225599	−	0.694323i
$576$		0			0
$577$	30.2256	−	21.9602i	1.25831	−	0.914216i	0.259636	−	0.965706i	$-0.416397\pi$
$577$	30.2256	−	21.9602i	1.25831	−	0.914216i	0.998673	+	0.0514908i	$0.0163973\pi$
$578$	48.8232	−	35.4721i	2.03078	−	1.47544i
$579$		0			0
$580$	0.126293	−	0.388691i	0.00524405	−	0.0161395i
$581$	2.83941	+	2.06295i	0.117799	+	0.0855856i
$582$		0			0
$583$	22.7971	−	5.11827i	0.944159	−	0.211977i
$584$	−3.94378			−0.163195
$585$		0			0
$586$	−10.7477	+	33.0779i	−0.443982	+	1.36644i
$587$	0.642674	+	1.97795i	0.0265260	+	0.0816386i	0.963443	−	0.267913i	$-0.0863340\pi$
$587$	0.642674	+	1.97795i	0.0265260	+	0.0816386i	−0.936917	+	0.349552i	$0.886334\pi$
$588$		0			0
$589$	−34.4143	+	25.0035i	−1.41802	+	1.03025i
$590$	1.08353	+	3.33478i	0.0446084	+	0.137291i
$591$		0			0
$592$	−31.0516	−	22.5603i	−1.27621	−	0.927223i
$593$	−6.54983			−0.268969			−0.134485	−	0.990916i	$-0.542938\pi$
$593$	−6.54983			−0.268969			−0.134485	+	0.990916i	$0.542938\pi$
$594$		0			0
$595$	−4.21508			−0.172802
$596$	11.5601	+	8.39892i	0.473521	+	0.344033i
$597$		0			0
$598$	−3.18291	−	9.79598i	−0.130159	−	0.400587i
$599$	−4.03042	+	2.92827i	−0.164679	+	0.119646i	−0.667072	−	0.744993i	$-0.732453\pi$
$599$	−4.03042	+	2.92827i	−0.164679	+	0.119646i	0.502394	+	0.864639i	$0.332453\pi$
$600$		0			0
$601$	−10.0342	−	30.8821i	−0.409303	−	1.25971i	−0.917248	−	0.398316i	$-0.869595\pi$
$601$	−10.0342	−	30.8821i	−0.409303	−	1.25971i	0.507945	−	0.861389i	$-0.330405\pi$
$602$	−5.99878	+	18.4623i	−0.244492	+	0.752469i
$603$		0			0
$604$	0.374827			0.0152515
$605$	−4.45104	−	4.72205i	−0.180961	−	0.191979i
$606$		0			0
$607$	−2.53536	−	1.84205i	−0.102907	−	0.0747665i	0.535142	−	0.844762i	$-0.320258\pi$
$607$	−2.53536	−	1.84205i	−0.102907	−	0.0747665i	−0.638049	+	0.769996i	$0.720258\pi$
$608$	−11.0581	+	34.0333i	−0.448465	+	1.38023i
$609$		0			0
$610$	2.85076	−	2.07119i	0.115424	−	0.0838602i
$611$	12.7537	−	9.26609i	0.515959	−	0.374866i
$612$		0			0
$613$	14.4769	−	44.5555i	0.584718	−	1.79958i	−0.0156800	−	0.999877i	$-0.504991\pi$
$613$	14.4769	−	44.5555i	0.584718	−	1.79958i	0.600398	−	0.799701i	$-0.295009\pi$
$614$	−24.4937	−	17.7957i	−0.988484	−	0.718175i
$615$		0			0
$616$	−3.33630	+	3.79147i	−0.134423	+	0.152763i
$617$	−26.5924			−1.07057			−0.535286	−	0.844671i	$-0.679796\pi$
$617$	−26.5924			−1.07057			−0.535286	+	0.844671i	$0.679796\pi$
$618$		0			0
$619$	−10.1903	+	31.3625i	−0.409582	+	1.26056i	0.507426	+	0.861695i	$0.330597\pi$
$619$	−10.1903	+	31.3625i	−0.409582	+	1.26056i	−0.917008	+	0.398869i	$0.869403\pi$
$620$	1.42899	+	4.39798i	0.0573896	+	0.176627i
$621$		0			0
$622$	10.3711	−	7.53505i	0.415844	−	0.302128i
$623$	2.51878	+	7.75202i	0.100913	+	0.310578i
$624$		0			0
$625$	−16.1002	−	11.6975i	−0.644007	−	0.467899i
$626$	−24.4185			−0.975959
$627$		0			0
$628$	−3.05828			−0.122039
$629$	−44.5500	−	32.3675i	−1.77632	−	1.29058i
$630$		0			0
$631$	3.45237	+	10.6253i	0.137437	+	0.422987i	0.995961	−	0.0897862i	$-0.0286184\pi$
$631$	3.45237	+	10.6253i	0.137437	+	0.422987i	−0.858524	+	0.512773i	$0.828618\pi$
