LMFDB - Embedded newform 693.2.m.c.631.1

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			631.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.c.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +2.85410 q^{10} +(-3.04508 - 1.31433i) q^{11} +(1.00000 + 0.726543i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.809017 - 0.587785i) q^{16} +(6.35410 - 4.61653i) q^{17} +(0.809017 - 2.48990i) q^{19} +(2.30902 + 1.67760i) q^{20} +(1.69098 + 2.85317i) q^{22} +3.09017 q^{23} +(0.972136 - 2.99193i) q^{25} +(-0.381966 - 1.17557i) q^{26} +(0.809017 - 0.587785i) q^{28} +(0.618034 + 1.90211i) q^{29} +(5.92705 + 4.30625i) q^{31} +5.00000 q^{32} -7.85410 q^{34} +(-2.30902 - 1.67760i) q^{35} +(-3.73607 - 11.4984i) q^{37} +(-2.11803 + 1.53884i) q^{38} +(-2.64590 - 8.14324i) q^{40} +(3.35410 - 10.3229i) q^{41} -1.23607 q^{43} +(-0.309017 + 3.30220i) q^{44} +(-2.50000 - 1.81636i) q^{46} +(-0.618034 + 1.90211i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-2.54508 + 1.84911i) q^{50} +(0.381966 - 1.17557i) q^{52} +(9.85410 + 7.15942i) q^{53} +(9.23607 - 2.07363i) q^{55} -3.00000 q^{56} +(0.618034 - 1.90211i) q^{58} +(-2.09017 - 6.43288i) q^{59} +(-7.23607 + 5.25731i) q^{61} +(-2.26393 - 6.96767i) q^{62} +(-5.66312 - 4.11450i) q^{64} -3.52786 q^{65} +8.00000 q^{67} +(-6.35410 - 4.61653i) q^{68} +(0.881966 + 2.71441i) q^{70} +(7.23607 - 5.25731i) q^{71} +(-1.61803 - 4.97980i) q^{73} +(-3.73607 + 11.4984i) q^{74} -2.61803 q^{76} +(0.309017 - 3.30220i) q^{77} +(11.3262 + 8.22899i) q^{79} +(-0.881966 + 2.71441i) q^{80} +(-8.78115 + 6.37988i) q^{82} +(2.38197 - 1.73060i) q^{83} +(-6.92705 + 21.3193i) q^{85} +(1.00000 + 0.726543i) q^{86} +(6.57295 - 7.46969i) q^{88} -1.09017 q^{89} +(-0.381966 + 1.17557i) q^{91} +(-0.954915 - 2.93893i) q^{92} +(1.61803 - 1.17557i) q^{94} +(2.30902 + 7.10642i) q^{95} +(2.85410 + 2.07363i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	0.263792	−	0.964580i	$-0.415027\pi$
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	−0.835853	+	0.548953i	$0.815027\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−2.30902	+	1.67760i	−1.03262	+	0.750245i	−0.968832	−	0.247718i	$-0.920319\pi$
$5$	−2.30902	+	1.67760i	−1.03262	+	0.750245i	−0.0637916	+	0.997963i	$0.520319\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.927051	+	2.85317i	−0.327762	+	1.00875i
$9$		0			0
$10$	2.85410			0.902546
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$12$		0			0
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	0.717761	−	0.696290i	$-0.245167\pi$
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	−0.440411	+	0.897796i	$0.645167\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	6.35410	−	4.61653i	1.54110	−	1.11967i	0.591452	−	0.806340i	$-0.298555\pi$
$17$	6.35410	−	4.61653i	1.54110	−	1.11967i	0.949644	−	0.313332i	$-0.101445\pi$
$18$		0			0
$19$	0.809017	−	2.48990i	0.185601	−	0.571222i	−0.814357	−	0.580364i	$-0.802910\pi$
$19$	0.809017	−	2.48990i	0.185601	−	0.571222i	0.999958	+	0.00914245i	$0.00291017\pi$
$20$	2.30902	+	1.67760i	0.516312	+	0.375123i
$21$		0			0
$22$	1.69098	+	2.85317i	0.360519	+	0.608298i
$23$	3.09017			0.644345			0.322172	−	0.946681i	$-0.395587\pi$
$23$	3.09017			0.644345			0.322172	+	0.946681i	$0.395587\pi$
$24$		0			0
$25$	0.972136	−	2.99193i	0.194427	−	0.598385i
$26$	−0.381966	−	1.17557i	−0.0749097	−	0.230548i
$27$		0			0
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	0.618034	+	1.90211i	0.114766	+	0.353214i	0.991898	−	0.127036i	$-0.0405463\pi$
$29$	0.618034	+	1.90211i	0.114766	+	0.353214i	−0.877132	+	0.480249i	$0.840546\pi$
$30$		0			0
$31$	5.92705	+	4.30625i	1.06453	+	0.773426i	0.974921	−	0.222551i	$-0.0714384\pi$
$31$	5.92705	+	4.30625i	1.06453	+	0.773426i	0.0896087	+	0.995977i	$0.471438\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−7.85410			−1.34697
$35$	−2.30902	−	1.67760i	−0.390295	−	0.283566i
$36$		0			0
$37$	−3.73607	−	11.4984i	−0.614206	−	1.89033i	−0.412794	−	0.910824i	$-0.635447\pi$
$37$	−3.73607	−	11.4984i	−0.614206	−	1.89033i	−0.201412	−	0.979507i	$-0.564553\pi$
$38$	−2.11803	+	1.53884i	−0.343590	+	0.249633i
$39$		0			0
$40$	−2.64590	−	8.14324i	−0.418353	−	1.28756i
$41$	3.35410	−	10.3229i	0.523823	−	1.61216i	−0.242809	−	0.970074i	$-0.578069\pi$
$41$	3.35410	−	10.3229i	0.523823	−	1.61216i	0.766632	−	0.642087i	$-0.221931\pi$
$42$		0			0
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	−0.309017	+	3.30220i	−0.0465861	+	0.497825i
$45$		0			0
$46$	−2.50000	−	1.81636i	−0.368605	−	0.267807i
$47$	−0.618034	+	1.90211i	−0.0901495	+	0.277452i	−0.985959	−	0.166986i	$-0.946597\pi$
$47$	−0.618034	+	1.90211i	−0.0901495	+	0.277452i	0.895810	+	0.444438i	$0.146597\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−2.54508	+	1.84911i	−0.359929	+	0.261504i
$51$		0			0
$52$	0.381966	−	1.17557i	0.0529692	−	0.163022i
$53$	9.85410	+	7.15942i	1.35357	+	0.983423i	0.998825	+	0.0484575i	$0.0154305\pi$
$53$	9.85410	+	7.15942i	1.35357	+	0.983423i	0.354740	+	0.934965i	$0.384569\pi$
$54$		0			0
$55$	9.23607	−	2.07363i	1.24539	−	0.279608i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	0.618034	−	1.90211i	0.0811518	−	0.249760i
$59$	−2.09017	−	6.43288i	−0.272117	−	0.837490i	−0.989968	−	0.141293i	$-0.954874\pi$
$59$	−2.09017	−	6.43288i	−0.272117	−	0.837490i	0.717851	−	0.696197i	$-0.245126\pi$
$60$		0			0
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	−0.945129	−	0.326696i	$-0.894065\pi$
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	0.0186458	+	0.999826i	$0.494065\pi$
$62$	−2.26393	−	6.96767i	−0.287520	−	0.884895i
$63$		0			0
