LMFDB - Embedded newform 693.2.m.c.64.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	693.64
Dual form			693.2.m.c.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.19098 - 3.66547i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.19098 - 3.66547i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} -3.85410 q^{10} +(2.54508 + 2.12663i) q^{11} +(1.00000 - 3.07768i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.354102 - 1.08981i) q^{17} +(-0.309017 + 0.224514i) q^{19} +(1.19098 - 3.66547i) q^{20} +(2.80902 - 1.76336i) q^{22} -8.09017 q^{23} +(-7.97214 + 5.79210i) q^{25} +(-2.61803 - 1.90211i) q^{26} +(-0.309017 - 0.951057i) q^{28} +(-1.61803 - 1.17557i) q^{29} +(2.57295 - 7.91872i) q^{31} +5.00000 q^{32} -1.14590 q^{34} +(-1.19098 + 3.66547i) q^{35} +(0.736068 + 0.534785i) q^{37} +(0.118034 + 0.363271i) q^{38} +(-9.35410 - 6.79615i) q^{40} +(-3.35410 + 2.43690i) q^{41} +3.23607 q^{43} +(0.809017 + 3.21644i) q^{44} +(-2.50000 + 7.69421i) q^{46} +(1.61803 - 1.17557i) q^{47} +(0.309017 + 0.951057i) q^{49} +(3.04508 + 9.37181i) q^{50} +(2.61803 - 1.90211i) q^{52} +(3.14590 - 9.68208i) q^{53} +(4.76393 - 11.8617i) q^{55} -3.00000 q^{56} +(-1.61803 + 1.17557i) q^{58} +(9.09017 + 6.60440i) q^{59} +(-2.76393 - 8.50651i) q^{61} +(-6.73607 - 4.89404i) q^{62} +(2.16312 - 6.65740i) q^{64} -12.4721 q^{65} +8.00000 q^{67} +(0.354102 - 1.08981i) q^{68} +(3.11803 + 2.26538i) q^{70} +(2.76393 + 8.50651i) q^{71} +(0.618034 + 0.449028i) q^{73} +(0.736068 - 0.534785i) q^{74} -0.381966 q^{76} +(-0.809017 - 3.21644i) q^{77} +(-4.32624 + 13.3148i) q^{79} +(-3.11803 + 2.26538i) q^{80} +(1.28115 + 3.94298i) q^{82} +(4.61803 + 14.2128i) q^{83} +(-3.57295 + 2.59590i) q^{85} +(1.00000 - 3.07768i) q^{86} +(9.92705 + 0.673542i) q^{88} +10.0902 q^{89} +(-2.61803 + 1.90211i) q^{91} +(-6.54508 - 4.75528i) q^{92} +(-0.618034 - 1.90211i) q^{94} +(1.19098 + 0.865300i) q^{95} +(-3.85410 + 11.8617i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} - 7 q^{5} - q^{7} + 3 q^{8}+O(q^{10}) $ 4 * q - q^2 + q^4 - 7 * q^5 - q^7 + 3 * q^8	$ 4 q - q^{2} + q^{4} - 7 q^{5} - q^{7} + 3 q^{8} - 2 q^{10} - q^{11} + 4 q^{13} - q^{14} + q^{16} + 12 q^{17} + q^{19} + 7 q^{20} + 9 q^{22} - 10 q^{23} - 14 q^{25} - 6 q^{26} + q^{28} - 2 q^{29} + 17 q^{31} + 20 q^{32} - 18 q^{34} - 7 q^{35} - 6 q^{37} - 4 q^{38} - 24 q^{40} + 4 q^{43} + q^{44} - 10 q^{46} + 2 q^{47} - q^{49} + q^{50} + 6 q^{52} + 26 q^{53} + 28 q^{55} - 12 q^{56} - 2 q^{58} + 14 q^{59} - 20 q^{61} - 18 q^{62} - 7 q^{64} - 32 q^{65} + 32 q^{67} - 12 q^{68} + 8 q^{70} + 20 q^{71} - 2 q^{73} - 6 q^{74} - 6 q^{76} - q^{77} + 14 q^{79} - 8 q^{80} - 15 q^{82} + 14 q^{83} - 21 q^{85} + 4 q^{86} + 33 q^{88} + 18 q^{89} - 6 q^{91} - 15 q^{92} + 2 q^{94} + 7 q^{95} - 2 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^4 - 7 * q^5 - q^7 + 3 * q^8 - 2 * q^10 - q^11 + 4 * q^13 - q^14 + q^16 + 12 * q^17 + q^19 + 7 * q^20 + 9 * q^22 - 10 * q^23 - 14 * q^25 - 6 * q^26 + q^28 - 2 * q^29 + 17 * q^31 + 20 * q^32 - 18 * q^34 - 7 * q^35 - 6 * q^37 - 4 * q^38 - 24 * q^40 + 4 * q^43 + q^44 - 10 * q^46 + 2 * q^47 - q^49 + q^50 + 6 * q^52 + 26 * q^53 + 28 * q^55 - 12 * q^56 - 2 * q^58 + 14 * q^59 - 20 * q^61 - 18 * q^62 - 7 * q^64 - 32 * q^65 + 32 * q^67 - 12 * q^68 + 8 * q^70 + 20 * q^71 - 2 * q^73 - 6 * q^74 - 6 * q^76 - q^77 + 14 * q^79 - 8 * q^80 - 15 * q^82 + 14 * q^83 - 21 * q^85 + 4 * q^86 + 33 * q^88 + 18 * q^89 - 6 * q^91 - 15 * q^92 + 2 * q^94 + 7 * q^95 - 2 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i	−0.780378	−	0.625308i	$-0.784973\pi$
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i	0.998886	−	0.0471903i	$-0.0150267\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.19098	−	3.66547i	−0.532624	−	1.63925i	−0.748728	−	0.662877i	$-0.769335\pi$
$5$	−1.19098	−	3.66547i	−0.532624	−	1.63925i	0.216104	−	0.976370i	$-0.430665\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	2.42705	−	1.76336i	0.858092	−	0.623440i
$9$		0			0
$10$	−3.85410			−1.21877
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$12$		0			0
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	−0.711238	−	0.702951i	$-0.751865\pi$
$13$	1.00000	−	3.07768i	0.277350	−	0.853596i	0.988588	−	0.150644i	$-0.0481349\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.354102	−	1.08981i	−0.0858823	−	0.264319i	0.898888	−	0.438178i	$-0.144376\pi$
$17$	−0.354102	−	1.08981i	−0.0858823	−	0.264319i	−0.984770	+	0.173860i	$0.944376\pi$
$18$		0			0
$19$	−0.309017	+	0.224514i	−0.0708934	+	0.0515070i	−0.622667	−	0.782487i	$-0.713951\pi$
$19$	−0.309017	+	0.224514i	−0.0708934	+	0.0515070i	0.551774	+	0.833994i	$0.313951\pi$
$20$	1.19098	−	3.66547i	0.266312	−	0.819624i
$21$		0			0
$22$	2.80902	−	1.76336i	0.598884	−	0.375949i
$23$	−8.09017			−1.68692			−0.843459	−	0.537194i	$-0.819484\pi$
$23$	−8.09017			−1.68692			−0.843459	+	0.537194i	$0.819484\pi$
$24$		0			0
$25$	−7.97214	+	5.79210i	−1.59443	+	1.15842i
$26$	−2.61803	−	1.90211i	−0.513439	−	0.373035i
$27$		0			0
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−1.61803	−	1.17557i	−0.300461	−	0.218298i	0.427331	−	0.904095i	$-0.359454\pi$
$29$	−1.61803	−	1.17557i	−0.300461	−	0.218298i	−0.727793	+	0.685797i	$0.759454\pi$
$30$		0			0
$31$	2.57295	−	7.91872i	0.462115	−	1.42224i	−0.400459	−	0.916315i	$-0.631149\pi$
$31$	2.57295	−	7.91872i	0.462115	−	1.42224i	0.862575	−	0.505930i	$-0.168851\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−1.14590			−0.196520
$35$	−1.19098	+	3.66547i	−0.201313	+	0.619577i
$36$		0			0
$37$	0.736068	+	0.534785i	0.121009	+	0.0879181i	0.646644	−	0.762792i	$-0.276172\pi$
$37$	0.736068	+	0.534785i	0.121009	+	0.0879181i	−0.525635	+	0.850710i	$0.676172\pi$
$38$	0.118034	+	0.363271i	0.0191476	+	0.0589304i
$39$		0			0
$40$	−9.35410	−	6.79615i	−1.47901	−	1.07457i
$41$	−3.35410	+	2.43690i	−0.523823	+	0.380579i	−0.818042	−	0.575158i	$-0.804940\pi$
$41$	−3.35410	+	2.43690i	−0.523823	+	0.380579i	0.294219	+	0.955738i	$0.404940\pi$
$42$		0			0
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$	0.809017	+	3.21644i	0.121964	+	0.484897i
$45$		0			0
$46$	−2.50000	+	7.69421i	−0.368605	+	1.13445i
$47$	1.61803	−	1.17557i	0.236015	−	0.171475i	−0.463491	−	0.886101i	$-0.653403\pi$
$47$	1.61803	−	1.17557i	0.236015	−	0.171475i	0.699506	+	0.714627i	$0.253403\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	3.04508	+	9.37181i	0.430640	+	1.32537i
$51$		0			0
$52$	2.61803	−	1.90211i	0.363056	−	0.263776i
$53$	3.14590	−	9.68208i	0.432122	−	1.32994i	−0.463885	−	0.885896i	$-0.653545\pi$
$53$	3.14590	−	9.68208i	0.432122	−	1.32994i	0.896007	−	0.444040i	$-0.146455\pi$
$54$		0			0
$55$	4.76393	−	11.8617i	0.642368	−	1.59943i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−1.61803	+	1.17557i	−0.212458	+	0.154360i
$59$	9.09017	+	6.60440i	1.18344	+	0.859819i	0.992555	−	0.121794i	$-0.0388646\pi$
$59$	9.09017	+	6.60440i	1.18344	+	0.859819i	0.190884	+	0.981613i	$0.438865\pi$
$60$		0			0
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	−0.956653	−	0.291230i	$-0.905935\pi$
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	0.602768	−	0.797917i	$-0.294065\pi$
$62$	−6.73607	−	4.89404i	−0.855481	−	0.621544i
$63$		0			0
$64$	2.16312	−	6.65740i	0.270390	−	0.832174i
$65$	−12.4721			−1.54698
$66$		0			0
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	0.354102	−	1.08981i	0.0429412	−	0.132159i
$69$		0			0
$70$	3.11803	+	2.26538i	0.372676	+	0.270765i
$71$	2.76393	+	8.50651i	0.328018	+	1.00954i	0.970060	+	0.242867i	$0.0780878\pi$