$632$	5.74509	−	4.17405i	0.228527	−	0.166035i
$633$		0			0
$634$	−3.80959	−	11.7247i	−0.151298	−	0.465648i
$635$	−1.50429	+	4.62973i	−0.0596959	+	0.183725i
$636$		0			0
$637$	−1.54445			−0.0611932
$638$	−1.81995	−	3.07077i	−0.0720525	−	0.121573i
$639$		0			0
$640$	−5.27741	−	3.83426i	−0.208608	−	0.151563i
$641$	12.9526	−	39.8639i	0.511595	−	1.57453i	−0.277798	−	0.960640i	$-0.589605\pi$
$641$	12.9526	−	39.8639i	0.511595	−	1.57453i	0.789393	−	0.613888i	$-0.210395\pi$
$642$		0			0
$643$	−23.5321	+	17.0971i	−0.928017	+	0.674244i	−0.945506	−	0.325604i	$-0.894433\pi$
$643$	−23.5321	+	17.0971i	−0.928017	+	0.674244i	0.0174898	+	0.999847i	$0.494433\pi$
$644$	−3.47302	+	2.52330i	−0.136856	+	0.0994320i
$645$		0			0
$646$	−24.2238	+	74.5530i	−0.953071	+	2.93325i
$647$	1.53554	+	1.11564i	0.0603685	+	0.0438603i	0.617560	−	0.786524i	$-0.288121\pi$
$647$	1.53554	+	1.11564i	0.0603685	+	0.0438603i	−0.557192	+	0.830384i	$0.688121\pi$
$648$		0			0
$649$	10.2128	+	4.40807i	0.400887	+	0.173032i
$650$	−12.7330			−0.499428
$651$		0			0
$652$	−0.314330	+	0.967407i	−0.0123101	+	0.0378866i
$653$	−6.25817	−	19.2607i	−0.244901	−	0.753728i	−0.995653	−	0.0931434i	$-0.970308\pi$
$653$	−6.25817	−	19.2607i	−0.244901	−	0.753728i	0.750752	−	0.660585i	$-0.229692\pi$
$654$		0			0
$655$	−5.78258	+	4.20129i	−0.225944	+	0.164158i
$656$	11.5158	+	35.4421i	0.449618	+	1.38378i
$657$		0			0
$658$	−14.6346	−	10.6327i	−0.570517	−	0.414505i
$659$	11.5620			0.450392			0.225196	−	0.974314i	$-0.427698\pi$
$659$	11.5620			0.450392			0.225196	+	0.974314i	$0.427698\pi$
$660$		0			0
$661$	−32.6894			−1.27147			−0.635735	−	0.771907i	$-0.719303\pi$
$661$	−32.6894			−1.27147			−0.635735	+	0.771907i	$0.719303\pi$
$662$	−42.5394	−	30.9067i	−1.65334	−	1.20122i
$663$		0			0
$664$	1.65150	+	5.08279i	0.0640906	+	0.197251i
$665$	2.95452	−	2.14658i	0.114571	−	0.0832410i
$666$		0			0
$667$	0.706211	+	2.17349i	0.0273446	+	0.0841580i
$668$	−4.07548	+	12.5430i	−0.157685	+	0.485304i
$669$		0			0
$670$	−2.29104			−0.0885107
$671$	1.04152	−	11.1299i	0.0402076	−	0.429663i
$672$		0			0
$673$	16.2814	+	11.8291i	0.627602	+	0.455979i	0.855569	−	0.517690i	$-0.173208\pi$
$673$	16.2814	+	11.8291i	0.627602	+	0.455979i	−0.227967	+	0.973669i	$0.573208\pi$
$674$	−10.7182	+	32.9874i	−0.412851	+	1.27063i
$675$		0			0
$676$	9.79635	−	7.11747i	0.376783	−	0.273749i
$677$	19.0722	−	13.8568i	0.733006	−	0.532560i	−0.157507	−	0.987518i	$-0.550346\pi$
$677$	19.0722	−	13.8568i	0.733006	−	0.532560i	0.890513	+	0.454958i	$0.150346\pi$
$678$		0			0
$679$	1.48238	−	4.56231i	0.0568887	−	0.175085i
$680$	−5.19266	−	3.77269i	−0.199129	−	0.144676i
$681$		0			0
$682$	37.0824	+	16.0056i	1.41996	+	0.612886i
$683$	−11.5812			−0.443143			−0.221572	−	0.975144i	$-0.571119\pi$
$683$	−11.5812			−0.443143			−0.221572	+	0.975144i	$0.571119\pi$
$684$		0			0
$685$	−3.18195	+	9.79304i	−0.121576	+	0.374173i
$686$	0.547647	+	1.68548i	0.0209093	+	0.0643521i
$687$		0			0
$688$	−44.1332	+	32.0646i	−1.68256	+	1.22245i
$689$	3.36215	+	10.3476i	0.128088	+	0.394213i
$690$		0			0