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−3.52786			−0.437578
$66$		0			0
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−6.35410	−	4.61653i	−0.770548	−	0.559836i
$69$		0			0
$70$	0.881966	+	2.71441i	0.105415	+	0.324434i
$71$	7.23607	−	5.25731i	0.858763	−	0.623928i	−0.0687850	−	0.997632i	$-0.521912\pi$
$71$	7.23607	−	5.25731i	0.858763	−	0.623928i	0.927548	+	0.373703i	$0.121912\pi$
$72$		0			0
$73$	−1.61803	−	4.97980i	−0.189377	−	0.582841i	0.810620	−	0.585573i	$-0.199130\pi$
$73$	−1.61803	−	4.97980i	−0.189377	−	0.582841i	−0.999996	+	0.00273185i	$0.999130\pi$
$74$	−3.73607	+	11.4984i	−0.434309	+	1.33667i
$75$		0			0
$76$	−2.61803			−0.300309
$77$	0.309017	−	3.30220i	0.0352158	−	0.376320i
$78$		0			0
$79$	11.3262	+	8.22899i	1.27430	+	0.925834i	0.999365	−	0.0356284i	$-0.0113433\pi$
$79$	11.3262	+	8.22899i	1.27430	+	0.925834i	0.274936	+	0.961462i	$0.411343\pi$
$80$	−0.881966	+	2.71441i	−0.0986068	+	0.303481i
$81$		0			0
$82$	−8.78115	+	6.37988i	−0.969716	+	0.704540i
$83$	2.38197	−	1.73060i	0.261455	−	0.189958i	−0.449333	−	0.893364i	$-0.648338\pi$
$83$	2.38197	−	1.73060i	0.261455	−	0.189958i	0.710788	+	0.703406i	$0.248338\pi$
$84$		0			0
$85$	−6.92705	+	21.3193i	−0.751344	+	2.31240i
$86$	1.00000	+	0.726543i	0.107833	+	0.0783451i
$87$		0			0
$88$	6.57295	−	7.46969i	0.700679	−	0.796272i
$89$	−1.09017			−0.115558			−0.0577789	−	0.998329i	$-0.518402\pi$
$89$	−1.09017			−0.115558			−0.0577789	+	0.998329i	$0.518402\pi$
$90$		0			0
$91$	−0.381966	+	1.17557i	−0.0400409	+	0.123233i
$92$	−0.954915	−	2.93893i	−0.0995568	−	0.306404i
$93$		0			0
$94$	1.61803	−	1.17557i	0.166887	−	0.121251i
$95$	2.30902	+	7.10642i	0.236900	+	0.729104i
$96$		0			0
$97$	2.85410	+	2.07363i	0.289790	+	0.210545i	0.723176	−	0.690663i	$-0.242681\pi$
$97$	2.85410	+	2.07363i	0.289790	+	0.210545i	−0.433386	+	0.901208i	$0.642681\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−3.14590			−0.314590
$101$	−1.69098	−	1.22857i	−0.168259	−	0.122247i	0.500469	−	0.865754i	$-0.333161\pi$
$101$	−1.69098	−	1.22857i	−0.168259	−	0.122247i	−0.668728	+	0.743507i	$0.733161\pi$
$102$		0			0
$103$	−3.19098	−	9.82084i	−0.314417	−	0.967676i	−0.975994	−	0.217798i	$-0.930112\pi$
$103$	−3.19098	−	9.82084i	−0.314417	−	0.967676i	0.661577	−	0.749877i	$-0.269888\pi$
$104$	−3.00000	+	2.17963i	−0.294174	+	0.213730i
$105$		0			0
$106$	−3.76393	−	11.5842i	−0.365585	−	1.12516i
$107$	−1.51722	+	4.66953i	−0.146675	+	0.451420i	−0.997223	−	0.0744784i	$-0.976271\pi$
$107$	−1.51722	+	4.66953i	−0.146675	+	0.451420i	0.850547	+	0.525898i	$0.176271\pi$
$108$		0			0
$109$	10.5623			1.01169			0.505843	−	0.862626i	$-0.331182\pi$
$109$	10.5623			1.01169			0.505843	+	0.862626i	$0.331182\pi$
$110$	−8.69098	−	3.75123i	−0.828653	−	0.357665i
$111$		0			0
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	−0.236068	+	0.726543i	−0.0222074	+	0.0683474i	−0.961546	−	0.274644i	$-0.911440\pi$
$113$	−0.236068	+	0.726543i	−0.0222074	+	0.0683474i	0.939339	+	0.342991i	$0.111440\pi$
$114$		0			0
$115$	−7.13525	+	5.18407i	−0.665366	+	0.483417i
$116$	1.61803	−	1.17557i	0.150231	−	0.109149i
$117$		0			0
$118$	−2.09017	+	6.43288i	−0.192416	+	0.592195i
$119$	6.35410	+	4.61653i	0.582480	+	0.423196i
$120$		0			0
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	8.94427			0.809776
$123$		0			0
$124$	2.26393	−	6.96767i	0.203307	−	0.625715i
$125$	−1.63525	−	5.03280i	−0.146262	−	0.450147i
$126$		0			0
$127$	2.61803	−	1.90211i	0.232313	−	0.168785i	−0.465539	−	0.885027i	$-0.654139\pi$
$127$	2.61803	−	1.90211i	0.232313	−	0.168785i	0.697852	+	0.716242i	$0.254139\pi$
$128$	−0.927051	−	2.85317i	−0.0819405	−	0.252187i
$129$		0			0
$130$	2.85410	+	2.07363i	0.250321	+	0.181869i
$131$	−2.29180			−0.200235			−0.100118	−	0.994976i	$-0.531922\pi$
$131$	−2.29180			−0.200235			−0.100118	+	0.994976i	$0.531922\pi$
$132$		0			0
$133$	2.61803			0.227012
$134$	−6.47214	−	4.70228i	−0.559107	−	0.406215i
$135$		0			0
$136$	7.28115	+	22.4091i	0.624354	+	1.92156i
$137$	5.47214	−	3.97574i	0.467516	−	0.339670i	−0.328956	−	0.944345i	$-0.606697\pi$
$137$	5.47214	−	3.97574i	0.467516	−	0.339670i	0.796472	+	0.604675i	$0.206697\pi$
$138$		0			0
$139$	1.48278	+	4.56352i	0.125768	+	0.387073i	0.994040	−	0.109014i	$-0.0347695\pi$
$139$	1.48278	+	4.56352i	0.125768	+	0.387073i	−0.868272	+	0.496088i	$0.834769\pi$
$140$	−0.881966	+	2.71441i	−0.0745397	+	0.229410i
$141$		0			0
$142$	−8.94427			−0.750587
$143$	−2.09017	−	3.52671i	−0.174789	−	0.294918i
$144$		0			0
$145$	−4.61803	−	3.35520i	−0.383507	−	0.278634i
$146$	−1.61803	+	4.97980i	−0.133909	+	0.412131i
$147$		0			0
$148$	−9.78115	+	7.10642i	−0.804006	+	0.584144i
$149$	−16.1803	+	11.7557i	−1.32555	+	0.963065i	−0.325700	+	0.945473i	$0.605600\pi$
$149$	−16.1803	+	11.7557i	−1.32555	+	0.963065i	−0.999845	+	0.0175917i	$0.994400\pi$
$150$		0			0
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	−0.973050	−	0.230596i	$-0.925932\pi$
$151$	−0.618034	+	1.90211i	−0.0502949	+	0.154792i	0.922755	+	0.385388i	$0.125932\pi$
$152$	6.35410	+	4.61653i	0.515386	+	0.374450i
$153$		0			0
$154$	−2.19098	+	2.48990i	−0.176554	+	0.200642i
$155$	−20.9098			−1.67952
$156$		0			0
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	−4.32624	−	13.3148i	−0.344177	−	1.05927i
$159$		0			0
$160$	−11.5451	+	8.38800i	−0.912719	+	0.663129i
$161$	0.954915	+	2.93893i	0.0752578	+	0.231620i
$162$		0			0
$163$	4.38197	+	3.18368i	0.343222	+	0.249365i	0.746020	−	0.665923i	$-0.231962\pi$
$163$	4.38197	+	3.18368i	0.343222	+	0.249365i	−0.402798	+	0.915289i	$0.631962\pi$
$164$	−10.8541			−0.847563
$165$		0			0
$166$	−2.94427			−0.228520