$71$	2.76393	+	8.50651i	0.328018	+	1.00954i	−0.642041	+	0.766670i	$0.721912\pi$
$72$		0			0
$73$	0.618034	+	0.449028i	0.0723354	+	0.0525547i	0.623365	−	0.781931i	$-0.285765\pi$
$73$	0.618034	+	0.449028i	0.0723354	+	0.0525547i	−0.551030	+	0.834486i	$0.685765\pi$
$74$	0.736068	−	0.534785i	0.0855662	−	0.0621675i
$75$		0			0
$76$	−0.381966			−0.0438145
$77$	−0.809017	−	3.21644i	−0.0921960	−	0.366547i
$78$		0			0
$79$	−4.32624	+	13.3148i	−0.486740	+	1.49803i	0.342705	+	0.939443i	$0.388657\pi$
$79$	−4.32624	+	13.3148i	−0.486740	+	1.49803i	−0.829445	+	0.558588i	$0.811343\pi$
$80$	−3.11803	+	2.26538i	−0.348607	+	0.253278i
$81$		0			0
$82$	1.28115	+	3.94298i	0.141480	+	0.435430i
$83$	4.61803	+	14.2128i	0.506895	+	1.56006i	0.797561	+	0.603238i	$0.206123\pi$
$83$	4.61803	+	14.2128i	0.506895	+	1.56006i	−0.290666	+	0.956825i	$0.593877\pi$
$84$		0			0
$85$	−3.57295	+	2.59590i	−0.387541	+	0.281565i
$86$	1.00000	−	3.07768i	0.107833	−	0.331875i
$87$		0			0
$88$	9.92705	+	0.673542i	1.05823	+	0.0717998i
$89$	10.0902			1.06956			0.534778	−	0.844993i	$-0.320395\pi$
$89$	10.0902			1.06956			0.534778	+	0.844993i	$0.320395\pi$
$90$		0			0
$91$	−2.61803	+	1.90211i	−0.274445	+	0.199396i
$92$	−6.54508	−	4.75528i	−0.682372	−	0.495772i
$93$		0			0
$94$	−0.618034	−	1.90211i	−0.0637453	−	0.196188i
$95$	1.19098	+	0.865300i	0.122192	+	0.0887779i
$96$		0			0
$97$	−3.85410	+	11.8617i	−0.391325	+	1.20437i	0.540462	+	0.841368i	$0.318249\pi$
$97$	−3.85410	+	11.8617i	−0.391325	+	1.20437i	−0.931787	+	0.363006i	$0.881751\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−9.85410			−0.985410
$101$	−2.80902	+	8.64527i	−0.279508	+	0.860236i	0.708484	+	0.705727i	$0.249380\pi$
$101$	−2.80902	+	8.64527i	−0.279508	+	0.860236i	−0.987991	+	0.154509i	$0.950620\pi$
$102$		0			0
$103$	−4.30902	−	3.13068i	−0.424580	−	0.308475i	0.354898	−	0.934905i	$-0.384516\pi$
$103$	−4.30902	−	3.13068i	−0.424580	−	0.308475i	−0.779478	+	0.626430i	$0.784516\pi$
$104$	−3.00000	−	9.23305i	−0.294174	−	0.905375i
$105$		0			0
$106$	−8.23607	−	5.98385i	−0.799958	−	0.581203i
$107$	13.0172	−	9.45756i	1.25842	−	0.914297i	0.259743	−	0.965678i	$-0.416362\pi$
$107$	13.0172	−	9.45756i	1.25842	−	0.914297i	0.998679	+	0.0513805i	$0.0163621\pi$
$108$		0			0
$109$	−9.56231			−0.915903			−0.457951	−	0.888977i	$-0.651417\pi$
$109$	−9.56231			−0.915903			−0.457951	+	0.888977i	$0.651417\pi$
$110$	−9.80902	−	8.19624i	−0.935253	−	0.781481i
$111$		0			0
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	4.23607	−	3.07768i	0.398496	−	0.289524i	−0.370432	−	0.928859i	$-0.620790\pi$
$113$	4.23607	−	3.07768i	0.398496	−	0.289524i	0.768928	+	0.639335i	$0.220790\pi$
$114$		0			0
$115$	9.63525	+	29.6543i	0.898492	+	2.76527i
$116$	−0.618034	−	1.90211i	−0.0573830	−	0.176607i
$117$		0			0
$118$	9.09017	−	6.60440i	0.836818	−	0.607984i
$119$	−0.354102	+	1.08981i	−0.0324605	+	0.0999031i
$120$		0			0
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	−8.94427			−0.809776
$123$		0			0
$124$	6.73607	−	4.89404i	0.604917	−	0.439498i
$125$	15.1353	+	10.9964i	1.35374	+	0.983548i
$126$		0			0
$127$	0.381966	+	1.17557i	0.0338940	+	0.104315i	0.966572	−	0.256394i	$-0.0825346\pi$
$127$	0.381966	+	1.17557i	0.0338940	+	0.104315i	−0.932678	+	0.360709i	$0.882535\pi$
$128$	2.42705	+	1.76336i	0.214523	+	0.155860i
$129$		0			0
$130$	−3.85410	+	11.8617i	−0.338027	+	1.04034i
$131$	−15.7082			−1.37243			−0.686216	−	0.727398i	$-0.740730\pi$
$131$	−15.7082			−1.37243			−0.686216	+	0.727398i	$0.740730\pi$
$132$		0			0
$133$	0.381966			0.0331207
$134$	2.47214	−	7.60845i	0.213560	−	0.657270i
$135$		0			0
$136$	−2.78115	−	2.02063i	−0.238482	−	0.173267i
$137$	−3.47214	−	10.6861i	−0.296645	−	0.912978i	−0.982664	−	0.185395i	$-0.940644\pi$
$137$	−3.47214	−	10.6861i	−0.296645	−	0.912978i	0.686019	−	0.727583i	$-0.259356\pi$
$138$		0			0
$139$	16.0172	+	11.6372i	1.35856	+	0.987054i	0.998535	+	0.0541123i	$0.0172329\pi$
$139$	16.0172	+	11.6372i	1.35856	+	0.987054i	0.360028	+	0.932941i	$0.382767\pi$
$140$	−3.11803	+	2.26538i	−0.263522	+	0.191460i
$141$		0			0
$142$	8.94427			0.750587
$143$	9.09017	−	5.70634i	0.760158	−	0.477188i
$144$		0			0
$145$	−2.38197	+	7.33094i	−0.197812	+	0.608801i
$146$	0.618034	−	0.449028i	0.0511489	−	0.0371618i
$147$		0			0
$148$	0.281153	+	0.865300i	0.0231106	+	0.0711272i
$149$	6.18034	+	19.0211i	0.506313	+	1.55827i	0.798552	+	0.601926i	$0.205600\pi$
$149$	6.18034	+	19.0211i	0.506313	+	1.55827i	−0.292239	+	0.956345i	$0.594400\pi$
$150$		0			0
$151$	1.61803	−	1.17557i	0.131674	−	0.0956666i	−0.519999	−	0.854167i	$-0.674068\pi$
$151$	1.61803	−	1.17557i	0.131674	−	0.0956666i	0.651673	+	0.758500i	$0.274068\pi$
$152$	−0.354102	+	1.08981i	−0.0287215	+	0.0883956i
$153$		0			0
$154$	−3.30902	−	0.224514i	−0.266648	−	0.0180919i
$155$	−32.0902			−2.57754
$156$		0			0
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	11.3262	+	8.22899i	0.901067	+	0.654664i
$159$		0			0
$160$	−5.95492	−	18.3273i	−0.470777	−	1.44890i
$161$	6.54508	+	4.75528i	0.515825	+	0.374769i
$162$		0			0
$163$	6.61803	−	20.3682i	0.518364	−	1.59536i	−0.258711	−	0.965955i	$-0.583298\pi$
$163$	6.61803	−	20.3682i	0.518364	−	1.59536i	0.777076	−	0.629407i	$-0.216702\pi$
$164$	−4.14590			−0.323740
$165$		0			0
$166$	14.9443			1.15990
$167$	4.38197	−	13.4863i	0.339087	−	1.04360i	−0.625587	−	0.780154i	$-0.715141\pi$
$167$	4.38197	−	13.4863i	0.339087	−	1.04360i	0.964674	−	0.263447i	$-0.0848595\pi$
$168$		0			0
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$	1.36475	+	4.20025i	0.104671	+	0.322145i
$171$		0			0
$172$	2.61803	+	1.90211i	0.199623	+	0.145035i
$173$	10.6353	−	7.72696i	0.808583	−	0.587470i	−0.104836	−	0.994490i	$-0.533432\pi$
$173$	10.6353	−	7.72696i	0.808583	−	0.587470i	0.913420	+	0.407019i	$0.133432\pi$
$174$		0			0
$175$	9.85410			0.744900
$176$	1.23607	−	3.07768i	0.0931721	−	0.231989i
$177$		0			0
$178$	3.11803	−	9.59632i	0.233707	−	0.719275i
$179$	8.59017	−	6.24112i	0.642059	−	0.466483i	−0.218498	−	0.975837i	$-0.570116\pi$
$179$	8.59017	−	6.24112i	0.642059	−	0.466483i	0.860557	+	0.509354i	$0.170116\pi$
$180$		0			0
$181$	−0.326238	−	1.00406i	−0.0242491	−	0.0746310i	0.938200	−	0.346095i	$-0.112492\pi$
$181$	−0.326238	−	1.00406i	−0.0242491	−	0.0746310i	−0.962449	+	0.271464i	$0.912492\pi$
$182$	1.00000	+	3.07768i	0.0741249	+	0.228133i
$183$		0			0
$184$	−19.6353	+	14.2658i	−1.44753	+	1.05169i
$185$	1.08359	−	3.33495i	0.0796673	−	0.245191i
$186$		0			0
$187$	1.41641	−	3.52671i	0.103578	−	0.257899i
$188$	2.00000			0.145865
$189$		0			0
$190$	1.19098	−	0.865300i	0.0864030	−	0.0627754i
$191$	12.3541	+	8.97578i	0.893911	+	0.649465i	0.936895	−	0.349611i	$-0.113686\pi$
$191$	12.3541	+	8.97578i	0.893911	+	0.649465i	−0.0429835	+	0.999076i	$0.513686\pi$
$192$		0			0
$193$	6.37132	+	19.6089i	0.458618	+	1.41148i	0.866835	+	0.498596i	$0.166151\pi$
$193$	6.37132	+	19.6089i	0.458618	+	1.41148i	−0.408217	+	0.912885i	$0.633849\pi$
$194$	10.0902	+	7.33094i	0.724432	+	0.526331i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−4.00000			−0.284988			−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000			−0.284988			−0.142494	+	0.989796i	$0.545512\pi$
$198$		0			0
$199$	−0.381966			−0.0270769			−0.0135384	−	0.999908i	$-0.504310\pi$
$199$	−0.381966			−0.0270769			−0.0135384	+	0.999908i	$0.504310\pi$
$200$	−9.13525	+	28.1154i	−0.645960	+	1.98806i
$201$		0			0
$202$	7.35410	+	5.34307i	0.517433	+	0.375937i
$203$	0.618034	+	1.90211i	0.0433775	+	0.133502i
$204$		0			0
$205$	12.9271	+	9.39205i	0.902864	+	0.655969i
$206$	−4.30902	+	3.13068i	−0.300223	+	0.218125i
$207$		0			0