$691$	−35.4482	−	25.7546i	−1.34851	−	0.979752i	−0.999084	−	0.0427885i	$-0.986376\pi$
$691$	−35.4482	−	25.7546i	−1.34851	−	0.979752i	−0.349428	−	0.936963i	$-0.613624\pi$
$692$	−10.2547			−0.389826
$693$		0			0
$694$	−11.5050			−0.436723
$695$	7.04548	+	5.11884i	0.267250	+	0.194169i
$696$		0			0
$697$	16.5219	+	50.8491i	0.625811	+	1.92605i
$698$	11.2975	−	8.20813i	0.427617	−	0.310682i
$699$		0			0
$700$	1.63991	+	5.04713i	0.0619828	+	0.190764i
$701$	7.05070	−	21.6998i	0.266301	−	0.819591i	−0.725090	−	0.688655i	$-0.758202\pi$
$701$	7.05070	−	21.6998i	0.266301	−	0.819591i	0.991391	−	0.130936i	$-0.0417983\pi$
$702$		0			0
$703$	47.7104			1.79943
$704$	0.919022	−	0.206333i	0.0346370	−	0.00777648i
$705$		0			0
$706$	7.66479	+	5.56880i	0.288468	+	0.209584i
$707$	−0.440861	+	1.35683i	−0.0165803	+	0.0510289i
$708$		0			0
$709$	−32.3401	+	23.4965i	−1.21456	+	0.882428i	−0.995637	−	0.0933141i	$-0.970254\pi$
$709$	−32.3401	+	23.4965i	−1.21456	+	0.882428i	−0.218922	+	0.975742i	$0.570254\pi$
$710$	−11.7931	+	8.56822i	−0.442589	+	0.321559i
$711$		0			0
$712$	−3.83545	+	11.8043i	−0.143740	+	0.442385i
$713$	−20.9198	−	15.1991i	−0.783454	−	0.569212i
$714$		0			0
$715$	1.99622	−	2.26857i	0.0746545	−	0.0848396i
$716$	7.01108			0.262016
$717$		0			0
$718$	−9.77635	+	30.0885i	−0.364850	+	1.12289i
$719$	8.10242	+	24.9367i	0.302169	+	0.929981i	0.980718	+	0.195426i	$0.0626090\pi$
$719$	8.10242	+	24.9367i	0.302169	+	0.929981i	−0.678549	+	0.734555i	$0.737391\pi$
$720$		0			0
$721$	14.2526	−	10.3552i	0.530796	−	0.385646i
$722$	−10.5824	−	32.5692i	−0.393836	−	1.21210i
$723$		0			0
$724$	−13.8124	−	10.0353i	−0.513334	−	0.372959i
$725$	2.82514			0.104923
$726$		0			0
$727$	−22.2366			−0.824708			−0.412354	−	0.911024i	$-0.635293\pi$
$727$	−22.2366			−0.824708			−0.412354	+	0.911024i	$0.635293\pi$
$728$	−1.90264	−	1.38235i	−0.0705164	−	0.0512332i
$729$		0			0
$730$	−0.836730	−	2.57519i	−0.0309688	−	0.0953121i
$731$	−63.3182	+	46.0034i	−2.34191	+	1.70150i
$732$		0			0
$733$	−6.52903	−	20.0943i	−0.241155	−	0.742200i	−0.996245	−	0.0865782i	$-0.972407\pi$
$733$	−6.52903	−	20.0943i	−0.241155	−	0.742200i	0.755090	−	0.655621i	$-0.227593\pi$
$734$	16.3942	−	50.4562i	0.605121	−	1.86237i
$735$		0			0
$736$	−21.7529			−0.801822
$737$	−4.80127	+	5.45631i	−0.176857	+	0.200986i
$738$		0			0
$739$	−30.3410	−	22.0440i	−1.11611	−	0.810903i	−0.132497	−	0.991183i	$-0.542299\pi$
$739$	−30.3410	−	22.0440i	−1.11611	−	0.810903i	−0.983615	+	0.180280i	$0.942299\pi$
$740$	1.60273	−	4.93270i	0.0589175	−	0.181330i
$741$		0			0
$742$	10.1004	−	7.33836i	0.370797	−	0.269400i
$743$	−29.2430	+	21.2463i	−1.07282	+	0.779452i	−0.976418	−	0.215891i	$-0.930735\pi$
$743$	−29.2430	+	21.2463i	−1.07282	+	0.779452i	−0.0964055	+	0.995342i	$0.530735\pi$
$744$		0			0
$745$	2.28342	−	7.02763i	0.0836579	−	0.257473i
$746$	33.6812	+	24.4708i	1.23316	+	0.895940i
$747$		0			0
$748$	26.3770	−	5.92201i	0.964440	−	0.216530i
$749$	−7.20005			−0.263084
$750$		0			0
$751$	−13.4587	+	41.4216i	−0.491115	+	1.51150i	0.331810	+	0.943346i	$0.392341\pi$