$167$	6.61803	+	4.80828i	0.512119	+	0.372076i	0.813627	−	0.581388i	$-0.197490\pi$
$167$	6.61803	+	4.80828i	0.512119	+	0.372076i	−0.301508	+	0.953464i	$0.597490\pi$
$168$		0			0
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$	18.1353	−	13.1760i	1.39091	−	1.01056i
$171$		0			0
$172$	0.381966	+	1.17557i	0.0291246	+	0.0896364i
$173$	−6.13525	+	18.8824i	−0.466455	+	1.43560i	0.390689	+	0.920523i	$0.372237\pi$
$173$	−6.13525	+	18.8824i	−0.466455	+	1.43560i	−0.857144	+	0.515077i	$0.827763\pi$
$174$		0			0
$175$	3.14590			0.237808
$176$	−3.23607	+	0.726543i	−0.243928	+	0.0547652i
$177$		0			0
$178$	0.881966	+	0.640786i	0.0661061	+	0.0480289i
$179$	−2.59017	+	7.97172i	−0.193598	+	0.595835i	0.806392	+	0.591382i	$0.201417\pi$
$179$	−2.59017	+	7.97172i	−0.193598	+	0.595835i	−0.999990	+	0.00445278i	$0.998583\pi$
$180$		0			0
$181$	15.3262	−	11.1352i	1.13919	−	0.827670i	0.152184	−	0.988352i	$-0.451369\pi$
$181$	15.3262	−	11.1352i	1.13919	−	0.827670i	0.987006	+	0.160682i	$0.0513693\pi$
$182$	1.00000	−	0.726543i	0.0741249	−	0.0538549i
$183$		0			0
$184$	−2.86475	+	8.81678i	−0.211192	+	0.649982i
$185$	27.9164	+	20.2825i	2.05246	+	1.49120i
$186$		0			0
$187$	−25.4164	+	5.70634i	−1.85863	+	0.417289i
$188$	2.00000			0.145865
$189$		0			0
$190$	2.30902	−	7.10642i	0.167514	−	0.515554i
$191$	5.64590	+	17.3763i	0.408523	+	1.25730i	0.917918	+	0.396771i	$0.129869\pi$
$191$	5.64590	+	17.3763i	0.408523	+	1.25730i	−0.509395	+	0.860533i	$0.670131\pi$
$192$		0			0
$193$	−14.8713	+	10.8046i	−1.07046	+	0.777736i	−0.975995	−	0.217792i	$-0.930114\pi$
$193$	−14.8713	+	10.8046i	−1.07046	+	0.777736i	−0.0944661	+	0.995528i	$0.530114\pi$
$194$	−1.09017	−	3.35520i	−0.0782696	−	0.240889i
$195$		0			0
$196$	0.809017	+	0.587785i	0.0577869	+	0.0419847i
$197$	−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
$199$	−2.61803			−0.185588			−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803			−0.185588			−0.0927938	+	0.995685i	$0.529580\pi$
$200$	7.63525	+	5.54734i	0.539894	+	0.392256i
$201$		0			0
$202$	0.645898	+	1.98787i	0.0454452	+	0.139866i
$203$	−1.61803	+	1.17557i	−0.113564	+	0.0825089i
$204$		0			0
$205$	9.57295	+	29.4625i	0.668604	+	2.05775i
$206$	−3.19098	+	9.82084i	−0.222326	+	0.684250i
$207$		0			0
$208$	1.23607			0.0857059
$209$	−5.73607	+	6.51864i	−0.396772	+	0.450904i
$210$		0			0
$211$	1.61803	+	1.17557i	0.111390	+	0.0809296i	0.642086	−	0.766633i	$-0.278069\pi$
$211$	1.61803	+	1.17557i	0.111390	+	0.0809296i	−0.530696	+	0.847562i	$0.678069\pi$
$212$	3.76393	−	11.5842i	0.258508	−	0.795606i
$213$		0			0
$214$	3.97214	−	2.88593i	0.271530	−	0.197278i
$215$	2.85410	−	2.07363i	0.194648	−	0.141420i
$216$		0			0
$217$	−2.26393	+	6.96767i	−0.153686	+	0.472996i
$218$	−8.54508	−	6.20837i	−0.578746	−	0.420484i
$219$		0			0
$220$	−4.82624	−	8.14324i	−0.325385	−	0.549017i
$221$	9.70820			0.653044
$222$		0			0
$223$	6.42705	−	19.7804i	0.430387	−	1.32460i	−0.467353	−	0.884071i	$-0.654792\pi$
$223$	6.42705	−	19.7804i	0.430387	−	1.32460i	0.897740	−	0.440525i	$-0.145208\pi$
$224$	1.54508	+	4.75528i	0.103235	+	0.317726i
$225$		0			0
$226$	0.618034	−	0.449028i	0.0411110	−	0.0298689i
$227$	−6.61803	−	20.3682i	−0.439254	−	1.35189i	−0.888664	−	0.458560i	$-0.848365\pi$
$227$	−6.61803	−	20.3682i	−0.439254	−	1.35189i	0.449409	−	0.893326i	$-0.351635\pi$
$228$		0			0
$229$	−17.1803	−	12.4822i	−1.13531	−	0.824850i	−0.148850	−	0.988860i	$-0.547557\pi$
$229$	−17.1803	−	12.4822i	−1.13531	−	0.824850i	−0.986459	+	0.164010i	$0.947557\pi$
$230$	8.81966			0.581551
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−4.61803	−	3.35520i	−0.302537	−	0.219806i	0.426150	−	0.904652i	$-0.359869\pi$
$233$	−4.61803	−	3.35520i	−0.302537	−	0.219806i	−0.728688	+	0.684846i	$0.759869\pi$
$234$		0			0
$235$	−1.76393	−	5.42882i	−0.115066	−	0.354137i
$236$	−5.47214	+	3.97574i	−0.356206	+	0.258799i
$237$		0			0
$238$	−2.42705	−	7.46969i	−0.157322	−	0.484188i
$239$	0.482779	−	1.48584i	0.0312284	−	0.0961111i	−0.934227	−	0.356678i	$-0.883909\pi$
$239$	0.482779	−	1.48584i	0.0312284	−	0.0961111i	0.965456	+	0.260567i	$0.0839094\pi$
$240$		0			0
$241$	4.94427			0.318489			0.159244	−	0.987239i	$-0.449094\pi$
$241$	4.94427			0.318489			0.159244	+	0.987239i	$0.449094\pi$
$242$	−1.39919	−	10.9106i	−0.0899431	−	0.701363i
$243$		0			0
$244$	7.23607	+	5.25731i	0.463242	+	0.336565i
$245$	0.881966	−	2.71441i	0.0563467	−	0.173417i
$246$		0			0
$247$	2.61803	−	1.90211i	0.166582	−	0.121029i
$248$	−17.7812	+	12.9188i	−1.12910	+	0.820342i
$249$		0			0
$250$	−1.63525	+	5.03280i	−0.103423	+	0.318302i
$251$	19.5623	+	14.2128i	1.23476	+	0.897107i	0.997238	−	0.0742747i	$-0.0236642\pi$
$251$	19.5623	+	14.2128i	1.23476	+	0.897107i	0.237524	+	0.971382i	$0.423664\pi$
$252$		0			0
$253$	−9.40983	−	4.06150i	−0.591591	−	0.255344i
$254$	−3.23607			−0.203049
$255$		0			0
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−0.809017	−	2.48990i	−0.0504651	−	0.155316i	0.922648	−	0.385643i	$-0.126020\pi$
$257$	−0.809017	−	2.48990i	−0.0504651	−	0.155316i	−0.973113	+	0.230327i	$0.926020\pi$
$258$		0			0
$259$	9.78115	−	7.10642i	0.607771	−	0.441572i
$260$	1.09017	+	3.35520i	0.0676095	+	0.208081i
$261$		0			0
$262$	1.85410	+	1.34708i	0.114547	+	0.0832231i
$263$	−2.43769			−0.150315			−0.0751573	−	0.997172i	$-0.523946\pi$
$263$	−2.43769			−0.150315			−0.0751573	+	0.997172i	$0.523946\pi$
$264$		0			0
$265$	−34.7639			−2.13553
$266$	−2.11803	−	1.53884i	−0.129865	−	0.0943524i
$267$		0			0
$268$	−2.47214	−	7.60845i	−0.151010	−	0.464760i
$269$	22.5623	−	16.3925i	1.37565	−	0.999467i	0.378376	−	0.925652i	$-0.376483\pi$