$208$	−3.23607			−0.224381
$209$	−1.26393	−	0.0857567i	−0.0874280	−	0.00593192i
$210$		0			0
$211$	−0.618034	+	1.90211i	−0.0425472	+	0.130947i	−0.970074	−	0.242810i	$-0.921931\pi$
$211$	−0.618034	+	1.90211i	−0.0425472	+	0.130947i	0.927527	+	0.373757i	$0.121931\pi$
$212$	8.23607	−	5.98385i	0.565655	−	0.410973i
$213$		0			0
$214$	−4.97214	−	15.3027i	−0.339888	−	1.04607i
$215$	−3.85410	−	11.8617i	−0.262848	−	0.808962i
$216$		0			0
$217$	−6.73607	+	4.89404i	−0.457274	+	0.332229i
$218$	−2.95492	+	9.09429i	−0.200132	+	0.615943i
$219$		0			0
$220$	10.8262	−	6.79615i	0.729905	−	0.458197i
$221$	−3.70820			−0.249441
$222$		0			0
$223$	3.07295	−	2.23263i	0.205780	−	0.149508i	−0.480122	−	0.877202i	$-0.659408\pi$
$223$	3.07295	−	2.23263i	0.205780	−	0.149508i	0.685902	+	0.727694i	$0.259408\pi$
$224$	−4.04508	−	2.93893i	−0.270274	−	0.196365i
$225$		0			0
$226$	−1.61803	−	4.97980i	−0.107630	−	0.331251i
$227$	−4.38197	−	3.18368i	−0.290841	−	0.211309i	0.432791	−	0.901494i	$-0.357529\pi$
$227$	−4.38197	−	3.18368i	−0.290841	−	0.211309i	−0.723632	+	0.690186i	$0.757529\pi$
$228$		0			0
$229$	5.18034	−	15.9434i	0.342326	−	1.05357i	−0.620673	−	0.784070i	$-0.713141\pi$
$229$	5.18034	−	15.9434i	0.342326	−	1.05357i	0.963000	−	0.269503i	$-0.0868595\pi$
$230$	31.1803			2.05597
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−2.38197	+	7.33094i	−0.156048	+	0.480266i	−0.998266	−	0.0588718i	$-0.981250\pi$
$233$	−2.38197	+	7.33094i	−0.156048	+	0.480266i	0.842218	+	0.539137i	$0.181250\pi$
$234$		0			0
$235$	−6.23607	−	4.53077i	−0.406796	−	0.295555i
$236$	3.47214	+	10.6861i	0.226017	+	0.695608i
$237$		0			0
$238$	0.927051	+	0.673542i	0.0600918	+	0.0436592i
$239$	15.0172	−	10.9106i	0.971383	−	0.705751i	0.0156169	−	0.999878i	$-0.495029\pi$
$239$	15.0172	−	10.9106i	0.971383	−	0.705751i	0.955766	+	0.294127i	$0.0950288\pi$
$240$		0			0
$241$	−12.9443			−0.833814			−0.416907	−	0.908949i	$-0.636886\pi$
$241$	−12.9443			−0.833814			−0.416907	+	0.908949i	$0.636886\pi$
$242$	10.8992	+	1.48584i	0.700626	+	0.0955135i
$243$		0			0
$244$	2.76393	−	8.50651i	0.176943	−	0.544573i
$245$	3.11803	−	2.26538i	0.199204	−	0.144730i
$246$		0			0
$247$	0.381966	+	1.17557i	0.0243039	+	0.0747998i
$248$	−7.71885	−	23.7562i	−0.490147	−	1.50852i
$249$		0			0
$250$	15.1353	−	10.9964i	0.957238	−	0.695474i
$251$	−0.562306	+	1.73060i	−0.0354924	+	0.109234i	−0.967233	−	0.253890i	$-0.918290\pi$
$251$	−0.562306	+	1.73060i	−0.0354924	+	0.109234i	0.931741	+	0.363124i	$0.118290\pi$
$252$		0			0
$253$	−20.5902	−	17.2048i	−1.29449	−	1.08165i
$254$	1.23607			0.0775578
$255$		0			0
$256$	13.7533	−	9.99235i	0.859581	−	0.624522i
$257$	0.309017	+	0.224514i	0.0192760	+	0.0140048i	0.597382	−	0.801957i	$-0.296208\pi$
$257$	0.309017	+	0.224514i	0.0192760	+	0.0140048i	−0.578106	+	0.815962i	$0.696208\pi$
$258$		0			0
$259$	−0.281153	−	0.865300i	−0.0174700	−	0.0537671i
$260$	−10.0902	−	7.33094i	−0.625766	−	0.454645i
$261$		0			0
$262$	−4.85410	+	14.9394i	−0.299887	+	0.922959i
$263$	−22.5623			−1.39125			−0.695626	−	0.718404i	$-0.744873\pi$
$263$	−22.5623			−1.39125			−0.695626	+	0.718404i	$0.744873\pi$
$264$		0			0
$265$	−39.2361			−2.41025
$266$	0.118034	−	0.363271i	0.00723713	−	0.0222736i
$267$		0			0
$268$	6.47214	+	4.70228i	0.395349	+	0.287238i
$269$	2.43769	+	7.50245i	0.148629	+	0.457433i	0.997460	−	0.0712319i	$-0.0226930\pi$
$269$	2.43769	+	7.50245i	0.148629	+	0.457433i	−0.848831	+	0.528664i	$0.822693\pi$
$270$		0			0
$271$	−10.4443	−	7.58821i	−0.634444	−	0.460951i	0.223493	−	0.974706i	$-0.428254\pi$
$271$	−10.4443	−	7.58821i	−0.634444	−	0.460951i	−0.857937	+	0.513755i	$0.828254\pi$
$272$	−0.927051	+	0.673542i	−0.0562107	+	0.0408395i
$273$		0			0
$274$	−11.2361			−0.678796
$275$	−32.6074	−	2.21238i	−1.96630	−	0.133412i
$276$		0			0
$277$	−9.44427	+	29.0665i	−0.567451	+	1.74644i	0.0931022	+	0.995657i	$0.470322\pi$
$277$	−9.44427	+	29.0665i	−0.567451	+	1.74644i	−0.660554	+	0.750779i	$0.729678\pi$
$278$	16.0172	−	11.6372i	0.960649	−	0.697952i
$279$		0			0
$280$	3.57295	+	10.9964i	0.213525	+	0.657161i
$281$	−5.85410	−	18.0171i	−0.349226	−	1.07481i	−0.959282	−	0.282450i	$-0.908853\pi$
$281$	−5.85410	−	18.0171i	−0.349226	−	1.07481i	0.610056	−	0.792359i	$-0.291147\pi$
$282$		0			0
$283$	−27.1525	+	19.7274i	−1.61405	+	1.17267i	−0.765787	+	0.643095i	$0.777650\pi$
$283$	−27.1525	+	19.7274i	−1.61405	+	1.17267i	−0.848261	+	0.529579i	$0.822350\pi$
$284$	−2.76393	+	8.50651i	−0.164009	+	0.504768i
$285$		0			0
$286$	−2.61803	−	10.4086i	−0.154808	−	0.615475i
$287$	4.14590			0.244725
$288$		0			0
$289$	12.6910	−	9.22054i	0.746528	−	0.542385i
$290$	6.23607	+	4.53077i	0.366195	+	0.266056i
$291$		0			0
$292$	0.236068	+	0.726543i	0.0138148	+	0.0425177i
$293$	−3.88197	−	2.82041i	−0.226787	−	0.164770i	0.468590	−	0.883416i	$-0.344762\pi$
$293$	−3.88197	−	2.82041i	−0.226787	−	0.164770i	−0.695376	+	0.718646i	$0.744762\pi$
$294$		0			0
$295$	13.3820	−	41.1855i	0.779128	−	2.39791i
$296$	2.72949			0.158648
$297$		0			0
$298$	20.0000			1.15857
$299$	−8.09017	+	24.8990i	−0.467867	+	1.43995i
$300$		0			0
$301$	−2.61803	−	1.90211i	−0.150901	−	0.109636i
$302$	−0.618034	−	1.90211i	−0.0355639	−	0.109454i
$303$		0			0
$304$	0.309017	+	0.224514i	0.0177233	+	0.0128768i
$305$	−27.8885	+	20.2622i	−1.59689	+	1.16021i
$306$		0			0
$307$	9.27051			0.529096			0.264548	−	0.964373i	$-0.414777\pi$
$307$	9.27051			0.529096			0.264548	+	0.964373i	$0.414777\pi$
$308$	1.23607	−	3.07768i	0.0704315	−	0.175367i
$309$		0			0
$310$	−9.91641	+	30.5196i	−0.563214	+	1.73339i
$311$	−4.23607	+	3.07768i	−0.240205	+	0.174519i	−0.701375	−	0.712793i	$-0.747430\pi$
$311$	−4.23607	+	3.07768i	−0.240205	+	0.174519i	0.461169	+	0.887312i	$0.347430\pi$
$312$		0			0
$313$	−9.94427	−	30.6053i	−0.562083	−	1.72992i	−0.676462	−	0.736478i	$-0.736488\pi$
$313$	−9.94427	−	30.6053i	−0.562083	−	1.72992i	0.114378	−	0.993437i	$-0.463512\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$		0			0
$316$	−11.3262	+	8.22899i	−0.637151	+	0.462917i
$317$	−6.67376	+	20.5397i	−0.374836	+	1.15363i	0.568754	+	0.822508i	$0.307426\pi$
$317$	−6.67376	+	20.5397i	−0.374836	+	1.15363i	−0.943589	+	0.331118i	$0.892574\pi$
$318$		0			0
$319$	−1.61803	−	6.43288i	−0.0905925	−	0.360172i
$320$	−26.9787			−1.50816
$321$		0			0
$322$	6.54508	−	4.75528i	0.364743	−	0.265002i
$323$	0.354102	+	0.257270i	0.0197028	+	0.0143149i
$324$		0			0
$325$	9.85410	+	30.3278i	0.546607	+	1.68228i
$326$	−17.3262	−	12.5882i	−0.959612	−	0.697199i
$327$		0			0
$328$	−3.84346	+	11.8290i	−0.212220	+	0.653145i
$329$	−2.00000			−0.110264
$330$		0			0
$331$	−14.3607			−0.789334			−0.394667	−	0.918824i	$-0.629140\pi$
$331$	−14.3607			−0.789334			−0.394667	+	0.918824i	$0.629140\pi$
$332$	−4.61803	+	14.2128i	−0.253448	+	0.780031i
$333$		0			0
$334$	−11.4721	−	8.33499i	−0.627727	−	0.456071i
$335$	−9.52786	−	29.3238i	−0.520563	−	1.60213i
$336$		0			0
$337$	27.3885	+	19.8989i	1.49195	+	1.08396i	0.973454	+	0.228884i	$0.0735076\pi$
$337$	27.3885	+	19.8989i	1.49195	+	1.08396i	0.518495	+	0.855080i	$0.326492\pi$
$338$	2.04508	−	1.48584i	0.111238	−	0.0808191i
$339$		0			0
$340$	−4.41641			−0.239513
$341$	23.3885	−	14.6821i	1.26656	−	0.795081i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	7.85410	−	5.70634i	0.423465	−	0.307665i
$345$		0			0
$346$	−4.06231	−	12.5025i	−0.218391	−	0.672138i
$347$	4.51722	+	13.9026i	0.242497	+	0.746329i	0.996038	+	0.0889284i	$0.0283442\pi$
$347$	4.51722	+	13.9026i	0.242497	+	0.746329i	−0.753541	+	0.657401i	$0.771656\pi$
$348$		0			0
$349$	−22.0344	+	16.0090i	−1.17948	+	0.856940i	−0.992113	−	0.125351i	$-0.959994\pi$