$751$	−13.4587	+	41.4216i	−0.491115	+	1.51150i	−0.822925	+	0.568150i	$0.807659\pi$
$752$	−15.7084	−	48.3456i	−0.572828	−	1.76298i
$753$		0			0
$754$	1.34478	−	0.977038i	0.0489739	−	0.0355816i
$755$	−0.0598978	−	0.184346i	−0.00217990	−	0.00670905i
$756$		0			0
$757$	35.9561	+	26.1236i	1.30685	+	0.949479i	0.999997	−	0.00227928i	$-0.000725518\pi$
$757$	35.9561	+	26.1236i	1.30685	+	0.949479i	0.306848	+	0.951758i	$0.400726\pi$
$758$	55.7421			2.02464
$759$		0			0
$760$	5.56103			0.201720
$761$	−12.9130	−	9.38184i	−0.468096	−	0.340091i	0.328603	−	0.944468i	$-0.393422\pi$
$761$	−12.9130	−	9.38184i	−0.468096	−	0.340091i	−0.796699	+	0.604377i	$0.793422\pi$
$762$		0			0
$763$	2.74617	+	8.45183i	0.0994179	+	0.305977i
$764$	9.11231	−	6.62048i	0.329672	−	0.239521i
$765$		0			0
$766$	−3.08188	−	9.48505i	−0.111353	−	0.342709i
$767$	−1.60066	+	4.92633i	−0.0577966	+	0.177880i
$768$		0			0
$769$	5.19899			0.187480			0.0937402	−	0.995597i	$-0.470118\pi$
$769$	5.19899			0.187480			0.0937402	+	0.995597i	$0.470118\pi$
$770$	−3.18358	−	1.37410i	−0.114728	−	0.0495192i
$771$		0			0
$772$	5.70460	+	4.14463i	0.205313	+	0.149169i
$773$	3.75809	−	11.5662i	0.135169	−	0.416007i	−0.860447	−	0.509539i	$-0.829816\pi$
$773$	3.75809	−	11.5662i	0.135169	−	0.416007i	0.995616	+	0.0935321i	$0.0298158\pi$
$774$		0			0
$775$	−25.8610	+	18.7891i	−0.928956	+	0.674926i
$776$	5.90965	−	4.29361i	0.212144	−	0.154132i
$777$		0			0
$778$	14.2976	−	44.0033i	0.512592	−	1.57760i
$779$	−37.4764	−	27.2282i	−1.34273	−	0.975551i
$780$		0			0
$781$	−4.30862	+	46.0425i	−0.154175	+	1.64753i
$782$	−47.6516			−1.70402
$783$		0			0
$784$	−1.53896	+	4.73644i	−0.0549629	+	0.169158i
$785$	0.488718	+	1.50412i	0.0174431	+	0.0536843i
$786$		0			0
$787$	32.0718	−	23.3015i	1.14324	−	0.830610i	0.155670	−	0.987809i	$-0.450246\pi$
$787$	32.0718	−	23.3015i	1.14324	−	0.830610i	0.987567	+	0.157199i	$0.0502463\pi$
$788$	6.72324	+	20.6920i	0.239505	+	0.737122i
$789$		0			0
$790$	3.94445	+	2.86581i	0.140337	+	0.101961i
$791$	−7.80862			−0.277643
$792$		0			0
$793$	5.20546			0.184851
$794$	14.8864	+	10.8156i	0.528297	+	0.383830i
$795$		0			0
$796$	−4.17662	−	12.8543i	−0.148036	−	0.455609i
$797$	−28.4060	+	20.6382i	−1.00619	+	0.731043i	−0.963407	−	0.268042i	$-0.913624\pi$
$797$	−28.4060	+	20.6382i	−1.00619	+	0.731043i	−0.0427865	+	0.999084i	$0.513624\pi$
$798$		0			0
$799$	−22.5370	−	69.3618i	−0.797302	−	2.45384i
$800$	−8.30974	+	25.5747i	−0.293794	+	0.904204i
$801$		0			0
$802$	6.53731			0.230840
$803$	−7.88654	−	3.40401i	−0.278310	−	0.120125i
$804$		0			0
$805$	1.79600	+	1.30487i	0.0633006	+	0.0459906i
$806$	−5.81197	+	17.8874i	−0.204718	+	0.630057i
$807$		0			0
$808$	−1.75753	+	1.27692i	−0.0618297	+	0.0449219i
$809$	−33.8066	+	24.5619i	−1.18858	+	0.863552i	−0.993113	−	0.117159i	$-0.962621\pi$
$809$	−33.8066	+	24.5619i	−1.18858	+	0.863552i	−0.195464	+	0.980711i	$0.562621\pi$
$810$		0			0
$811$	−3.05889	+	9.41431i	−0.107412	+	0.330581i	−0.990289	−	0.139024i	$-0.955604\pi$
$811$	−3.05889	+	9.41431i	−0.107412	+	0.330581i	0.882877	+	0.469605i	$0.155604\pi$