$269$	22.5623	−	16.3925i	1.37565	−	0.999467i	0.997272	−	0.0738149i	$-0.0235174\pi$
$270$		0			0
$271$	7.44427	+	22.9111i	0.452207	+	1.39175i	0.874383	+	0.485237i	$0.161267\pi$
$271$	7.44427	+	22.9111i	0.452207	+	1.39175i	−0.422175	+	0.906514i	$0.638733\pi$
$272$	2.42705	−	7.46969i	0.147162	−	0.452917i
$273$		0			0
$274$	−6.76393			−0.408624
$275$	−6.89261	+	7.83297i	−0.415640	+	0.472346i
$276$		0			0
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	0.811824	−	0.583902i	$-0.198475\pi$
$277$	8.44427	+	6.13512i	0.507367	+	0.368624i	−0.304457	+	0.952526i	$0.598475\pi$
$278$	1.48278	−	4.56352i	0.0889312	−	0.273702i
$279$		0			0
$280$	6.92705	−	5.03280i	0.413970	−	0.300767i
$281$	0.854102	−	0.620541i	0.0509515	−	0.0370184i	−0.562018	−	0.827125i	$-0.689975\pi$
$281$	0.854102	−	0.620541i	0.0509515	−	0.0370184i	0.612969	+	0.790107i	$0.289975\pi$
$282$		0			0
$283$	4.15248	−	12.7800i	0.246839	−	0.759693i	−0.748489	−	0.663147i	$-0.769221\pi$
$283$	4.15248	−	12.7800i	0.246839	−	0.759693i	0.995329	−	0.0965459i	$-0.0307794\pi$
$284$	−7.23607	−	5.25731i	−0.429382	−	0.311964i
$285$		0			0
$286$	−0.381966	+	4.08174i	−0.0225861	+	0.241358i
$287$	10.8541			0.640697
$288$		0			0
$289$	13.8090	−	42.4998i	0.812295	−	2.49999i
$290$	1.76393	+	5.42882i	0.103582	+	0.318792i
$291$		0			0
$292$	−4.23607	+	3.07768i	−0.247897	+	0.180108i
$293$	−6.11803	−	18.8294i	−0.357419	−	1.10002i	−0.954593	−	0.297912i	$-0.903710\pi$
$293$	−6.11803	−	18.8294i	−0.357419	−	1.10002i	0.597174	−	0.802112i	$-0.296290\pi$
$294$		0			0
$295$	15.6180	+	11.3472i	0.909317	+	0.660658i
$296$	36.2705			2.10818
$297$		0			0
$298$	20.0000			1.15857
$299$	3.09017	+	2.24514i	0.178709	+	0.129840i
$300$		0			0
$301$	−0.381966	−	1.17557i	−0.0220162	−	0.0677588i
$302$	1.61803	−	1.17557i	0.0931074	−	0.0676465i
$303$		0			0
$304$	−0.809017	−	2.48990i	−0.0464003	−	0.142805i
$305$	7.88854	−	24.2784i	0.451697	−	1.39018i
$306$		0			0
$307$	−24.2705			−1.38519			−0.692596	−	0.721326i	$-0.743533\pi$
$307$	−24.2705			−1.38519			−0.692596	+	0.721326i	$0.743533\pi$
$308$	−3.23607	+	0.726543i	−0.184392	+	0.0413986i
$309$		0			0
$310$	16.9164	+	12.2905i	0.960787	+	0.698053i
$311$	0.236068	−	0.726543i	0.0133862	−	0.0411984i	−0.944140	−	0.329544i	$-0.893105\pi$
$311$	0.236068	−	0.726543i	0.0133862	−	0.0411984i	0.957527	+	0.288345i	$0.0931051\pi$
$312$		0			0
$313$	7.94427	−	5.77185i	0.449037	−	0.326244i	−0.340179	−	0.940361i	$-0.610488\pi$
$313$	7.94427	−	5.77185i	0.449037	−	0.326244i	0.789215	+	0.614117i	$0.210488\pi$
$314$	−7.85410	+	5.70634i	−0.443233	+	0.322027i
$315$		0			0
$316$	4.32624	−	13.3148i	0.243370	−	0.749016i
$317$	−22.3262	−	16.2210i	−1.25397	−	0.911060i	−0.255521	−	0.966803i	$-0.582247\pi$
$317$	−22.3262	−	16.2210i	−1.25397	−	0.911060i	−0.998445	+	0.0557435i	$0.982247\pi$
$318$		0			0
$319$	0.618034	−	6.60440i	0.0346033	−	0.369775i
$320$	19.9787			1.11684
$321$		0			0
$322$	0.954915	−	2.93893i	0.0532153	−	0.163780i
$323$	−6.35410	−	19.5559i	−0.353552	−	1.08812i
$324$		0			0
$325$	3.14590	−	2.28563i	0.174503	−	0.126784i
$326$	−1.67376	−	5.15131i	−0.0927011	−	0.285305i
$327$		0			0
$328$	26.3435	+	19.1396i	1.45457	+	1.05681i
$329$	−2.00000			−0.110264
$330$		0			0
$331$	30.3607			1.66877			0.834387	−	0.551179i	$-0.185822\pi$
$331$	30.3607			1.66877			0.834387	+	0.551179i	$0.185822\pi$
$332$	−2.38197	−	1.73060i	−0.130727	−	0.0949790i
$333$		0			0
$334$	−2.52786	−	7.77997i	−0.138319	−	0.425701i
$335$	−18.4721	+	13.4208i	−1.00924	+	0.733256i
$336$		0			0
$337$	−8.38854	−	25.8173i	−0.456953	−	1.40636i	−0.868827	−	0.495116i	$-0.835126\pi$
$337$	−8.38854	−	25.8173i	−0.456953	−	1.40636i	0.411874	−	0.911241i	$-0.364874\pi$
$338$	−3.54508	+	10.9106i	−0.192827	+	0.593461i
$339$		0			0
$340$	22.4164			1.21570
$341$	−12.3885	−	20.9030i	−0.670877	−	1.13196i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	1.14590	−	3.52671i	0.0617827	−	0.190148i
$345$		0			0
$346$	16.0623	−	11.6699i	0.863515	−	0.627380i
$347$	−10.0172	+	7.27794i	−0.537753	+	0.390700i	−0.823250	−	0.567679i	$-0.807841\pi$
$347$	−10.0172	+	7.27794i	−0.537753	+	0.390700i	0.285497	+	0.958380i	$0.407841\pi$
$348$		0			0
$349$	7.03444	−	21.6498i	0.376545	−	1.15889i	−0.565885	−	0.824484i	$-0.691466\pi$
$349$	7.03444	−	21.6498i	0.376545	−	1.15889i	0.942430	−	0.334403i	$-0.108534\pi$
$350$	−2.54508	−	1.84911i	−0.136041	−	0.0988392i
$351$		0			0
$352$	−15.2254	−	6.57164i	−0.811518	−	0.350270i
$353$	−12.4721			−0.663825			−0.331912	−	0.943310i	$-0.607694\pi$
$353$	−12.4721			−0.663825			−0.331912	+	0.943310i	$0.607694\pi$
$354$		0			0
$355$	−7.88854	+	24.2784i	−0.418680	+	1.28857i
$356$	0.336881	+	1.03681i	0.0178547	+	0.0549510i
$357$		0			0
$358$	6.78115	−	4.92680i	0.358395	−	0.260389i
$359$	−2.17376	−	6.69015i	−0.114727	−	0.353093i	0.877163	−	0.480192i	$-0.159433\pi$
$359$	−2.17376	−	6.69015i	−0.114727	−	0.353093i	−0.991890	+	0.127100i	$0.959433\pi$
$360$		0			0
$361$	9.82624	+	7.13918i	0.517170	+	0.375746i
$362$	−18.9443			−0.995689
$363$		0			0
$364$	1.23607			0.0647876
$365$	12.0902	+	8.78402i	0.632828	+	0.459777i
$366$		0			0
$367$	5.02786	+	15.4742i	0.262452	+	0.807745i	0.992269	+	0.124103i	$0.0396053\pi$
$367$	5.02786	+	15.4742i	0.262452	+	0.807745i	−0.729817	+	0.683643i	$0.760395\pi$
$368$	2.50000	−	1.81636i	0.130322	−	0.0946841i
$369$		0			0
$370$	−10.6631	−	32.8177i	−0.554349	−	1.70611i
$371$	−3.76393	+	11.5842i	−0.195414	+	0.601421i
$372$		0			0
$373$	−23.3262			−1.20779			−0.603893	−	0.797065i	$-0.706385\pi$
$373$	−23.3262			−1.20779			−0.603893	+	0.797065i	$0.706385\pi$
$374$	23.9164	+	10.3229i	1.23669	+	0.533783i
$375$		0			0