$349$	−22.0344	+	16.0090i	−1.17948	+	0.856940i	−0.187364	+	0.982291i	$0.559994\pi$
$350$	3.04508	−	9.37181i	0.162767	−	0.500944i
$351$		0			0
$352$	12.7254	+	10.6331i	0.678267	+	0.566748i
$353$	−3.52786			−0.187769			−0.0938846	−	0.995583i	$-0.529928\pi$
$353$	−3.52786			−0.187769			−0.0938846	+	0.995583i	$0.529928\pi$
$354$		0			0
$355$	27.8885	−	20.2622i	1.48017	−	1.07541i
$356$	8.16312	+	5.93085i	0.432644	+	0.314335i
$357$		0			0
$358$	−3.28115	−	10.0984i	−0.173414	−	0.533714i
$359$	−17.8262	−	12.9515i	−0.940833	−	0.683555i	0.00778815	−	0.999970i	$-0.497521\pi$
$359$	−17.8262	−	12.9515i	−0.940833	−	0.683555i	−0.948621	+	0.316415i	$0.897521\pi$
$360$		0			0
$361$	−5.82624	+	17.9313i	−0.306644	+	0.943754i
$362$	−1.05573			−0.0554878
$363$		0			0
$364$	−3.23607			−0.169616
$365$	0.909830	−	2.80017i	0.0476227	−	0.146568i
$366$		0			0
$367$	13.9721	+	10.1514i	0.729340	+	0.529896i	0.889354	−	0.457218i	$-0.151154\pi$
$367$	13.9721	+	10.1514i	0.729340	+	0.529896i	−0.160015	+	0.987115i	$0.551154\pi$
$368$	2.50000	+	7.69421i	0.130322	+	0.401088i
$369$		0			0
$370$	−2.83688	−	2.06111i	−0.147482	−	0.107152i
$371$	−8.23607	+	5.98385i	−0.427595	+	0.310666i
$372$		0			0
$373$	−7.67376			−0.397332			−0.198666	−	0.980067i	$-0.563661\pi$
$373$	−7.67376			−0.397332			−0.198666	+	0.980067i	$0.563661\pi$
$374$	−2.91641	−	2.43690i	−0.150804	−	0.126009i
$375$		0			0
$376$	1.85410	−	5.70634i	0.0956180	−	0.294282i
$377$	−5.23607	+	3.80423i	−0.269671	+	0.195928i
$378$		0			0
$379$	−2.00000	−	6.15537i	−0.102733	−	0.316180i	0.886459	−	0.462808i	$-0.153158\pi$
$379$	−2.00000	−	6.15537i	−0.102733	−	0.316180i	−0.989192	+	0.146628i	$0.953158\pi$
$380$	0.454915	+	1.40008i	0.0233366	+	0.0718228i
$381$		0			0
$382$	12.3541	−	8.97578i	0.632091	−	0.459241i
$383$	9.56231	−	29.4298i	0.488611	−	1.50379i	−0.338071	−	0.941121i	$-0.609774\pi$
$383$	9.56231	−	29.4298i	0.488611	−	1.50379i	0.826682	−	0.562669i	$-0.190226\pi$
$384$		0			0
$385$	−10.8262	+	6.79615i	−0.551756	+	0.346364i
$386$	20.6180			1.04943
$387$		0			0
$388$	−10.0902	+	7.33094i	−0.512251	+	0.372172i
$389$	−0.145898	−	0.106001i	−0.00739732	−	0.00537447i	0.584080	−	0.811696i	$-0.301455\pi$
$389$	−0.145898	−	0.106001i	−0.00739732	−	0.00537447i	−0.591478	+	0.806321i	$0.701455\pi$
$390$		0			0
$391$	2.86475	+	8.81678i	0.144876	+	0.445884i
$392$	2.42705	+	1.76336i	0.122585	+	0.0890629i
$393$		0			0
$394$	−1.23607	+	3.80423i	−0.0622722	+	0.191654i
$395$	53.9574			2.71489
$396$		0			0
$397$	−16.6525			−0.835764			−0.417882	−	0.908501i	$-0.637227\pi$
$397$	−16.6525			−0.835764			−0.417882	+	0.908501i	$0.637227\pi$
$398$	−0.118034	+	0.363271i	−0.00591651	+	0.0182091i
$399$		0			0
$400$	7.97214	+	5.79210i	0.398607	+	0.289605i
$401$	−2.94427	−	9.06154i	−0.147030	−	0.452512i	0.850237	−	0.526401i	$-0.176459\pi$
$401$	−2.94427	−	9.06154i	−0.147030	−	0.452512i	−0.997266	+	0.0738893i	$0.976459\pi$
$402$		0			0
$403$	−21.7984	−	15.8374i	−1.08585	−	0.788919i
$404$	−7.35410	+	5.34307i	−0.365880	+	0.265828i
$405$		0			0
$406$	2.00000			0.0992583
$407$	0.736068	+	2.92641i	0.0364855	+	0.145057i
$408$		0			0
$409$	10.2705	−	31.6094i	0.507844	−	1.56298i	−0.288092	−	0.957603i	$-0.593021\pi$
$409$	10.2705	−	31.6094i	0.507844	−	1.56298i	0.795936	−	0.605381i	$-0.206979\pi$
$410$	12.9271	−	9.39205i	0.638422	−	0.463840i
$411$		0			0
$412$	−1.64590	−	5.06555i	−0.0810876	−	0.249562i
$413$	−3.47214	−	10.6861i	−0.170853	−	0.525830i
$414$		0			0
$415$	46.5967	−	33.8545i	2.28734	−	1.66185i
$416$	5.00000	−	15.3884i	0.245145	−	0.754479i
$417$		0			0
$418$	−0.472136	+	1.17557i	−0.0230929	+	0.0574990i
$419$	−19.2361			−0.939743			−0.469872	−	0.882735i	$-0.655700\pi$
$419$	−19.2361			−0.939743			−0.469872	+	0.882735i	$0.655700\pi$
$420$		0			0
$421$	−9.16312	+	6.65740i	−0.446583	+	0.324462i	−0.788245	−	0.615361i	$-0.789010\pi$
$421$	−9.16312	+	6.65740i	−0.446583	+	0.324462i	0.341662	+	0.939823i	$0.389010\pi$
$422$	1.61803	+	1.17557i	0.0787647	+	0.0572259i
$423$		0			0
$424$	−9.43769	−	29.0462i	−0.458335	−	1.41061i
$425$	9.13525	+	6.63715i	0.443125	+	0.321949i
$426$		0			0
$427$	−2.76393	+	8.50651i	−0.133756	+	0.411659i
$428$	16.0902			0.777748
$429$		0			0
$430$	−12.4721			−0.601460
$431$	−2.80902	+	8.64527i	−0.135306	+	0.416428i	−0.995637	−	0.0933066i	$-0.970256\pi$
$431$	−2.80902	+	8.64527i	−0.135306	+	0.416428i	0.860332	+	0.509734i	$0.170256\pi$
$432$		0			0
$433$	10.3262	+	7.50245i	0.496247	+	0.360545i	0.807582	−	0.589756i	$-0.200776\pi$
$433$	10.3262	+	7.50245i	0.496247	+	0.360545i	−0.311334	+	0.950300i	$0.600776\pi$
$434$	2.57295	+	7.91872i	0.123506	+	0.380111i
$435$		0			0
$436$	−7.73607	−	5.62058i	−0.370490	−	0.269177i
$437$	2.50000	−	1.81636i	0.119591	−	0.0868881i
$438$		0			0
$439$	2.79837			0.133559			0.0667795	−	0.997768i	$-0.478728\pi$
$439$	2.79837			0.133559			0.0667795	+	0.997768i	$0.478728\pi$
$440$	−9.35410	−	37.1895i	−0.445939	−	1.77294i
$441$		0			0
$442$	−1.14590	+	3.52671i	−0.0545048	+	0.167749i
$443$	13.0172	−	9.45756i	0.618467	−	0.449342i	−0.233919	−	0.972256i	$-0.575155\pi$
$443$	13.0172	−	9.45756i	0.618467	−	0.449342i	0.852386	+	0.522914i	$0.175155\pi$
$444$		0			0
$445$	−12.0172	−	36.9852i	−0.569671	−	1.75327i
$446$	−1.17376	−	3.61247i	−0.0555792	−	0.171055i
$447$		0			0
$448$	−5.66312	+	4.11450i	−0.267557	+	0.194392i
$449$	−1.88854	+	5.81234i	−0.0891259	+	0.274301i	−0.985678	−	0.168636i	$-0.946064\pi$
$449$	−1.88854	+	5.81234i	−0.0891259	+	0.274301i	0.896552	+	0.442938i	$0.146064\pi$
$450$		0			0
$451$	−13.7188	−	0.930812i	−0.645995	−	0.0438302i
$452$	5.23607			0.246284
$453$		0			0
$454$	−4.38197	+	3.18368i	−0.205656	+	0.149418i
$455$	10.0902	+	7.33094i	0.473034	+	0.343680i
$456$		0			0
$457$	1.09017	+	3.35520i	0.0509960	+	0.156950i	0.973311	−	0.229488i	$-0.0737053\pi$
$457$	1.09017	+	3.35520i	0.0509960	+	0.156950i	−0.922315	+	0.386438i	$0.873705\pi$
$458$	−13.5623	−	9.85359i	−0.633725	−	0.460428i
$459$		0			0
$460$	−9.63525	+	29.6543i	−0.449246	+	1.38264i
$461$	−38.3607			−1.78663			−0.893317	−	0.449426i	$-0.851628\pi$
$461$	−38.3607			−1.78663			−0.893317	+	0.449426i	$0.851628\pi$
$462$		0			0
$463$	−15.4164			−0.716461			−0.358231	−	0.933633i	$-0.616620\pi$
$463$	−15.4164			−0.716461			−0.358231	+	0.933633i	$0.616620\pi$
$464$	−0.618034	+	1.90211i	−0.0286915	+	0.0883034i
$465$		0			0
$466$	6.23607	+	4.53077i	0.288880	+	0.209884i
$467$	−4.56231	−	14.0413i	−0.211118	−	0.649755i	−0.999406	−	0.0344491i	$-0.989032\pi$
$467$	−4.56231	−	14.0413i	−0.211118	−	0.649755i	0.788288	−	0.615306i	$-0.210968\pi$
$468$		0			0
$469$	−6.47214	−	4.70228i	−0.298855	−	0.217131i
$470$	−6.23607	+	4.53077i	−0.287648	+	0.208989i
$471$		0			0
$472$	33.7082			1.55155
$473$	8.23607	+	6.88191i	0.378695	+	0.316431i
$474$		0			0
$475$	1.16312	−	3.57971i	0.0533676	−	0.164248i
$476$	−0.927051	+	0.673542i	−0.0424913	+	0.0308717i
$477$		0			0
$478$	−5.73607	−	17.6538i	−0.262362	−	0.807466i
$479$	8.94427	+	27.5276i	0.408674	+	1.25777i	0.917788	+	0.397071i	$0.129973\pi$
$479$	8.94427	+	27.5276i	0.408674	+	1.25777i	−0.509114	+	0.860699i	$0.670027\pi$
$480$		0			0
$481$	2.38197	−	1.73060i	0.108608	−	0.0789085i
$482$	−4.00000	+	12.3107i	−0.182195	+	0.560739i
$483$		0			0
$484$	−4.78115	+	9.90659i	−0.217325	+	0.450300i
$485$	48.0689			2.18270
$486$		0			0
$487$	28.1246	−	20.4337i	1.27445	−	0.925941i	0.275077	−	0.961422i	$-0.411296\pi$
$487$	28.1246	−	20.4337i	1.27445	−	0.925941i	0.999370	+	0.0354815i	$0.0112965\pi$
$488$	−21.7082	−	15.7719i	−0.982684	−	0.713962i
$489$		0			0