$812$	−0.560478	−	0.407211i	−0.0196689	−	0.0142903i
$813$		0			0
$814$	−23.0961	−	38.9697i	−0.809518	−	1.36589i
$815$	0.526018			0.0184256
$816$		0			0
$817$	20.9545	−	64.4912i	0.733103	−	2.25626i
$818$	−0.591581	−	1.82070i	−0.0206842	−	0.0636593i
$819$		0			0
$820$	−4.07402	+	2.95995i	−0.142271	+	0.103366i
$821$	−5.00410	−	15.4010i	−0.174644	−	0.537500i	0.824973	−	0.565173i	$-0.191190\pi$
$821$	−5.00410	−	15.4010i	−0.174644	−	0.537500i	−0.999617	+	0.0276726i	$0.991190\pi$
$822$		0			0
$823$	3.12800	+	2.27262i	0.109035	+	0.0792187i	0.640967	−	0.767569i	$-0.278534\pi$
$823$	3.12800	+	2.27262i	0.109035	+	0.0792187i	−0.531932	+	0.846787i	$0.678534\pi$
$824$	26.8265			0.934545
$825$		0			0
$826$	5.94378			0.206811
$827$	−37.8765	−	27.5189i	−1.31709	−	0.956925i	−0.999964	−	0.00854365i	$-0.997280\pi$
$827$	−37.8765	−	27.5189i	−1.31709	−	0.956925i	−0.317131	−	0.948382i	$-0.602720\pi$
$828$		0			0
$829$	−12.8427	−	39.5258i	−0.446046	−	1.37279i	−0.881332	−	0.472497i	$-0.843353\pi$
$829$	−12.8427	−	39.5258i	−0.446046	−	1.37279i	0.435286	−	0.900292i	$-0.356647\pi$
$830$	−2.96855	+	2.15677i	−0.103040	+	0.0748627i
$831$		0			0
$832$	0.135539	+	0.417145i	0.00469896	+	0.0144619i
$833$	−2.20796	+	6.79540i	−0.0765013	+	0.235447i
$834$		0			0
$835$	6.82015			0.236021
$836$	−15.4729	+	17.5838i	−0.535140	+	0.608149i
$837$		0			0
$838$	−14.4474	−	10.4966i	−0.499076	−	0.362600i
$839$	−1.58872	+	4.88957i	−0.0548486	+	0.168807i	−0.974728	−	0.223394i	$-0.928286\pi$
$839$	−1.58872	+	4.88957i	−0.0548486	+	0.168807i	0.919880	+	0.392201i	$0.128286\pi$
$840$		0			0
$841$	23.1631	−	16.8290i	0.798728	−	0.580310i
$842$	17.1702	−	12.4749i	0.591725	−	0.429913i
$843$		0			0
$844$	−7.39621	+	22.7632i	−0.254588	+	0.783541i
$845$	−5.06597	−	3.68064i	−0.174275	−	0.126618i
$846$		0			0
$847$	−9.94427	+	4.70228i	−0.341689	+	0.161572i
$848$	35.0838			1.20478
$849$		0			0
$850$	−18.2032	+	56.0237i	−0.624365	+	1.92160i
$851$	8.96219	+	27.5828i	0.307220	+	0.945526i
$852$		0			0
$853$	−5.41758	+	3.93610i	−0.185494	+	0.134769i	−0.676657	−	0.736298i	$-0.736572\pi$
$853$	−5.41758	+	3.93610i	−0.185494	+	0.134769i	0.491163	+	0.871068i	$0.336572\pi$
$854$	−1.84581	−	5.68082i	−0.0631624	−	0.194394i
$855$		0			0
$856$	−8.86990	−	6.44436i	−0.303167	−	0.220264i
$857$	36.1064			1.23337			0.616686	−	0.787209i	$-0.288475\pi$
$857$	36.1064			1.23337			0.616686	+	0.787209i	$0.288475\pi$
$858$		0			0
$859$	−37.1034			−1.26595			−0.632976	−	0.774171i	$-0.718167\pi$
$859$	−37.1034			−1.26595			−0.632976	+	0.774171i	$0.718167\pi$
$860$	−5.96371	−	4.33289i	−0.203361	−	0.147750i
$861$		0			0
$862$	−0.300410	−	0.924567i	−0.0102320	−	0.0314909i
$863$	31.0439	−	22.5547i	1.05675	−	0.767771i	0.0832629	−	0.996528i	$-0.473466\pi$
$863$	31.0439	−	22.5547i	1.05675	−	0.767771i	0.973484	+	0.228756i	$0.0734659\pi$
$864$		0			0
$865$	1.63872	+	5.04345i	0.0557180	+	0.171482i
$866$	−10.7272	+	33.0150i	−0.364526	+	1.12190i
$867$		0			0
$868$	7.83880			0.266066
$869$	15.0914	−	3.38824i	0.511942	−	0.114938i
$870$		0			0
$871$	−2.73809	−	1.98934i	−0.0927766	−	0.0674062i