$376$	−4.85410	−	3.52671i	−0.250331	−	0.181876i
$377$	−0.763932	+	2.35114i	−0.0393445	+	0.121090i
$378$		0			0
$379$	−2.00000	+	1.45309i	−0.102733	+	0.0746400i	−0.637966	−	0.770065i	$-0.720224\pi$
$379$	−2.00000	+	1.45309i	−0.102733	+	0.0746400i	0.535233	+	0.844705i	$0.320224\pi$
$380$	6.04508	−	4.39201i	0.310106	−	0.225305i
$381$		0			0
$382$	5.64590	−	17.3763i	0.288869	−	0.889048i
$383$	−10.5623	−	7.67396i	−0.539709	−	0.392121i	0.284268	−	0.958745i	$-0.408249\pi$
$383$	−10.5623	−	7.67396i	−0.539709	−	0.392121i	−0.823977	+	0.566624i	$0.808249\pi$
$384$		0			0
$385$	4.82624	+	8.14324i	0.245968	+	0.415018i
$386$	18.3820			0.935617
$387$		0			0
$388$	1.09017	−	3.35520i	0.0553450	−	0.170334i
$389$	−6.85410	−	21.0948i	−0.347517	−	1.06955i	−0.960223	−	0.279236i	$-0.909919\pi$
$389$	−6.85410	−	21.0948i	−0.347517	−	1.06955i	0.612706	−	0.790311i	$-0.290081\pi$
$390$		0			0
$391$	19.6353	−	14.2658i	0.992998	−	0.721455i
$392$	−0.927051	−	2.85317i	−0.0468231	−	0.144107i
$393$		0			0
$394$	3.23607	+	2.35114i	0.163031	+	0.118449i
$395$	−39.9574			−2.01048
$396$		0			0
$397$	14.6525			0.735387			0.367693	−	0.929947i	$-0.380148\pi$
$397$	14.6525			0.735387			0.367693	+	0.929947i	$0.380148\pi$
$398$	2.11803	+	1.53884i	0.106167	+	0.0771352i
$399$		0			0
$400$	−0.972136	−	2.99193i	−0.0486068	−	0.149596i
$401$	14.9443	−	10.8576i	0.746281	−	0.542205i	−0.148391	−	0.988929i	$-0.547409\pi$
$401$	14.9443	−	10.8576i	0.746281	−	0.542205i	0.894672	+	0.446724i	$0.147409\pi$
$402$		0			0
$403$	2.79837	+	8.61251i	0.139397	+	0.429020i
$404$	−0.645898	+	1.98787i	−0.0321346	+	0.0989002i
$405$		0			0
$406$	2.00000			0.0992583
$407$	−3.73607	+	39.9241i	−0.185190	+	1.97897i
$408$		0			0
$409$	−23.2705	−	16.9070i	−1.15065	−	0.835998i	−0.162085	−	0.986777i	$-0.551822\pi$
$409$	−23.2705	−	16.9070i	−1.15065	−	0.835998i	−0.988568	+	0.150779i	$0.951822\pi$
$410$	9.57295	−	29.4625i	0.472774	−	1.45505i
$411$		0			0
$412$	−8.35410	+	6.06961i	−0.411577	+	0.299028i
$413$	5.47214	−	3.97574i	0.269266	−	0.195633i
$414$		0			0
$415$	−2.59675	+	7.99197i	−0.127469	+	0.392310i
$416$	5.00000	+	3.63271i	0.245145	+	0.178108i
$417$		0			0
$418$	8.47214	−	1.90211i	0.414386	−	0.0930354i
$419$	−14.7639			−0.721265			−0.360633	−	0.932708i	$-0.617439\pi$
$419$	−14.7639			−0.721265			−0.360633	+	0.932708i	$0.617439\pi$
$420$		0			0
$421$	−1.33688	+	4.11450i	−0.0651556	+	0.200528i	−0.978334	−	0.207031i	$-0.933620\pi$
$421$	−1.33688	+	4.11450i	−0.0651556	+	0.200528i	0.913179	+	0.407559i	$0.133620\pi$
$422$	−0.618034	−	1.90211i	−0.0300854	−	0.0925934i
$423$		0			0
$424$	−29.5623	+	21.4783i	−1.43567	+	1.04308i
$425$	−7.63525	−	23.4989i	−0.370364	−	1.13986i
$426$		0			0
$427$	−7.23607	−	5.25731i	−0.350178	−	0.254419i
$428$	4.90983			0.237326
$429$		0			0
$430$	−3.52786			−0.170129
$431$	−1.69098	−	1.22857i	−0.0814518	−	0.0591782i	0.546314	−	0.837580i	$-0.316030\pi$
$431$	−1.69098	−	1.22857i	−0.0814518	−	0.0591782i	−0.627766	+	0.778402i	$0.716030\pi$
$432$		0			0
$433$	−5.32624	−	16.3925i	−0.255963	−	0.787772i	−0.993638	−	0.112617i	$-0.964077\pi$
$433$	−5.32624	−	16.3925i	−0.255963	−	0.787772i	0.737676	−	0.675155i	$-0.235923\pi$
$434$	5.92705	−	4.30625i	0.284508	−	0.206707i
$435$		0			0
$436$	−3.26393	−	10.0453i	−0.156314	−	0.481085i
$437$	2.50000	−	7.69421i	0.119591	−	0.368064i
$438$		0			0
$439$	−21.7984			−1.04038			−0.520190	−	0.854051i	$-0.674139\pi$
$439$	−21.7984			−1.04038			−0.520190	+	0.854051i	$0.674139\pi$
$440$	−2.64590	+	28.2744i	−0.126138	+	1.34793i
$441$		0			0
$442$	−7.85410	−	5.70634i	−0.373582	−	0.271423i
$443$	−1.51722	+	4.66953i	−0.0720853	+	0.221856i	−0.980608	−	0.195980i	$-0.937211\pi$
$443$	−1.51722	+	4.66953i	−0.0720853	+	0.221856i	0.908523	+	0.417836i	$0.137211\pi$
$444$		0			0
$445$	2.51722	−	1.82887i	0.119328	−	0.0866967i
$446$	−16.8262	+	12.2250i	−0.796745	+	0.578869i
$447$		0			0
$448$	2.16312	−	6.65740i	0.102198	−	0.314532i
$449$	33.8885	+	24.6215i	1.59930	+	1.16196i	0.888837	+	0.458224i	$0.151514\pi$
$449$	33.8885	+	24.6215i	1.59930	+	1.16196i	0.710462	+	0.703735i	$0.248486\pi$
$450$		0			0
$451$	−23.7812	+	27.0256i	−1.11981	+	1.27259i
$452$	0.763932			0.0359323
$453$		0			0
$454$	−6.61803	+	20.3682i	−0.310600	+	0.955928i
$455$	−1.09017	−	3.35520i	−0.0511080	−	0.157294i
$456$		0			0
$457$	−10.0902	+	7.33094i	−0.471998	+	0.342927i	−0.798220	−	0.602367i	$-0.794225\pi$
$457$	−10.0902	+	7.33094i	−0.471998	+	0.342927i	0.326221	+	0.945293i	$0.394225\pi$
$458$	6.56231	+	20.1967i	0.306636	+	0.943730i
$459$		0			0
$460$	7.13525	+	5.18407i	0.332683	+	0.241708i
$461$	6.36068			0.296246			0.148123	−	0.988969i	$-0.452677\pi$
$461$	6.36068			0.296246			0.148123	+	0.988969i	$0.452677\pi$
$462$		0			0
$463$	11.4164			0.530565			0.265283	−	0.964171i	$-0.414535\pi$
$463$	11.4164			0.530565			0.265283	+	0.964171i	$0.414535\pi$
$464$	1.61803	+	1.17557i	0.0751153	+	0.0545745i
$465$		0			0
$466$	1.76393	+	5.42882i	0.0817126	+	0.251485i
$467$	15.5623	−	11.3067i	0.720138	−	0.523211i	−0.166291	−	0.986077i	$-0.553179\pi$
$467$	15.5623	−	11.3067i	0.720138	−	0.523211i	0.886428	+	0.462866i	$0.153179\pi$
$468$		0			0
$469$	2.47214	+	7.60845i	0.114153	+	0.351326i
$470$	−1.76393	+	5.42882i	−0.0813641	+	0.250413i
$471$		0			0
$472$	20.2918			0.934006
$473$	3.76393	+	1.62460i	0.173066	+	0.0746991i
$474$		0			0
$475$	−6.66312	−	4.84104i	−0.305725	−	0.222122i
$476$	2.42705	−	7.46969i	0.111244	−	0.342373i
$477$		0			0
$478$	−1.26393	+	0.918300i	−0.0578109	+	0.0420021i
$479$	−8.94427	+	6.49839i	−0.408674	+	0.296919i	−0.773065	−	0.634327i	$-0.781277\pi$