$490$	−1.19098	−	3.66547i	−0.0538031	−	0.165589i
$491$	12.3992	+	9.00854i	0.559567	+	0.406550i	0.831301	−	0.555823i	$-0.187597\pi$
$491$	12.3992	+	9.00854i	0.559567	+	0.406550i	−0.271733	+	0.962373i	$0.587597\pi$
$492$		0			0
$493$	−0.708204	+	2.17963i	−0.0318959	+	0.0981655i
$494$	1.23607			0.0556133
$495$		0			0
$496$	−8.32624			−0.373859
$497$	2.76393	−	8.50651i	0.123979	−	0.381569i
$498$		0			0
$499$	−3.09017	−	2.24514i	−0.138335	−	0.100506i	0.516466	−	0.856308i	$-0.327247\pi$
$499$	−3.09017	−	2.24514i	−0.138335	−	0.100506i	−0.654801	+	0.755802i	$0.727247\pi$
$500$	5.78115	+	17.7926i	0.258541	+	0.795707i
$501$		0			0
$502$	1.47214	+	1.06957i	0.0657046	+	0.0477372i
$503$	−22.1803	+	16.1150i	−0.988972	+	0.718531i	−0.959696	−	0.281041i	$-0.909320\pi$
$503$	−22.1803	+	16.1150i	−0.988972	+	0.718531i	−0.0292766	+	0.999571i	$0.509320\pi$
$504$		0			0
$505$	35.0344			1.55901
$506$	−22.7254	+	14.2658i	−1.01027	+	0.634194i
$507$		0			0
$508$	−0.381966	+	1.17557i	−0.0169470	+	0.0521575i
$509$	−13.8262	+	10.0453i	−0.612837	+	0.445252i	−0.850412	−	0.526117i	$-0.823647\pi$
$509$	−13.8262	+	10.0453i	−0.612837	+	0.445252i	0.237575	+	0.971369i	$0.423647\pi$
$510$		0			0
$511$	−0.236068	−	0.726543i	−0.0104430	−	0.0321403i
$512$	−3.39919	−	10.4616i	−0.150224	−	0.462343i
$513$		0			0
$514$	0.309017	−	0.224514i	0.0136302	−	0.00990289i
$515$	−6.34346	+	19.5232i	−0.279526	+	0.860293i
$516$		0			0
$517$	6.61803	+	0.449028i	0.291061	+	0.0197482i
$518$	−0.909830			−0.0399756
$519$		0			0
$520$	−30.2705	+	21.9928i	−1.32745	+	0.964449i
$521$	−7.59017	−	5.51458i	−0.332531	−	0.241598i	0.408973	−	0.912547i	$-0.365887\pi$
$521$	−7.59017	−	5.51458i	−0.332531	−	0.241598i	−0.741504	+	0.670948i	$0.765887\pi$
$522$		0			0
$523$	4.35410	+	13.4005i	0.190392	+	0.585965i	0.999999	−	0.00100602i	$-0.000320226\pi$
$523$	4.35410	+	13.4005i	0.190392	+	0.585965i	−0.809608	+	0.586971i	$0.800320\pi$
$524$	−12.7082	−	9.23305i	−0.555160	−	0.403348i
$525$		0			0
$526$	−6.97214	+	21.4580i	−0.304000	+	0.935614i
$527$	−9.54102			−0.415613
$528$		0			0
$529$	42.4508			1.84569
$530$	−12.1246	+	37.3157i	−0.526659	+	1.62089i
$531$		0			0
$532$	0.309017	+	0.224514i	0.0133976	+	0.00973392i
$533$	4.14590	+	12.7598i	0.179579	+	0.552687i
$534$		0			0
$535$	−50.1697	−	36.4504i	−2.16903	−	1.57589i
$536$	19.4164	−	14.1068i	0.838661	−	0.609323i
$537$		0			0
$538$	7.88854			0.340099
$539$	−1.23607	+	3.07768i	−0.0532412	+	0.132565i
$540$		0			0
$541$	3.13525	−	9.64932i	0.134795	−	0.414857i	−0.860763	−	0.509006i	$-0.830013\pi$
$541$	3.13525	−	9.64932i	0.134795	−	0.414857i	0.995558	+	0.0941492i	$0.0300131\pi$
$542$	−10.4443	+	7.58821i	−0.448620	+	0.325941i
$543$		0			0
$544$	−1.77051	−	5.44907i	−0.0759100	−	0.233627i
$545$	11.3885	+	35.0503i	0.487832	+	1.50139i
$546$		0			0
$547$	22.2705	−	16.1805i	0.952218	−	0.691827i	0.000887764	−	1.00000i	$-0.499717\pi$
$547$	22.2705	−	16.1805i	0.952218	−	0.691827i	0.951330	+	0.308173i	$0.0997174\pi$
$548$	3.47214	−	10.6861i	0.148322	−	0.456489i
$549$		0			0
$550$	−12.1803	+	30.3278i	−0.519371	+	1.29318i
$551$	0.763932			0.0325446
$552$		0			0
$553$	11.3262	−	8.22899i	0.481641	−	0.349932i
$554$	24.7254	+	17.9641i	1.05048	+	0.763220i
$555$		0			0
$556$	6.11803	+	18.8294i	0.259462	+	0.798543i
$557$	4.38197	+	3.18368i	0.185670	+	0.134897i	0.676737	−	0.736224i	$-0.263393\pi$
$557$	4.38197	+	3.18368i	0.185670	+	0.134897i	−0.491068	+	0.871121i	$0.663393\pi$
$558$		0			0
$559$	3.23607	−	9.95959i	0.136871	−	0.421246i
$560$	3.85410			0.162866
$561$		0			0
$562$	−18.9443			−0.799116
$563$	1.34752	−	4.14725i	0.0567914	−	0.174786i	−0.918637	−	0.395103i	$-0.870709\pi$
$563$	1.34752	−	4.14725i	0.0567914	−	0.174786i	0.975428	+	0.220317i	$0.0707091\pi$
$564$		0			0
$565$	−16.3262	−	11.8617i	−0.686850	−	0.499026i
$566$	10.3713	+	31.9196i	0.435939	+	1.34168i
$567$		0			0
$568$	21.7082	+	15.7719i	0.910856	+	0.661776i
$569$	3.38197	−	2.45714i	0.141779	−	0.103009i	−0.514635	−	0.857410i	$-0.672072\pi$
$569$	3.38197	−	2.45714i	0.141779	−	0.103009i	0.656414	+	0.754401i	$0.272072\pi$
$570$		0			0
$571$	−38.5410			−1.61289			−0.806446	−	0.591308i	$-0.798612\pi$
$571$	−38.5410			−1.61289			−0.806446	+	0.591308i	$0.798612\pi$
$572$	10.7082	+	0.726543i	0.447732	+	0.0303783i
$573$		0			0
$574$	1.28115	−	3.94298i	0.0534743	−	0.164577i
$575$	64.4959	−	46.8590i	2.68967	−	1.95416i
$576$		0			0
$577$	5.14590	+	15.8374i	0.214227	+	0.659321i	0.999208	+	0.0398017i	$0.0126726\pi$
$577$	5.14590	+	15.8374i	0.214227	+	0.659321i	−0.784981	+	0.619520i	$0.787327\pi$
$578$	−4.84752	−	14.9191i	−0.201630	−	0.620555i
$579$		0			0
$580$	−6.23607	+	4.53077i	−0.258939	+	0.188130i
$581$	4.61803	−	14.2128i	0.191588	−	0.589648i
$582$		0			0
$583$	28.5967	−	17.9516i	1.18436	−	0.743478i
$584$	2.29180			0.0948352
$585$		0			0
$586$	−3.88197	+	2.82041i	−0.160363	+	0.116510i
$587$	−25.7984	−	18.7436i	−1.06481	−	0.773632i	−0.0898401	−	0.995956i	$-0.528636\pi$
$587$	−25.7984	−	18.7436i	−1.06481	−	0.773632i	−0.974973	+	0.222324i	$0.928636\pi$
$588$		0			0
$589$	0.982779	+	3.02468i	0.0404947	+	0.124630i
$590$	−35.0344	−	25.4540i	−1.44235	−	1.04793i
$591$		0			0
$592$	0.281153	−	0.865300i	0.0115553	−	0.0355636i
$593$	−23.5623			−0.967588			−0.483794	−	0.875182i	$-0.660742\pi$
$593$	−23.5623			−0.967588			−0.483794	+	0.875182i	$0.660742\pi$
$594$		0			0
$595$	4.41641			0.181055
$596$	−6.18034	+	19.0211i	−0.253157	+	0.779136i
$597$		0			0
$598$	21.1803	+	15.3884i	0.866129	+	0.629279i
$599$	−5.73607	−	17.6538i	−0.234369	−	0.721315i	−0.997204	−	0.0747217i	$-0.976193\pi$
$599$	−5.73607	−	17.6538i	−0.234369	−	0.721315i	0.762835	−	0.646593i	$-0.223807\pi$
$600$		0			0
$601$	−4.85410	−	3.52671i	−0.198003	−	0.143858i	0.484366	−	0.874865i	$-0.339050\pi$
$601$	−4.85410	−	3.52671i	−0.198003	−	0.143858i	−0.682369	+	0.731008i	$0.739050\pi$
$602$	−2.61803	+	1.90211i	−0.106703	+	0.0775243i
$603$		0			0
$604$	2.00000			0.0813788
$605$	37.3500	−	20.0579i	1.51849	−	0.815471i
$606$		0			0
$607$	1.64590	−	5.06555i	0.0668049	−	0.205604i	−0.912082	−	0.410009i	$-0.865526\pi$
$607$	1.64590	−	5.06555i	0.0668049	−	0.205604i	0.978887	+	0.204404i	$0.0655257\pi$
$608$	−1.54508	+	1.12257i	−0.0626615	+	0.0455262i
$609$		0			0
$610$	10.6525	+	32.7849i	0.431306	+	1.32742i
$611$	−2.00000	−	6.15537i	−0.0809113	−	0.249019i
$612$		0			0
$613$	−0.690983	+	0.502029i	−0.0279085	+	0.0202767i	−0.601652	−	0.798758i	$-0.705491\pi$
$613$	−0.690983	+	0.502029i	−0.0279085	+	0.0202767i	0.573744	+	0.819035i	$0.305491\pi$
$614$	2.86475	−	8.81678i	0.115612	−	0.355816i
$615$		0			0
$616$	−7.63525	−	6.37988i	−0.307633	−	0.257053i
$617$	−13.3475			−0.537351			−0.268676	−	0.963231i	$-0.586586\pi$
$617$	−13.3475			−0.537351			−0.268676	+	0.963231i	$0.586586\pi$
$618$		0			0
$619$	−21.4443	+	15.5802i	−0.861918	+	0.626220i	−0.928406	−	0.371567i	$-0.878821\pi$
$619$	−21.4443	+	15.5802i	−0.861918	+	0.626220i	0.0664880	+	0.997787i	$0.478821\pi$
$620$	−25.9615	−	18.8621i	−1.04264	−	0.757521i
$621$		0			0
$622$	1.61803	+	4.97980i	0.0648773	+	0.199672i
$623$	−8.16312	−	5.93085i	−0.327048	−	0.237615i
$624$		0			0
$625$	7.05573	−	21.7153i	0.282229	−	0.868612i
$626$	−32.1803			−1.28619
$627$		0			0
$628$	3.70820			0.147973
$629$	0.322173	−	0.991545i	0.0128459	−	0.0395355i
$630$		0			0
$631$	4.76393	+	3.46120i	0.189649	+	0.137788i	0.678558	−	0.734547i	$-0.262605\pi$
$631$	4.76393	+	3.46120i	0.189649	+	0.137788i	−0.488909	+	0.872335i	$0.662605\pi$
$632$	12.9787	+	39.9444i	0.516266	+	1.58890i
$633$		0			0
$634$	17.4721	+	12.6942i	0.693907	+	0.504153i