$872$	−4.18170	+	12.8699i	−0.141610	+	0.435831i
$873$		0			0
$874$	33.4009	−	24.2672i	1.12980	−	0.820850i
$875$	4.60651	−	3.34682i	0.155728	−	0.113143i
$876$		0			0
$877$	−0.250661	+	0.771456i	−0.00846423	+	0.0260502i	−0.955199	−	0.295963i	$-0.904360\pi$
$877$	−0.250661	+	0.771456i	−0.00846423	+	0.0260502i	0.946735	+	0.322013i	$0.104360\pi$
$878$	53.6325	+	38.9663i	1.81001	+	1.31505i
$879$		0			0
$880$	−4.96800	−	8.38244i	−0.167471	−	0.282572i
$881$	32.5076			1.09521			0.547605	−	0.836737i	$-0.315540\pi$
$881$	32.5076			1.09521			0.547605	+	0.836737i	$0.315540\pi$
$882$		0			0
$883$	14.8636	−	45.7453i	0.500199	−	1.53945i	−0.308497	−	0.951225i	$-0.599826\pi$
$883$	14.8636	−	45.7453i	0.500199	−	1.53945i	0.808695	−	0.588228i	$-0.200174\pi$
$884$	3.89012	+	11.9726i	0.130839	+	0.402681i
$885$		0			0
$886$	−30.7510	+	22.3419i	−1.03310	+	0.750590i
$887$	−3.51806	−	10.8275i	−0.118125	−	0.363551i	0.874461	−	0.485096i	$-0.161215\pi$
$887$	−3.51806	−	10.8275i	−0.118125	−	0.363551i	−0.992586	+	0.121545i	$0.961215\pi$
$888$		0			0
$889$	6.67589	+	4.85032i	0.223902	+	0.162675i
$890$	−8.52166			−0.285647
$891$		0			0
$892$	3.86563			0.129431
$893$	51.1205	+	37.1412i	1.71068	+	1.24288i
$894$		0			0
$895$	−1.12038	−	3.44817i	−0.0374502	−	0.115260i
$896$	−8.94589	+	6.49957i	−0.298861	+	0.217135i
$897$		0			0
$898$	3.50441	+	10.7855i	0.116944	+	0.359916i
$899$	1.28954	−	3.96879i	0.0430085	−	0.132366i
$900$		0			0
$901$	50.3351			1.67690
$902$	−4.09797	+	43.7915i	−0.136448	+	1.45810i
$903$		0			0
$904$	−9.61962	−	6.98906i	−0.319944	−	0.232453i
$905$	−2.72830	+	8.39683i	−0.0906917	+	0.279120i
$906$		0			0
$907$	−10.8618	+	7.89153i	−0.360659	+	0.262034i	−0.753327	−	0.657646i	$-0.771552\pi$
$907$	−10.8618	+	7.89153i	−0.360659	+	0.262034i	0.392668	+	0.919680i	$0.371552\pi$
$908$	17.9018	−	13.0065i	0.594094	−	0.431634i
$909$		0			0
$910$	0.498966	−	1.53566i	0.0165406	−	0.0509066i
$911$	2.74502	+	1.99437i	0.0909464	+	0.0660765i	0.632329	−	0.774700i	$-0.282099\pi$
$911$	2.74502	+	1.99437i	0.0909464	+	0.0660765i	−0.541383	+	0.840776i	$0.682099\pi$
$912$		0			0
$913$	−1.08456	+	11.5897i	−0.0358936	+	0.383564i
$914$	65.4712			2.16560
$915$		0			0
$916$	−3.47726	+	10.7019i	−0.114892	+	0.353601i
$917$	3.74411	+	11.5232i	0.123642	+	0.380530i
$918$		0			0
$919$	36.0553	−	26.1957i	1.18936	−	0.864117i	0.196160	−	0.980572i	$-0.437153\pi$
$919$	36.0553	−	26.1957i	1.18936	−	0.864117i	0.993196	+	0.116455i	$0.0371530\pi$
$920$	1.04461	+	3.21499i	0.0344399	+	0.105995i
$921$		0			0
$922$	−10.6073	−	7.70665i	−0.349333	−	0.253805i
$923$	−21.5342			−0.708807
$924$		0			0
$925$	35.8525			1.17882
$926$	−20.6056	−	14.9708i	−0.677141	−	0.491972i
$927$		0			0
$928$	−1.08480	−	3.33868i	−0.0356104	−	0.109597i
$929$	−5.78613	+	4.20387i	−0.189837	+	0.137924i	−0.678644	−	0.734467i	$-0.737432\pi$
$929$	−5.78613	+	4.20387i	−0.189837	+	0.137924i	0.488807	+	0.872392i	$0.337432\pi$
$930$		0			0
$931$	−1.91300	−	5.88760i	−0.0626959	−	0.192958i
$932$	−2.51211	+	7.73149i	−0.0822871	+	0.253254i
$933$		0			0
$934$	64.0883			2.09703