$479$	−8.94427	+	6.49839i	−0.408674	+	0.296919i	0.364391	+	0.931246i	$0.381277\pi$
$480$		0			0
$481$	4.61803	−	14.2128i	0.210564	−	0.648050i
$482$	−4.00000	−	2.90617i	−0.182195	−	0.132372i
$483$		0			0
$484$	5.28115	−	9.64932i	0.240052	−	0.438606i
$485$	−10.0689			−0.457204
$486$		0			0
$487$	−12.1246	+	37.3157i	−0.549419	+	1.69094i	0.160827	+	0.986983i	$0.448584\pi$
$487$	−12.1246	+	37.3157i	−0.549419	+	1.69094i	−0.710246	+	0.703954i	$0.751416\pi$
$488$	−8.29180	−	25.5195i	−0.375352	−	1.15521i
$489$		0			0
$490$	−2.30902	+	1.67760i	−0.104311	+	0.0757862i
$491$	0.100813	+	0.310271i	0.00454963	+	0.0140023i	0.953306	−	0.302007i	$-0.0976568\pi$
$491$	0.100813	+	0.310271i	0.00454963	+	0.0140023i	−0.948756	+	0.316010i	$0.897657\pi$
$492$		0			0
$493$	12.7082	+	9.23305i	0.572349	+	0.415836i
$494$	−3.23607			−0.145598
$495$		0			0
$496$	7.32624			0.328958
$497$	7.23607	+	5.25731i	0.324582	+	0.235823i
$498$		0			0
$499$	8.09017	+	24.8990i	0.362166	+	1.11463i	0.951737	+	0.306915i	$0.0992968\pi$
$499$	8.09017	+	24.8990i	0.362166	+	1.11463i	−0.589571	+	0.807716i	$0.700703\pi$
$500$	−4.28115	+	3.11044i	−0.191459	+	0.139103i
$501$		0			0
$502$	−7.47214	−	22.9969i	−0.333498	−	1.02640i
$503$	0.180340	−	0.555029i	0.00804096	−	0.0247475i	−0.946956	−	0.321365i	$-0.895858\pi$
$503$	0.180340	−	0.555029i	0.00804096	−	0.0247475i	0.954996	+	0.296617i	$0.0958585\pi$
$504$		0			0
$505$	5.96556			0.265464
$506$	5.22542	+	8.81678i	0.232298	+	0.391954i
$507$		0			0
$508$	−2.61803	−	1.90211i	−0.116156	−	0.0843926i
$509$	1.82624	−	5.62058i	0.0809466	−	0.249128i	−0.902391	−	0.430919i	$-0.858189\pi$
$509$	1.82624	−	5.62058i	0.0809466	−	0.249128i	0.983337	+	0.181791i	$0.0581895\pi$
$510$		0			0
$511$	4.23607	−	3.07768i	0.187393	−	0.136149i
$512$	8.89919	−	6.46564i	0.393292	−	0.285744i
$513$		0			0
$514$	−0.809017	+	2.48990i	−0.0356842	+	0.109825i
$515$	23.8435	+	17.3233i	1.05067	+	0.763355i
$516$		0			0
$517$	4.38197	−	4.97980i	0.192719	−	0.219011i
$518$	−12.0902			−0.531212
$519$		0			0
$520$	3.27051	−	10.0656i	0.143421	−	0.441406i
$521$	3.59017	+	11.0494i	0.157288	+	0.484083i	0.998386	−	0.0568005i	$-0.0180899\pi$
$521$	3.59017	+	11.0494i	0.157288	+	0.484083i	−0.841097	+	0.540884i	$0.818090\pi$
$522$		0			0
$523$	−2.35410	+	1.71036i	−0.102938	+	0.0747886i	−0.638063	−	0.769984i	$-0.720264\pi$
$523$	−2.35410	+	1.71036i	−0.102938	+	0.0747886i	0.535126	+	0.844772i	$0.320264\pi$
$524$	0.708204	+	2.17963i	0.0309380	+	0.0952175i
$525$		0			0
$526$	1.97214	+	1.43284i	0.0859892	+	0.0624748i
$527$	57.5410			2.50653
$528$		0			0
$529$	−13.4508			−0.584820
$530$	28.1246	+	20.4337i	1.22166	+	0.887584i
$531$		0			0
$532$	−0.809017	−	2.48990i	−0.0350753	−	0.107951i
$533$	10.8541	−	7.88597i	0.470143	−	0.341579i
$534$		0			0
$535$	−4.33030	−	13.3273i	−0.187215	−	0.576190i
$536$	−7.41641	+	22.8254i	−0.320340	+	0.985905i
$537$		0			0
$538$	−27.8885			−1.20236
$539$	3.23607	−	0.726543i	0.139387	−	0.0312944i
$540$		0			0
$541$	−13.6353	−	9.90659i	−0.586225	−	0.425918i	0.254738	−	0.967010i	$-0.418011\pi$
$541$	−13.6353	−	9.90659i	−0.586225	−	0.425918i	−0.840963	+	0.541093i	$0.818011\pi$
$542$	7.44427	−	22.9111i	0.319759	−	0.984117i
$543$		0			0
$544$	31.7705	−	23.0826i	1.36215	−	0.989659i
$545$	−24.3885	+	17.7193i	−1.04469	+	0.759012i
$546$		0			0
$547$	−11.2705	+	34.6871i	−0.481892	+	1.48311i	0.354540	+	0.935041i	$0.384638\pi$
$547$	−11.2705	+	34.6871i	−0.481892	+	1.48311i	−0.836432	+	0.548071i	$0.815362\pi$
$548$	−5.47214	−	3.97574i	−0.233758	−	0.169835i
$549$		0			0
$550$	10.1803	−	2.28563i	0.434091	−	0.0974595i
$551$	5.23607			0.223064
$552$		0			0
$553$	−4.32624	+	13.3148i	−0.183970	+	0.566203i
$554$	−3.22542	−	9.92684i	−0.137035	−	0.421751i
$555$		0			0
$556$	3.88197	−	2.82041i	0.164632	−	0.119612i
$557$	6.61803	+	20.3682i	0.280415	+	0.863029i	0.987736	+	0.156136i	$0.0499038\pi$
$557$	6.61803	+	20.3682i	0.280415	+	0.863029i	−0.707320	+	0.706893i	$0.750096\pi$
$558$		0			0
$559$	−1.23607	−	0.898056i	−0.0522801	−	0.0379837i
$560$	−2.85410			−0.120608
$561$		0			0
$562$	−1.05573			−0.0445332
$563$	32.6525	+	23.7234i	1.37614	+	0.999823i	0.997229	+	0.0743885i	$0.0237005\pi$
$563$	32.6525	+	23.7234i	1.37614	+	0.999823i	0.378908	+	0.925434i	$0.376300\pi$
$564$		0			0
$565$	−0.673762	−	2.07363i	−0.0283454	−	0.0872381i
$566$	−10.8713	+	7.89848i	−0.456956	+	0.331998i
$567$		0			0
$568$	8.29180	+	25.5195i	0.347916	+	1.07078i
$569$	5.61803	−	17.2905i	0.235520	−	0.724857i	−0.761532	−	0.648128i	$-0.775552\pi$
$569$	5.61803	−	17.2905i	0.235520	−	0.724857i	0.997052	−	0.0767291i	$-0.0244477\pi$
$570$		0			0
$571$	28.5410			1.19440			0.597202	−	0.802091i	$-0.296279\pi$
$571$	28.5410			1.19440			0.597202	+	0.802091i	$0.296279\pi$
$572$	−2.70820	+	3.07768i	−0.113236	+	0.128684i
$573$		0			0
$574$	−8.78115	−	6.37988i	−0.366518	−	0.266291i
$575$	3.00407	−	9.24556i	0.125278	−	0.385567i
$576$		0			0
$577$	11.8541	−	8.61251i	0.493493	−	0.358543i	−0.313033	−	0.949742i	$-0.601345\pi$
$577$	11.8541	−	8.61251i	0.493493	−	0.358543i	0.806526	+	0.591199i	$0.201345\pi$
$578$	−36.1525	+	26.2663i	−1.50374	+	1.09253i
$579$		0			0
$580$	−1.76393	+	5.42882i	−0.0732433	+	0.225420i
$581$	2.38197	+	1.73060i	0.0988206	+	0.0717974i
$582$		0			0
$583$	−20.5967	−	34.7526i	−0.853030	−	1.43930i
$584$	15.7082			0.650010
$585$		0			0
$586$	−6.11803	+	18.8294i	−0.252734	+	0.777834i
$587$	−1.20163	−	3.69822i	−0.0495964	−	0.152642i	0.923191	−	0.384341i	$-0.125571\pi$
$587$	−1.20163	−	3.69822i	−0.0495964	−	0.152642i	−0.972787	+	0.231699i	$0.925571\pi$
$588$		0			0
$589$	15.5172	−	11.2739i	0.639376	−	0.464534i
$590$	−5.96556	−	18.3601i	−0.245598	−	0.755873i