$635$	3.85410	−	2.80017i	0.152945	−	0.111121i
$636$		0			0
$637$	3.23607			0.128218
$638$	−6.61803	−	0.449028i	−0.262010	−	0.0177772i
$639$		0			0
$640$	3.57295	−	10.9964i	0.141233	−	0.434671i
$641$	−18.3262	+	13.3148i	−0.723843	+	0.525903i	−0.887610	−	0.460596i	$-0.847636\pi$
$641$	−18.3262	+	13.3148i	−0.723843	+	0.525903i	0.163767	+	0.986499i	$0.447636\pi$
$642$		0			0
$643$	−5.22949	−	16.0947i	−0.206231	−	0.634714i	−0.999661	−	0.0260516i	$-0.991707\pi$
$643$	−5.22949	−	16.0947i	−0.206231	−	0.634714i	0.793430	−	0.608662i	$-0.208293\pi$
$644$	2.50000	+	7.69421i	0.0985138	+	0.303194i
$645$		0			0
$646$	0.354102	−	0.257270i	0.0139320	−	0.0101222i
$647$	−4.43769	+	13.6578i	−0.174464	+	0.536944i	−0.999609	−	0.0279770i	$-0.991093\pi$
$647$	−4.43769	+	13.6578i	−0.174464	+	0.536944i	0.825145	+	0.564921i	$0.191093\pi$
$648$		0			0
$649$	9.09017	+	36.1401i	0.356820	+	1.41862i
$650$	31.8885			1.25077
$651$		0			0
$652$	17.3262	−	12.5882i	0.678548	−	0.492994i
$653$	8.00000	+	5.81234i	0.313064	+	0.227454i	0.733210	−	0.680002i	$-0.238021\pi$
$653$	8.00000	+	5.81234i	0.313064	+	0.227454i	−0.420146	+	0.907457i	$0.638021\pi$
$654$		0			0
$655$	18.7082	+	57.5779i	0.730990	+	2.24976i
$656$	3.35410	+	2.43690i	0.130956	+	0.0951449i
$657$		0			0
$658$	−0.618034	+	1.90211i	−0.0240935	+	0.0741521i
$659$	5.96556			0.232385			0.116193	−	0.993227i	$-0.462931\pi$
$659$	5.96556			0.232385			0.116193	+	0.993227i	$0.462931\pi$
$660$		0			0
$661$	21.7082			0.844351			0.422176	−	0.906514i	$-0.361267\pi$
$661$	21.7082			0.844351			0.422176	+	0.906514i	$0.361267\pi$
$662$	−4.43769	+	13.6578i	−0.172476	+	0.530826i
$663$		0			0
$664$	36.2705	+	26.3521i	1.40757	+	1.02266i
$665$	−0.454915	−	1.40008i	−0.0176408	−	0.0542929i
$666$		0			0
$667$	13.0902	+	9.51057i	0.506853	+	0.368251i
$668$	11.4721	−	8.33499i	0.443870	−	0.322491i
$669$		0			0
$670$	−30.8328			−1.19118
$671$	11.0557	−	27.5276i	0.426802	−	1.06269i
$672$		0			0
$673$	0.0344419	−	0.106001i	0.00132764	−	0.00408604i	−0.950391	−	0.311059i	$-0.899316\pi$
$673$	0.0344419	−	0.106001i	0.00132764	−	0.00408604i	0.951718	+	0.306973i	$0.0993162\pi$
$674$	27.3885	−	19.8989i	1.05497	−	0.766479i
$675$		0			0
$676$	0.781153	+	2.40414i	0.0300443	+	0.0924670i
$677$	3.67376	+	11.3067i	0.141194	+	0.434551i	0.996502	−	0.0835693i	$-0.0266320\pi$
$677$	3.67376	+	11.3067i	0.141194	+	0.434551i	−0.855308	+	0.518120i	$0.826632\pi$
$678$		0			0
$679$	10.0902	−	7.33094i	0.387225	−	0.281336i
$680$	−4.09424	+	12.6008i	−0.157007	+	0.483217i
$681$		0			0
$682$	−6.73607	−	26.7809i	−0.257937	−	1.02549i
$683$	23.9230			0.915388			0.457694	−	0.889110i	$-0.348676\pi$
$683$	23.9230			0.915388			0.457694	+	0.889110i	$0.348676\pi$
$684$		0			0
$685$	−35.0344	+	25.4540i	−1.33860	+	0.972548i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$		0			0
$688$	−1.00000	−	3.07768i	−0.0381246	−	0.117336i
$689$	−26.6525	−	19.3642i	−1.01538	−	0.737716i
$690$		0			0
$691$	−7.70163	+	23.7032i	−0.292984	+	0.901711i	0.690908	+	0.722943i	$0.257211\pi$
$691$	−7.70163	+	23.7032i	−0.292984	+	0.901711i	−0.983891	+	0.178768i	$0.942789\pi$
$692$	13.1459			0.499732
$693$		0			0
$694$	14.6180			0.554893
$695$	23.5795	−	72.5703i	0.894422	−	2.75275i
$696$		0			0
$697$	3.84346	+	2.79244i	0.145581	+	0.105771i
$698$	8.41641	+	25.9030i	0.318566	+	0.980445i
$699$		0			0
$700$	7.97214	+	5.79210i	0.301318	+	0.218921i
$701$	−27.5623	+	20.0252i	−1.04101	+	0.756341i	−0.970483	−	0.241169i	$-0.922469\pi$
$701$	−27.5623	+	20.0252i	−1.04101	+	0.756341i	−0.0705307	+	0.997510i	$0.522469\pi$
$702$		0			0
$703$	−0.347524			−0.0131071
$704$	19.6631	−	12.3435i	0.741082	−	0.465213i
$705$		0			0
$706$	−1.09017	+	3.35520i	−0.0410291	+	0.126275i
$707$	7.35410	−	5.34307i	0.276579	−	0.200947i
$708$		0			0
$709$	12.5729	+	38.6956i	0.472187	+	1.45324i	0.849714	+	0.527244i	$0.176774\pi$
$709$	12.5729	+	38.6956i	0.472187	+	1.45324i	−0.377527	+	0.925999i	$0.623226\pi$
$710$	−10.6525	−	32.7849i	−0.399780	−	1.23040i
$711$		0			0
$712$	24.4894	−	17.7926i	0.917777	−	0.666804i
$713$	−20.8156	+	64.0638i	−0.779550	+	2.39921i
$714$		0			0
$715$	−31.7426	−	26.5236i	−1.18711	−	0.991926i
$716$	10.6180			0.396815
$717$		0			0
$718$	−17.8262	+	12.9515i	−0.665269	+	0.483346i
$719$	36.5066	+	26.5236i	1.36147	+	0.989163i	0.998350	+	0.0574185i	$0.0182869\pi$
$719$	36.5066	+	26.5236i	1.36147	+	0.989163i	0.363115	+	0.931744i	$0.381713\pi$
$720$		0			0
$721$	1.64590	+	5.06555i	0.0612964	+	0.188651i
$722$	15.2533	+	11.0822i	0.567669	+	0.412435i
$723$		0			0
$724$	0.326238	−	1.00406i	0.0121245	−	0.0373155i
$725$	19.7082			0.731944
$726$		0			0
$727$	−16.7426			−0.620950			−0.310475	−	0.950581i	$-0.600488\pi$
$727$	−16.7426			−0.620950			−0.310475	+	0.950581i	$0.600488\pi$
$728$	−3.00000	+	9.23305i	−0.111187	+	0.342200i
$729$		0			0
$730$	−2.38197	−	1.73060i	−0.0881605	−	0.0640524i
$731$	−1.14590	−	3.52671i	−0.0423826	−	0.130440i
$732$		0			0
$733$	7.38197	+	5.36331i	0.272659	+	0.198098i	0.715709	−	0.698398i	$-0.246104\pi$
$733$	7.38197	+	5.36331i	0.272659	+	0.198098i	−0.443050	+	0.896497i	$0.646104\pi$
$734$	13.9721	−	10.1514i	0.515721	−	0.374693i
$735$		0			0
$736$	−40.4508			−1.49104
$737$	20.3607	+	17.0130i	0.749995	+	0.626683i
$738$		0			0
$739$	−8.34752	+	25.6910i	−0.307069	+	0.945060i	0.671829	+	0.740707i	$0.265509\pi$
$739$	−8.34752	+	25.6910i	−0.307069	+	0.945060i	−0.978897	+	0.204353i	$0.934491\pi$
$740$	2.83688	−	2.06111i	0.104286	−	0.0757681i
$741$		0			0
$742$	3.14590	+	9.68208i	0.115490	+	0.355440i
$743$	−0.517221	−	1.59184i	−0.0189750	−	0.0583990i	0.941121	−	0.338071i	$-0.109774\pi$
$743$	−0.517221	−	1.59184i	−0.0189750	−	0.0583990i	−0.960096	+	0.279672i	$0.909774\pi$
$744$		0			0
$745$	62.3607	−	45.3077i	2.28472	−	1.65995i
$746$	−2.37132	+	7.29818i	−0.0868203	+	0.267205i
$747$		0			0
$748$	3.21885	−	2.02063i	0.117693	−	0.0738814i
$749$	−16.0902			−0.587922
$750$		0			0
$751$	1.23607	−	0.898056i	0.0451048	−	0.0327705i	−0.565004	−	0.825088i	$-0.691126\pi$
$751$	1.23607	−	0.898056i	0.0451048	−	0.0327705i	0.610109	+	0.792317i	$0.291126\pi$
$752$	−1.61803	−	1.17557i	−0.0590036	−	0.0428686i
$753$		0			0
$754$	2.00000	+	6.15537i	0.0728357	+	0.224165i
$755$	−6.23607	−	4.53077i	−0.226954	−	0.164892i
$756$		0			0
$757$	−4.73607	+	14.5761i	−0.172135	+	0.529778i	−0.999491	−	0.0319002i	$-0.989844\pi$
$757$	−4.73607	+	14.5761i	−0.172135	+	0.529778i	0.827356	+	0.561678i	$0.189844\pi$
$758$	−6.47214			−0.235079
$759$		0			0
$760$	4.41641			0.160200
$761$	7.96556	−	24.5155i	0.288751	−	0.888685i	−0.696498	−	0.717559i	$-0.745259\pi$
$761$	7.96556	−	24.5155i	0.288751	−	0.888685i	0.985249	−	0.171126i	$-0.0547406\pi$
$762$		0			0
$763$	7.73607	+	5.62058i	0.280064	+	0.203479i
$764$	4.71885	+	14.5231i	0.170722	+	0.525428i
$765$		0			0
$766$	−25.0344	−	18.1886i	−0.904531	−	0.657180i
$767$	29.4164	−	21.3723i	1.06216	−	0.771708i
$768$		0			0
$769$	41.4164			1.49351			0.746757	−	0.665097i	$-0.231610\pi$
$769$	41.4164			1.49351			0.746757	+	0.665097i	$0.231610\pi$
$770$	3.11803	+	12.3965i	0.112366	+	0.446739i
$771$		0			0
$772$	−6.37132	+	19.6089i	−0.229309	+	0.705740i
$773$	−17.0344	+	12.3762i	−0.612686	+	0.445143i	−0.850359	−	0.526203i	$-0.823615\pi$
$773$	−17.0344	+	12.3762i	−0.612686	+	0.445143i	0.237673	+	0.971345i	$0.423615\pi$
$774$		0			0
$775$	25.3541	+	78.0319i	0.910746	+	2.80299i
$776$	11.5623	+	35.5851i	0.415063	+	1.27743i
$777$		0			0
$778$	−0.145898	+	0.106001i	−0.00523070	+	0.00380032i
$779$	0.489357	−	1.50609i	0.0175330	−	0.0539611i
$780$		0			0
$781$	−11.0557	+	27.5276i	−0.395605	+	0.985016i