$935$	−7.12763	−	12.0263i	−0.233099	−	0.393304i
$936$		0			0
$937$	1.05828	+	0.768889i	0.0345727	+	0.0251185i	0.604937	−	0.796273i	$-0.293198\pi$
$937$	1.05828	+	0.768889i	0.0345727	+	0.0251185i	−0.570365	+	0.821392i	$0.693198\pi$
$938$	−1.20010	+	3.69353i	−0.0391847	+	0.120598i
$939$		0			0
$940$	5.55725	−	4.03758i	0.181258	−	0.131691i
$941$	−17.8975	+	13.0033i	−0.583442	+	0.423896i	−0.839963	−	0.542643i	$-0.817424\pi$
$941$	−17.8975	+	13.0033i	−0.583442	+	0.423896i	0.256521	+	0.966539i	$0.417424\pi$
$942$		0			0
$943$	8.70164	−	26.7809i	0.283365	−	0.872106i
$944$	13.5129	+	9.81767i	0.439806	+	0.319538i
$945$		0			0
$946$	−62.8200	+	14.1040i	−2.04245	+	0.458560i
$947$	17.6842			0.574658			0.287329	−	0.957832i	$-0.407233\pi$
$947$	17.6842			0.574658			0.287329	+	0.957832i	$0.407233\pi$
$948$		0			0
$949$	1.23607	−	3.80423i	0.0401245	−	0.123490i
$950$	−15.7714	−	48.5395i	−0.511693	−	1.57483i
$951$		0			0
$952$	−8.80222	+	6.39519i	−0.285282	+	0.207269i
$953$	7.34659	+	22.6105i	0.237980	+	0.732426i	0.996712	+	0.0810235i	$0.0258189\pi$
$953$	7.34659	+	22.6105i	0.237980	+	0.732426i	−0.758733	+	0.651402i	$0.774181\pi$
$954$		0			0
$955$	−4.71223	−	3.42364i	−0.152484	−	0.110786i
$956$	−25.4272			−0.822374
$957$		0			0
$958$	28.4003			0.917573
$959$	14.1212	+	10.2597i	0.455997	+	0.331301i
$960$		0			0
$961$	5.01138	+	15.4234i	0.161657	+	0.497530i
$962$	17.0659	−	12.3991i	0.550227	−	0.399764i
$963$		0			0
$964$	5.24380	+	16.1388i	0.168891	+	0.519795i
$965$	1.12680	−	3.46794i	0.0362730	−	0.111637i
$966$		0			0
$967$	21.1829			0.681195			0.340597	−	0.940209i	$-0.389371\pi$
$967$	21.1829			0.681195			0.340597	+	0.940209i	$0.389371\pi$
$968$	−16.4593	−	3.10771i	−0.529023	−	0.0998857i
$969$		0			0
$970$	4.05744	+	2.94790i	0.130276	+	0.0946514i
$971$	14.6585	−	45.1143i	0.470415	−	1.44779i	−0.381628	−	0.924316i	$-0.624637\pi$
$971$	14.6585	−	45.1143i	0.470415	−	1.44779i	0.852043	−	0.523472i	$-0.175363\pi$
$972$		0			0
$973$	11.9430	−	8.67709i	0.382875	−	0.278175i
$974$	2.22318	−	1.61523i	0.0712351	−	0.0517554i
$975$		0			0
$976$	5.18698	−	15.9639i	0.166031	−	0.510991i
$977$	−10.6677	−	7.75055i	−0.341290	−	0.247962i	0.403916	−	0.914796i	$-0.367649\pi$
$977$	−10.6677	−	7.75055i	−0.341290	−	0.247962i	−0.745206	+	0.666834i	$0.767649\pi$
$978$		0			0
$979$	−17.8586	+	20.2950i	−0.570763	+	0.648632i
$980$	−0.672972			−0.0214973
$981$		0			0
$982$	−0.0181619	+	0.0558965i	−0.000579569	+	0.00178373i
$983$	1.25999	+	3.87784i	0.0401873	+	0.123684i	0.969137	−	0.246521i	$-0.0792875\pi$
$983$	1.25999	+	3.87784i	0.0401873	+	0.123684i	−0.928950	+	0.370205i	$0.879287\pi$
$984$		0			0
$985$	9.10231	−	6.61321i	0.290024	−	0.210714i
$986$	−2.37635	−	7.31366i	−0.0756785	−	0.232915i
$987$		0			0
$988$	−8.82393	−	6.41096i	−0.280726	−	0.203960i
$989$	41.2204			1.31073
$990$		0			0
$991$	−5.49154			−0.174445			−0.0872223	−	0.996189i	$-0.527799\pi$
$991$	−5.49154			−0.174445			−0.0872223	+	0.996189i	$0.527799\pi$
$992$	32.1347	+	23.3472i	1.02028	+	0.741275i
$993$		0			0
$994$	7.63584	+	23.5007i	0.242194	+	0.745397i