$591$		0			0
$592$	−9.78115	−	7.10642i	−0.402003	−	0.292072i
$593$	−3.43769			−0.141169			−0.0705846	−	0.997506i	$-0.522486\pi$
$593$	−3.43769			−0.141169			−0.0705846	+	0.997506i	$0.522486\pi$
$594$		0			0
$595$	−22.4164			−0.918983
$596$	16.1803	+	11.7557i	0.662773	+	0.481532i
$597$		0			0
$598$	−1.18034	−	3.63271i	−0.0482677	−	0.148553i
$599$	−1.26393	+	0.918300i	−0.0516429	+	0.0375207i	−0.613307	−	0.789844i	$-0.710161\pi$
$599$	−1.26393	+	0.918300i	−0.0516429	+	0.0375207i	0.561664	+	0.827365i	$0.310161\pi$
$600$		0			0
$601$	1.85410	+	5.70634i	0.0756304	+	0.232766i	0.981724	−	0.190311i	$-0.0609497\pi$
$601$	1.85410	+	5.70634i	0.0756304	+	0.232766i	−0.906093	+	0.423078i	$0.860950\pi$
$602$	−0.381966	+	1.17557i	−0.0155678	+	0.0479127i
$603$		0			0
$604$	2.00000			0.0813788
$605$	−30.8500	−	5.82485i	−1.25423	−	0.236814i
$606$		0			0
$607$	8.35410	+	6.06961i	0.339083	+	0.246358i	0.744275	−	0.667874i	$-0.232795\pi$
$607$	8.35410	+	6.06961i	0.339083	+	0.246358i	−0.405192	+	0.914232i	$0.632795\pi$
$608$	4.04508	−	12.4495i	0.164050	−	0.504894i
$609$		0			0
$610$	−20.6525	+	15.0049i	−0.836194	+	0.607531i
$611$	−2.00000	+	1.45309i	−0.0809113	+	0.0587855i
$612$		0			0
$613$	−1.80902	+	5.56758i	−0.0730655	+	0.224873i	−0.980920	−	0.194414i	$-0.937720\pi$
$613$	−1.80902	+	5.56758i	−0.0730655	+	0.224873i	0.907854	+	0.419286i	$0.137720\pi$
$614$	19.6353	+	14.2658i	0.792414	+	0.575723i
$615$		0			0
$616$	9.13525	+	3.94298i	0.368070	+	0.158867i
$617$	−44.6525			−1.79764			−0.898820	−	0.438317i	$-0.855575\pi$
$617$	−44.6525			−1.79764			−0.898820	+	0.438317i	$0.855575\pi$
$618$		0			0
$619$	−3.55573	+	10.9434i	−0.142917	+	0.439853i	−0.996737	−	0.0807150i	$-0.974280\pi$
$619$	−3.55573	+	10.9434i	−0.142917	+	0.439853i	0.853820	+	0.520568i	$0.174280\pi$
$620$	6.46149	+	19.8864i	0.259500	+	0.798658i
$621$		0			0
$622$	−0.618034	+	0.449028i	−0.0247809	+	0.0180044i
$623$	−0.336881	−	1.03681i	−0.0134969	−	0.0415390i
$624$		0			0
$625$	24.9443	+	18.1231i	0.997771	+	0.724923i
$626$	−9.81966			−0.392473
$627$		0			0
$628$	−9.70820			−0.387400
$629$	−76.8222	−	55.8146i	−3.06310	−	2.22547i
$630$		0			0
$631$	9.23607	+	28.4257i	0.367682	+	1.13161i	0.948284	+	0.317422i	$0.102817\pi$
$631$	9.23607	+	28.4257i	0.367682	+	1.13161i	−0.580602	+	0.814187i	$0.697183\pi$
$632$	−33.9787	+	24.6870i	−1.35160	+	0.981995i
$633$		0			0
$634$	8.52786	+	26.2461i	0.338685	+	1.04236i
$635$	−2.85410	+	8.78402i	−0.113262	+	0.348583i
$636$		0			0
$637$	−1.23607			−0.0489748
$638$	−4.38197	+	4.97980i	−0.173484	+	0.197152i
$639$		0			0
$640$	6.92705	+	5.03280i	0.273816	+	0.198939i
$641$	−2.67376	+	8.22899i	−0.105607	+	0.325026i	−0.989872	−	0.141959i	$-0.954660\pi$
$641$	−2.67376	+	8.22899i	−0.105607	+	0.325026i	0.884265	+	0.466985i	$0.154660\pi$
$642$		0			0
$643$	−38.7705	+	28.1684i	−1.52896	+	1.11085i	−0.572146	+	0.820152i	$0.693889\pi$
$643$	−38.7705	+	28.1684i	−1.52896	+	1.11085i	−0.956813	+	0.290703i	$0.906111\pi$
$644$	2.50000	−	1.81636i	0.0985138	−	0.0715745i
$645$		0			0
$646$	−6.35410	+	19.5559i	−0.249999	+	0.769417i
$647$	−24.5623	−	17.8456i	−0.965644	−	0.701581i	−0.0111892	−	0.999937i	$-0.503562\pi$
$647$	−24.5623	−	17.8456i	−0.965644	−	0.701581i	−0.954455	+	0.298356i	$0.903562\pi$
$648$		0			0
$649$	−2.09017	+	22.3358i	−0.0820463	+	0.876758i
$650$	−3.88854			−0.152521
$651$		0			0
$652$	1.67376	−	5.15131i	0.0655496	−	0.201741i
$653$	8.00000	+	24.6215i	0.313064	+	0.963513i	0.976544	+	0.215318i	$0.0690789\pi$
$653$	8.00000	+	24.6215i	0.313064	+	0.963513i	−0.663480	+	0.748194i	$0.730921\pi$
$654$		0			0
$655$	5.29180	−	3.84471i	0.206768	−	0.150225i
$656$	−3.35410	−	10.3229i	−0.130956	−	0.403040i
$657$		0			0
$658$	1.61803	+	1.17557i	0.0630775	+	0.0458285i
$659$	35.0344			1.36475			0.682374	−	0.731003i	$-0.260948\pi$
$659$	35.0344			1.36475			0.682374	+	0.731003i	$0.260948\pi$
$660$		0			0
$661$	8.29180			0.322513			0.161257	−	0.986912i	$-0.448445\pi$
$661$	8.29180			0.322513			0.161257	+	0.986912i	$0.448445\pi$
$662$	−24.5623	−	17.8456i	−0.954641	−	0.693587i
$663$		0			0
$664$	2.72949	+	8.40051i	0.105925	+	0.326003i
$665$	−6.04508	+	4.39201i	−0.234418	+	0.170315i
$666$		0			0
$667$	1.90983	+	5.87785i	0.0739489	+	0.227591i
$668$	2.52786	−	7.77997i	0.0978060	−	0.301016i
$669$		0			0
$670$	22.8328			0.882109
$671$	28.9443	−	6.49839i	1.11738	−	0.250868i
$672$		0			0
$673$	−29.0344	−	21.0948i	−1.11920	−	0.813143i	−0.135109	−	0.990831i	$-0.543138\pi$
$673$	−29.0344	−	21.0948i	−1.11920	−	0.813143i	−0.984087	+	0.177688i	$0.943138\pi$
$674$	−8.38854	+	25.8173i	−0.323115	+	0.994445i
$675$		0			0
$676$	−9.28115	+	6.74315i	−0.356967	+	0.259352i
$677$	19.3262	−	14.0413i	0.742768	−	0.539652i	−0.150809	−	0.988563i	$-0.548188\pi$
$677$	19.3262	−	14.0413i	0.742768	−	0.539652i	0.893577	+	0.448911i	$0.148188\pi$
$678$		0			0
$679$	−1.09017	+	3.35520i	−0.0418369	+	0.128761i
$680$	−54.4058	−	39.5281i	−2.08637	−	1.51583i
$681$		0			0
$682$	−2.26393	+	24.1927i	−0.0866904	+	0.926386i
$683$	−40.9230			−1.56587			−0.782937	−	0.622101i	$-0.786279\pi$
$683$	−40.9230			−1.56587			−0.782937	+	0.622101i	$0.786279\pi$
$684$		0			0
$685$	−5.96556	+	18.3601i	−0.227932	+	0.701503i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$		0			0
$688$	−1.00000	+	0.726543i	−0.0381246	+	0.0276992i
$689$	4.65248	+	14.3188i	0.177245	+	0.545505i
$690$		0			0
$691$	−32.2984	−	23.4661i	−1.22869	−	0.892694i	−0.231897	−	0.972740i	$-0.574493\pi$
$691$	−32.2984	−	23.4661i	−1.22869	−	0.892694i	−0.996791	+	0.0800463i	$0.974493\pi$
$692$	19.8541			0.754740
$693$		0			0
$694$	12.3820			0.470013