$782$	9.27051			0.331513
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−11.5623	−	8.40051i	−0.412676	−	0.299827i
$786$		0			0
$787$	−6.57295	−	20.2295i	−0.234300	−	0.721102i	−0.997213	−	0.0746012i	$-0.976232\pi$
$787$	−6.57295	−	20.2295i	−0.234300	−	0.721102i	0.762913	−	0.646501i	$-0.223768\pi$
$788$	−3.23607	−	2.35114i	−0.115280	−	0.0837559i
$789$		0			0
$790$	16.6738	−	51.3166i	0.593226	−	1.82576i
$791$	−5.23607			−0.186173
$792$		0			0
$793$	−28.9443			−1.02784
$794$	−5.14590	+	15.8374i	−0.182621	+	0.562050i
$795$		0			0
$796$	−0.309017	−	0.224514i	−0.0109528	−	0.00795769i
$797$	7.19098	+	22.1316i	0.254718	+	0.783940i	0.993885	+	0.110419i	$0.0352192\pi$
$797$	7.19098	+	22.1316i	0.254718	+	0.783940i	−0.739167	+	0.673522i	$0.764781\pi$
$798$		0			0
$799$	−1.85410	−	1.34708i	−0.0655934	−	0.0476564i
$800$	−39.8607	+	28.9605i	−1.40929	+	1.02391i
$801$		0			0
$802$	−9.52786			−0.336441
$803$	0.618034	+	2.45714i	0.0218099	+	0.0867107i
$804$		0			0
$805$	9.63525	−	29.6543i	0.339598	−	1.04518i
$806$	−21.7984	+	15.8374i	−0.767815	+	0.557850i
$807$		0			0
$808$	8.42705	+	25.9358i	0.296463	+	0.912418i
$809$	−0.819660	−	2.52265i	−0.0288177	−	0.0886918i	0.935613	−	0.353027i	$-0.114848\pi$
$809$	−0.819660	−	2.52265i	−0.0288177	−	0.0886918i	−0.964431	+	0.264335i	$0.914848\pi$
$810$		0			0
$811$	−22.9443	+	16.6700i	−0.805682	+	0.585362i	−0.912576	−	0.408908i	$-0.865910\pi$
$811$	−22.9443	+	16.6700i	−0.805682	+	0.585362i	0.106893	+	0.994271i	$0.465910\pi$
$812$	−0.618034	+	1.90211i	−0.0216887	+	0.0667511i
$813$		0			0
$814$	3.01064	+	0.204270i	0.105523	+	0.00715964i
$815$	−82.5410			−2.89129
$816$		0			0
$817$	−1.00000	+	0.726543i	−0.0349856	+	0.0254185i
$818$	−26.8885	−	19.5357i	−0.940136	−	0.683049i
$819$		0			0
$820$	4.93769	+	15.1967i	0.172432	+	0.530690i
$821$	−11.6180	−	8.44100i	−0.405472	−	0.294593i	0.366294	−	0.930499i	$-0.380626\pi$
$821$	−11.6180	−	8.44100i	−0.405472	−	0.294593i	−0.771766	+	0.635906i	$0.780626\pi$
$822$		0			0
$823$	4.79837	−	14.7679i	0.167261	−	0.514776i	−0.831935	−	0.554873i	$-0.812767\pi$
$823$	4.79837	−	14.7679i	0.167261	−	0.514776i	0.999196	+	0.0400973i	$0.0127668\pi$
$824$	−15.9787			−0.556645
$825$		0			0
$826$	−11.2361			−0.390953
$827$	−3.50000	+	10.7719i	−0.121707	+	0.374575i	−0.993287	−	0.115678i	$-0.963096\pi$
$827$	−3.50000	+	10.7719i	−0.121707	+	0.374575i	0.871580	+	0.490254i	$0.163096\pi$
$828$		0			0
$829$	−8.94427	−	6.49839i	−0.310647	−	0.225699i	0.421527	−	0.906816i	$-0.361494\pi$
$829$	−8.94427	−	6.49839i	−0.310647	−	0.225699i	−0.732174	+	0.681117i	$0.761494\pi$
$830$	−17.7984	−	54.7778i	−0.617791	−	1.90136i
$831$		0			0
$832$	−18.3262	−	13.3148i	−0.635348	−	0.461607i
$833$	0.927051	−	0.673542i	0.0321204	−	0.0233368i
$834$		0			0
$835$	−54.6525			−1.89133
$836$	−0.972136	−	0.812299i	−0.0336220	−	0.0280940i
$837$		0			0
$838$	−5.94427	+	18.2946i	−0.205341	+	0.631976i
$839$	5.32624	−	3.86974i	0.183882	−	0.133598i	−0.492036	−	0.870575i	$-0.663747\pi$
$839$	5.32624	−	3.86974i	0.183882	−	0.133598i	0.675918	+	0.736977i	$0.263747\pi$
$840$		0			0
$841$	−7.72542	−	23.7764i	−0.266394	−	0.819876i
$842$	3.50000	+	10.7719i	0.120618	+	0.371224i
$843$		0			0
$844$	−1.61803	+	1.17557i	−0.0556950	+	0.0404648i
$845$	3.01064	−	9.26581i	0.103569	−	0.318753i
$846$		0			0
$847$	4.78115	−	9.90659i	0.164282	−	0.340395i
$848$	−10.1803			−0.349594
$849$		0			0
$850$	9.13525	−	6.63715i	0.313337	−	0.227652i
$851$	−5.95492	−	4.32650i	−0.204132	−	0.148310i
$852$		0			0
$853$	−0.708204	−	2.17963i	−0.0242484	−	0.0746290i	0.938200	−	0.346094i	$-0.112492\pi$
$853$	−0.708204	−	2.17963i	−0.0242484	−	0.0746290i	−0.962448	+	0.271465i	$0.912492\pi$
$854$	7.23607	+	5.25731i	0.247613	+	0.179901i
$855$		0			0
$856$	14.9164	−	45.9080i	0.509832	−	1.56910i
$857$	1.05573			0.0360630			0.0180315	−	0.999837i	$-0.494260\pi$
$857$	1.05573			0.0360630			0.0180315	+	0.999837i	$0.494260\pi$
$858$		0			0
$859$	29.8885			1.01978			0.509892	−	0.860238i	$-0.329685\pi$
$859$	29.8885			1.01978			0.509892	+	0.860238i	$0.329685\pi$
$860$	3.85410	−	11.8617i	0.131424	−	0.404481i
$861$		0			0
$862$	7.35410	+	5.34307i	0.250482	+	0.181986i
$863$	7.01064	+	21.5765i	0.238645	+	0.734474i	0.996617	+	0.0821868i	$0.0261904\pi$
$863$	7.01064	+	21.5765i	0.238645	+	0.734474i	−0.757972	+	0.652287i	$0.773810\pi$
$864$		0			0
$865$	−40.9894	−	29.7805i	−1.39368	−	1.01257i
$866$	10.3262	−	7.50245i	0.350900	−	0.254944i
$867$		0			0
$868$	−8.32624			−0.282611
$869$	−39.3262	+	24.6870i	−1.33405	+	0.837448i
$870$		0			0
$871$	8.00000	−	24.6215i	0.271070	−	0.834267i
$872$	−23.2082	+	16.8617i	−0.785929	+	0.571011i
$873$		0			0
$874$	−0.954915	−	2.93893i	−0.0323005	−	0.0994107i
$875$	−5.78115	−	17.7926i	−0.195439	−	0.601498i
$876$		0			0
$877$	1.32624	−	0.963568i	0.0447839	−	0.0325374i	−0.565168	−	0.824976i	$-0.691189\pi$
$877$	1.32624	−	0.963568i	0.0447839	−	0.0325374i	0.609952	+	0.792438i	$0.291189\pi$
$878$	0.864745	−	2.66141i	0.0291837	−	0.0898183i
$879$		0			0
$880$	−12.7533	−	0.865300i	−0.429913	−	0.0291693i
$881$	−22.4508			−0.756388			−0.378194	−	0.925726i	$-0.623455\pi$
$881$	−22.4508			−0.756388			−0.378194	+	0.925726i	$0.623455\pi$
$882$		0			0
$883$	4.61803	−	3.35520i	0.155409	−	0.112911i	−0.507363	−	0.861732i	$-0.669380\pi$
$883$	4.61803	−	3.35520i	0.155409	−	0.112911i	0.662772	+	0.748821i	$0.269380\pi$
$884$	−3.00000	−	2.17963i	−0.100901	−	0.0733088i
$885$		0			0
$886$	−4.97214	−	15.3027i	−0.167042	−	0.514103i
$887$	16.6180	+	12.0737i	0.557979	+	0.405395i	0.830719	−	0.556692i	$-0.187930\pi$
$887$	16.6180	+	12.0737i	0.557979	+	0.405395i	−0.272740	+	0.962088i	$0.587930\pi$
$888$		0			0
$889$	0.381966	−	1.17557i	0.0128107	−	0.0394274i
$890$	−38.8885			−1.30355
$891$		0			0
$892$	3.79837			0.127179
$893$	−0.236068	+	0.726543i	−0.00789971	+	0.0243128i
$894$		0			0
$895$	−33.1074	−	24.0539i	−1.10666	−	0.804034i
$896$	−0.927051	−	2.85317i	−0.0309706	−	0.0953177i
$897$		0			0
$898$	4.94427	+	3.59222i	0.164992	+	0.119874i
$899$	−13.4721	+	9.78808i	−0.449321	+	0.326451i
$900$		0			0
$901$	−11.6656			−0.388639
$902$	−5.12461	+	12.7598i	−0.170631	+	0.424854i
$903$		0			0
$904$	4.85410	−	14.9394i	0.161445	−	0.496877i
$905$	−3.29180	+	2.39163i	−0.109423	+	0.0795005i
$906$		0			0
$907$	−13.2148	−	40.6709i	−0.438790	−	1.35046i	−0.889153	−	0.457610i	$-0.848706\pi$
$907$	−13.2148	−	40.6709i	−0.438790	−	1.35046i	0.450363	−	0.892845i	$-0.351294\pi$
$908$	−1.67376	−	5.15131i	−0.0555457	−	0.170952i
$909$		0			0
$910$	10.0902	−	7.33094i	0.334486	−	0.243018i
$911$	8.94427	−	27.5276i	0.296337	−	0.912031i	−0.686432	−	0.727194i	$-0.740824\pi$
$911$	8.94427	−	27.5276i	0.296337	−	0.912031i	0.982769	−	0.184837i	$-0.0591759\pi$
$912$		0			0
$913$	−18.4721	+	45.9937i	−0.611338	+	1.52217i
$914$	3.52786			0.116691
$915$		0			0
$916$	13.5623	−	9.85359i	0.448111	−	0.325572i
$917$	12.7082	+	9.23305i	0.419662	+	0.304902i
$918$		0			0
$919$	−6.00000	−	18.4661i	−0.197922	−	0.609140i	−0.999930	−	0.0118276i	$-0.996235\pi$
$919$	−6.00000	−	18.4661i	−0.197922	−	0.609140i	0.802008	−	0.597313i	$-0.203765\pi$
$920$	75.6763	+	54.9820i	2.49497	+	1.81270i
$921$		0			0
$922$	−11.8541	+	36.4832i	−0.390394	+	1.20151i
$923$	28.9443			0.952712
$924$		0			0
$925$	−8.96556			−0.294786
$926$	−4.76393	+	14.6619i	−0.156553	+	0.481819i
$927$		0			0
$928$	−8.09017	−	5.87785i	−0.265573	−	0.192950i
$929$	1.29837	+	3.99598i	0.0425983	+	0.131104i	0.970094	−	0.242730i	$-0.0780429\pi$
$929$	1.29837	+	3.99598i	0.0425983	+	0.131104i	−0.927496	+	0.373834i	$0.878043\pi$
$930$		0			0