$995$	−5.65454	+	4.10827i	−0.179261	+	0.130241i
$996$		0			0
$997$	7.09891	+	21.8482i	0.224825	+	0.691939i	0.998309	+	0.0581241i	$0.0185119\pi$
$997$	7.09891	+	21.8482i	0.224825	+	0.691939i	−0.773485	+	0.633815i	$0.781488\pi$
$998$	14.8037	−	45.5610i	0.468602	−	1.44221i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.f.631.2		8
3.2	odd	2		231.2.j.f.169.1	✓	8
11.3	even	5	inner	693.2.m.f.190.2		8
11.5	even	5		7623.2.a.ci.1.1		4
11.6	odd	10		7623.2.a.cl.1.4		4
33.5	odd	10		2541.2.a.bn.1.4		4
33.14	odd	10		231.2.j.f.190.1	yes	8
33.17	even	10		2541.2.a.bm.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.169.1	✓	8	3.2	odd	2
231.2.j.f.190.1	yes	8	33.14	odd	10
693.2.m.f.190.2		8	11.3	even	5	inner
693.2.m.f.631.2		8	1.1	even	1	trivial
2541.2.a.bm.1.1		4	33.17	even	10
2541.2.a.bn.1.4		4	33.5	odd	10
7623.2.a.ci.1.1		4	11.5	even	5
7623.2.a.cl.1.4		4	11.6	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43376 + 1.04169i) q^{2} +(0.352519 + 1.08494i) q^{4} +(0.477260 - 0.346750i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(0.470553 - 1.44821i) q^{8} +O(q^{10})\)	\(q+(1.43376 + 1.04169i) q^{2} +(0.352519 + 1.08494i) q^{4} +(0.477260 - 0.346750i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(0.470553 - 1.44821i) q^{8} +1.04548 q^{10} +(2.19098 - 2.48990i) q^{11} +(1.24948 + 0.907802i) q^{13} +(0.547647 - 1.68548i) q^{14} +(4.02905 - 2.92728i) q^{16} +(5.78051 - 4.19979i) q^{17} +(-1.91300 + 5.88760i) q^{19} +(0.544446 + 0.395563i) q^{20} +(5.73503 - 1.28760i) q^{22} -3.76314 q^{23} +(-1.43754 + 4.42430i) q^{25} +(0.845811 + 2.60314i) q^{26} +(0.922906 - 0.670530i) q^{28} +(-0.187665 - 0.577574i) q^{29} +(5.55914 + 4.03895i) q^{31} +5.78051 q^{32} +12.6627 q^{34} +(-0.477260 - 0.346750i) q^{35} +(-2.38157 - 7.32972i) q^{37} +(-8.87581 + 6.44865i) q^{38} +(-0.277591 - 0.854338i) q^{40} +(-2.31233 + 7.11663i) q^{41} -10.9537 q^{43} +(3.47375 + 1.49935i) q^{44} +(-5.39544 - 3.92001i) q^{46} +(3.15419 - 9.70760i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-6.66983 + 4.84591i) q^{50} +(-0.544446 + 1.67563i) q^{52} +(5.69927 + 4.14076i) q^{53} +(0.182297 - 1.94805i) q^{55} -1.52274 q^{56} +(0.332585 - 1.02359i) q^{58} +(1.03640 + 3.18971i) q^{59} +(2.72674 - 1.98109i) q^{61} +(3.76314 + 11.5818i) q^{62} +(0.229756 + 0.166927i) q^{64} +0.911108 q^{65} -2.19138 q^{67} +(6.59426 + 4.79101i) q^{68} +(-0.323071 - 0.994311i) q^{70} +(-11.2801 + 8.19549i) q^{71} +(-0.800331 - 2.46317i) q^{73} +(4.22067 - 12.9899i) q^{74} -7.06206 q^{76} +(-3.04508 - 1.31433i) q^{77} +(3.77286 + 2.74114i) q^{79} +(0.907873 - 2.79415i) q^{80} +(-10.7286 + 7.79481i) q^{82} +(-2.83941 + 2.06295i) q^{83} +(1.30253 - 4.00878i) q^{85} +(-15.7050 - 11.4104i) q^{86} +(-2.57493 - 4.34464i) q^{88} -8.15095 q^{89} +(0.477260 - 1.46886i) q^{91} +(-1.32658 - 4.08279i) q^{92} +(14.6346 - 10.6327i) q^{94} +(1.12853 + 3.47325i) q^{95} +(3.88093 + 2.81966i) q^{97} -1.77222 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

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