$931$	−0.309017	−	0.224514i	−0.0101276	−	0.00735815i
$932$	−6.23607	+	4.53077i	−0.204269	+	0.148410i
$933$		0			0
$934$	−14.7639			−0.483091
$935$	−14.6140	−	0.991545i	−0.477928	−	0.0324270i
$936$		0			0
$937$	−0.527864	+	1.62460i	−0.0172446	+	0.0530733i	−0.959309	−	0.282360i	$-0.908883\pi$
$937$	−0.527864	+	1.62460i	−0.0172446	+	0.0530733i	0.942064	+	0.335433i	$0.108883\pi$
$938$	−6.47214	+	4.70228i	−0.211323	+	0.153535i
$939$		0			0
$940$	−2.38197	−	7.33094i	−0.0776912	−	0.239109i
$941$	1.59017	+	4.89404i	0.0518381	+	0.159541i	0.973624	−	0.228158i	$-0.0732701\pi$
$941$	1.59017	+	4.89404i	0.0518381	+	0.159541i	−0.921786	+	0.387699i	$0.873270\pi$
$942$		0			0
$943$	27.1353	−	19.7149i	0.883645	−	0.642006i
$944$	3.47214	−	10.6861i	0.113008	−	0.347804i
$945$		0			0
$946$	9.09017	−	5.70634i	0.295547	−	0.185529i
$947$	43.5623			1.41558			0.707792	−	0.706421i	$-0.249691\pi$
$947$	43.5623			1.41558			0.707792	+	0.706421i	$0.249691\pi$
$948$		0			0
$949$	2.00000	−	1.45309i	0.0649227	−	0.0471691i
$950$	−3.04508	−	2.21238i	−0.0987956	−	0.0717792i
$951$		0			0
$952$	1.06231	+	3.26944i	0.0344295	+	0.105963i
$953$	−39.5066	−	28.7032i	−1.27974	−	0.929788i	−0.280198	−	0.959942i	$-0.590400\pi$
$953$	−39.5066	−	28.7032i	−1.27974	−	0.929788i	−0.999545	+	0.0301540i	$0.990400\pi$
$954$		0			0
$955$	18.1869	−	55.9736i	0.588515	−	1.81126i
$956$	18.5623			0.600348
$957$		0			0
$958$	28.9443			0.935147
$959$	−3.47214	+	10.6861i	−0.112121	+	0.345073i
$960$		0			0
$961$	−31.0066	−	22.5276i	−1.00021	−	0.726697i
$962$	−0.909830	−	2.80017i	−0.0293341	−	0.0902811i
$963$		0			0
$964$	−10.4721	−	7.60845i	−0.337285	−	0.245052i
$965$	64.2877	−	46.7078i	2.06950	−	1.50358i
$966$		0			0
$967$	−13.3050			−0.427858			−0.213929	−	0.976849i	$-0.568626\pi$
$967$	−13.3050			−0.427858			−0.213929	+	0.976849i	$0.568626\pi$
$968$	23.8328	+	22.8254i	0.766016	+	0.733635i
$969$		0			0
$970$	14.8541	−	45.7162i	0.476936	−	1.46786i
$971$	−13.0000	+	9.44505i	−0.417190	+	0.303106i	−0.776506	−	0.630110i	$-0.783010\pi$
$971$	−13.0000	+	9.44505i	−0.417190	+	0.303106i	0.359316	+	0.933216i	$0.383010\pi$
$972$		0			0
$973$	−6.11803	−	18.8294i	−0.196135	−	0.603642i
$974$	−10.7426	−	33.0625i	−0.344217	−	1.05939i
$975$		0			0
$976$	−7.23607	+	5.25731i	−0.231621	+	0.168282i
$977$	16.5066	−	50.8020i	0.528092	−	1.62530i	−0.230027	−	0.973184i	$-0.573881\pi$
$977$	16.5066	−	50.8020i	0.528092	−	1.62530i	0.758119	−	0.652116i	$-0.226119\pi$
$978$		0			0
$979$	25.6803	+	21.4580i	0.820747	+	0.685802i
$980$	3.85410			0.123115
$981$		0			0
$982$	12.3992	−	9.00854i	0.395674	−	0.287474i
$983$	31.9787	+	23.2339i	1.01996	+	0.741046i	0.966275	−	0.257512i	$-0.0829026\pi$
$983$	31.9787	+	23.2339i	1.01996	+	0.741046i	0.0536874	+	0.998558i	$0.482903\pi$
$984$		0			0
$985$	4.76393	+	14.6619i	0.151791	+	0.467166i
$986$	1.85410	+	1.34708i	0.0590466	+	0.0428999i
$987$		0			0
$988$	−0.381966	+	1.17557i	−0.0121520	+	0.0373999i
$989$	−26.1803			−0.832486
$990$		0			0
$991$	−12.6525			−0.401919			−0.200960	−	0.979600i	$-0.564406\pi$
$991$	−12.6525			−0.401919			−0.200960	+	0.979600i	$0.564406\pi$
$992$	12.8647	−	39.5936i	0.408456	−	1.25710i
$993$		0			0
$994$	−7.23607	−	5.25731i	−0.229514	−	0.166752i
$995$	0.454915	+	1.40008i	0.0144218	+	0.0443857i
$996$		0			0
$997$	−11.7639	−	8.54700i	−0.372567	−	0.270686i	0.385707	−	0.922621i	$-0.373957\pi$
$997$	−11.7639	−	8.54700i	−0.372567	−	0.270686i	−0.758275	+	0.651935i	$0.773957\pi$
$998$	−3.09017	+	2.24514i	−0.0978176	+	0.0710687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.c.64.1		4
3.2	odd	2		231.2.j.c.64.1	✓	4
11.4	even	5		7623.2.a.bu.1.1		2
11.5	even	5	inner	693.2.m.c.379.1		4
11.7	odd	10		7623.2.a.w.1.1		2
33.5	odd	10		231.2.j.c.148.1	yes	4
33.26	odd	10		2541.2.a.n.1.2		2
33.29	even	10		2541.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.64.1	✓	4	3.2	odd	2
231.2.j.c.148.1	yes	4	33.5	odd	10
693.2.m.c.64.1		4	1.1	even	1	trivial
693.2.m.c.379.1		4	11.5	even	5	inner
2541.2.a.n.1.2		2	33.26	odd	10
2541.2.a.bd.1.2		2	33.29	even	10
7623.2.a.w.1.1		2	11.7	odd	10
7623.2.a.bu.1.1		2	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.19098 - 3.66547i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.19098 - 3.66547i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.42705 - 1.76336i) q^{8} -3.85410 q^{10} +(2.54508 + 2.12663i) q^{11} +(1.00000 - 3.07768i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-0.354102 - 1.08981i) q^{17} +(-0.309017 + 0.224514i) q^{19} +(1.19098 - 3.66547i) q^{20} +(2.80902 - 1.76336i) q^{22} -8.09017 q^{23} +(-7.97214 + 5.79210i) q^{25} +(-2.61803 - 1.90211i) q^{26} +(-0.309017 - 0.951057i) q^{28} +(-1.61803 - 1.17557i) q^{29} +(2.57295 - 7.91872i) q^{31} +5.00000 q^{32} -1.14590 q^{34} +(-1.19098 + 3.66547i) q^{35} +(0.736068 + 0.534785i) q^{37} +(0.118034 + 0.363271i) q^{38} +(-9.35410 - 6.79615i) q^{40} +(-3.35410 + 2.43690i) q^{41} +3.23607 q^{43} +(0.809017 + 3.21644i) q^{44} +(-2.50000 + 7.69421i) q^{46} +(1.61803 - 1.17557i) q^{47} +(0.309017 + 0.951057i) q^{49} +(3.04508 + 9.37181i) q^{50} +(2.61803 - 1.90211i) q^{52} +(3.14590 - 9.68208i) q^{53} +(4.76393 - 11.8617i) q^{55} -3.00000 q^{56} +(-1.61803 + 1.17557i) q^{58} +(9.09017 + 6.60440i) q^{59} +(-2.76393 - 8.50651i) q^{61} +(-6.73607 - 4.89404i) q^{62} +(2.16312 - 6.65740i) q^{64} -12.4721 q^{65} +8.00000 q^{67} +(0.354102 - 1.08981i) q^{68} +(3.11803 + 2.26538i) q^{70} +(2.76393 + 8.50651i) q^{71} +(0.618034 + 0.449028i) q^{73} +(0.736068 - 0.534785i) q^{74} -0.381966 q^{76} +(-0.809017 - 3.21644i) q^{77} +(-4.32624 + 13.3148i) q^{79} +(-3.11803 + 2.26538i) q^{80} +(1.28115 + 3.94298i) q^{82} +(4.61803 + 14.2128i) q^{83} +(-3.57295 + 2.59590i) q^{85} +(1.00000 - 3.07768i) q^{86} +(9.92705 + 0.673542i) q^{88} +10.0902 q^{89} +(-2.61803 + 1.90211i) q^{91} +(-6.54508 - 4.75528i) q^{92} +(-0.618034 - 1.90211i) q^{94} +(1.19098 + 0.865300i) q^{95} +(-3.85410 + 11.8617i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} - 7 q^{5} - q^{7} + 3 q^{8}+O(q^{10}) \) 4 * q - q^2 + q^4 - 7 * q^5 - q^7 + 3 * q^8	\( 4 q - q^{2} + q^{4} - 7 q^{5} - q^{7} + 3 q^{8} - 2 q^{10} - q^{11} + 4 q^{13} - q^{14} + q^{16} + 12 q^{17} + q^{19} + 7 q^{20} + 9 q^{22} - 10 q^{23} - 14 q^{25} - 6 q^{26} + q^{28} - 2 q^{29} + 17 q^{31} + 20 q^{32} - 18 q^{34} - 7 q^{35} - 6 q^{37} - 4 q^{38} - 24 q^{40} + 4 q^{43} + q^{44} - 10 q^{46} + 2 q^{47} - q^{49} + q^{50} + 6 q^{52} + 26 q^{53} + 28 q^{55} - 12 q^{56} - 2 q^{58} + 14 q^{59} - 20 q^{61} - 18 q^{62} - 7 q^{64} - 32 q^{65} + 32 q^{67} - 12 q^{68} + 8 q^{70} + 20 q^{71} - 2 q^{73} - 6 q^{74} - 6 q^{76} - q^{77} + 14 q^{79} - 8 q^{80} - 15 q^{82} + 14 q^{83} - 21 q^{85} + 4 q^{86} + 33 q^{88} + 18 q^{89} - 6 q^{91} - 15 q^{92} + 2 q^{94} + 7 q^{95} - 2 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^4 - 7 * q^5 - q^7 + 3 * q^8 - 2 * q^10 - q^11 + 4 * q^13 - q^14 + q^16 + 12 * q^17 + q^19 + 7 * q^20 + 9 * q^22 - 10 * q^23 - 14 * q^25 - 6 * q^26 + q^28 - 2 * q^29 + 17 * q^31 + 20 * q^32 - 18 * q^34 - 7 * q^35 - 6 * q^37 - 4 * q^38 - 24 * q^40 + 4 * q^43 + q^44 - 10 * q^46 + 2 * q^47 - q^49 + q^50 + 6 * q^52 + 26 * q^53 + 28 * q^55 - 12 * q^56 - 2 * q^58 + 14 * q^59 - 20 * q^61 - 18 * q^62 - 7 * q^64 - 32 * q^65 + 32 * q^67 - 12 * q^68 + 8 * q^70 + 20 * q^71 - 2 * q^73 - 6 * q^74 - 6 * q^76 - q^77 + 14 * q^79 - 8 * q^80 - 15 * q^82 + 14 * q^83 - 21 * q^85 + 4 * q^86 + 33 * q^88 + 18 * q^89 - 6 * q^91 - 15 * q^92 + 2 * q^94 + 7 * q^95 - 2 * q^97 + 4 * q^98

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