$695$	−11.0795	−	8.04975i	−0.420270	−	0.305344i
$696$		0			0
$697$	−26.3435	−	81.0768i	−0.997830	−	3.07100i
$698$	−18.4164	+	13.3803i	−0.697071	+	0.506452i
$699$		0			0
$700$	−0.972136	−	2.99193i	−0.0367433	−	0.113084i
$701$	−7.43769	+	22.8909i	−0.280918	+	0.864576i	0.706675	+	0.707539i	$0.250194\pi$
$701$	−7.43769	+	22.8909i	−0.280918	+	0.864576i	−0.987593	+	0.157038i	$0.949806\pi$
$702$		0			0
$703$	−31.6525			−1.19380
$704$	11.8369	+	19.9722i	0.446119	+	0.752730i
$705$		0			0
$706$	10.0902	+	7.33094i	0.379749	+	0.275903i
$707$	0.645898	−	1.98787i	0.0242915	−	0.0747615i
$708$		0			0
$709$	15.9271	−	11.5717i	0.598153	−	0.434584i	−0.247070	−	0.968998i	$-0.579468\pi$
$709$	15.9271	−	11.5717i	0.598153	−	0.434584i	0.845223	+	0.534414i	$0.179468\pi$
$710$	20.6525	−	15.0049i	0.775074	−	0.563124i
$711$		0			0
$712$	1.01064	−	3.11044i	0.0378755	−	0.116569i
$713$	18.3156	+	13.3071i	0.685924	+	0.498353i
$714$		0			0
$715$	10.7426	+	4.63677i	0.401752	+	0.173405i
$716$	8.38197			0.313249
$717$		0			0
$718$	−2.17376	+	6.69015i	−0.0811241	+	0.249674i
$719$	−1.50658	−	4.63677i	−0.0561859	−	0.172922i	0.919025	−	0.394199i	$-0.128978\pi$
$719$	−1.50658	−	4.63677i	−0.0561859	−	0.172922i	−0.975211	+	0.221276i	$0.928978\pi$
$720$		0			0
$721$	8.35410	−	6.06961i	0.311123	−	0.226044i
$722$	−3.75329	−	11.5514i	−0.139683	−	0.429900i
$723$		0			0
$724$	−15.3262	−	11.1352i	−0.569595	−	0.413835i
$725$	6.29180			0.233671
$726$		0			0
$727$	25.7426			0.954742			0.477371	−	0.878702i	$-0.341590\pi$
$727$	25.7426			0.954742			0.477371	+	0.878702i	$0.341590\pi$
$728$	−3.00000	−	2.17963i	−0.111187	−	0.0807824i
$729$		0			0
$730$	−4.61803	−	14.2128i	−0.170921	−	0.526041i
$731$	−7.85410	+	5.70634i	−0.290494	+	0.211057i
$732$		0			0
$733$	9.61803	+	29.6013i	0.355250	+	1.09335i	0.955864	+	0.293809i	$0.0949228\pi$
$733$	9.61803	+	29.6013i	0.355250	+	1.09335i	−0.600614	+	0.799539i	$0.705077\pi$
$734$	5.02786	−	15.4742i	0.185582	−	0.571162i
$735$		0			0
$736$	15.4508			0.569526
$737$	−24.3607	−	10.5146i	−0.897337	−	0.387311i
$738$		0			0
$739$	−39.6525	−	28.8092i	−1.45864	−	1.05976i	−0.983715	−	0.179738i	$-0.942475\pi$
$739$	−39.6525	−	28.8092i	−1.45864	−	1.05976i	−0.474925	−	0.880026i	$-0.657525\pi$
$740$	10.6631	−	32.8177i	0.391984	−	1.20640i
$741$		0			0
$742$	9.85410	−	7.15942i	0.361755	−	0.262831i
$743$	14.0172	−	10.1841i	0.514242	−	0.373619i	−0.300188	−	0.953880i	$-0.597050\pi$
$743$	14.0172	−	10.1841i	0.514242	−	0.373619i	0.814430	+	0.580261i	$0.197050\pi$
$744$		0			0
$745$	17.6393	−	54.2882i	0.646255	−	1.98897i
$746$	18.8713	+	13.7108i	0.690928	+	0.501989i
$747$		0			0
$748$	13.2812	+	22.4091i	0.485607	+	0.819357i
$749$	−4.90983			−0.179401
$750$		0			0
$751$	−3.23607	+	9.95959i	−0.118086	+	0.363431i	−0.992578	−	0.121609i	$-0.961195\pi$
$751$	−3.23607	+	9.95959i	−0.118086	+	0.363431i	0.874492	+	0.485039i	$0.161195\pi$
$752$	0.618034	+	1.90211i	0.0225374	+	0.0693629i
$753$		0			0
$754$	2.00000	−	1.45309i	0.0728357	−	0.0529182i
$755$	−1.76393	−	5.42882i	−0.0641961	−	0.197575i
$756$		0			0
$757$	−0.263932	−	0.191758i	−0.00959277	−	0.00696956i	0.582979	−	0.812488i	$-0.301887\pi$
$757$	−0.263932	−	0.191758i	−0.00959277	−	0.00696956i	−0.592571	+	0.805518i	$0.701887\pi$
$758$	2.47214			0.0897920
$759$		0			0
$760$	−22.4164			−0.813129
$761$	37.0344	+	26.9071i	1.34250	+	0.975382i	0.999348	+	0.0361006i	$0.0114937\pi$
$761$	37.0344	+	26.9071i	1.34250	+	0.975382i	0.343149	+	0.939281i	$0.388506\pi$
$762$		0			0
$763$	3.26393	+	10.0453i	0.118162	+	0.363666i
$764$	14.7812	−	10.7391i	0.534763	−	0.388528i
$765$		0			0
$766$	4.03444	+	12.4167i	0.145770	+	0.448635i
$767$	2.58359	−	7.95148i	0.0932881	−	0.287111i
$768$		0			0
$769$	14.5836			0.525898			0.262949	−	0.964810i	$-0.415305\pi$
$769$	14.5836			0.525898			0.262949	+	0.964810i	$0.415305\pi$
$770$	0.881966	−	9.42481i	0.0317838	−	0.339647i
$771$		0			0
$772$	14.8713	+	10.8046i	0.535231	+	0.388868i
$773$	12.0344	−	37.0382i	0.432849	−	1.33217i	−0.462426	−	0.886658i	$-0.653021\pi$
$773$	12.0344	−	37.0382i	0.432849	−	1.33217i	0.895275	−	0.445514i	$-0.146979\pi$
$774$		0			0
$775$	18.6459	−	13.5470i	0.669780	−	0.486624i
$776$	−8.56231	+	6.22088i	−0.307369	+	0.223317i
$777$		0			0
$778$	−6.85410	+	21.0948i	−0.245731	+	0.756284i
$779$	−22.9894	−	16.7027i	−0.823679	−	0.598438i
$780$		0			0
$781$	−28.9443	+	6.49839i	−1.03571	+	0.232531i
$782$	−24.2705			−0.867912
$783$		0			0
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	8.56231	+	26.3521i	0.305602	+	0.940546i
$786$		0			0
$787$	−9.92705	+	7.21242i	−0.353861	+	0.257095i	−0.750487	−	0.660885i	$-0.770181\pi$
$787$	−9.92705	+	7.21242i	−0.353861	+	0.257095i	0.396626	+	0.917980i	$0.370181\pi$
$788$	1.23607	+	3.80423i	0.0440331	+	0.135520i
$789$		0			0
$790$	32.3262	+	23.4864i	1.15012	+	0.835608i
$791$	−0.763932			−0.0271623
$792$		0			0
$793$	−11.0557			−0.392600
$794$	−11.8541	−	8.61251i	−0.420686	−	0.305647i
$795$		0			0
$796$	0.809017	+	2.48990i	0.0286748	+	0.0882521i
$797$	8.30902	−	6.03685i	0.294320	−	0.213836i	−0.430819	−	0.902438i	$-0.641775\pi$
$797$	8.30902	−	6.03685i	0.294320	−	0.213836i	0.725139	+	0.688602i	$0.241775\pi$
$798$		0			0
$799$	4.85410	+	14.9394i	0.171726	+	0.528518i
$800$	4.86068	−	14.9596i	0.171851	−	0.528903i
$801$		0			0
$802$	−18.4721			−0.652274
$803$	−1.61803	+	17.2905i	−0.0570992	+	0.610170i
$804$		0			0
$805$	−7.13525	−	5.18407i	−0.251485	−	0.182714i
$806$	2.79837	−	8.61251i	0.0985685	−	0.303363i
$807$		0			0
$808$	5.07295	−	3.68571i	0.178466	−	0.129663i
$809$	−23.1803	+	16.8415i	−0.814977	+	0.592116i	−0.915269	−	0.402842i	$-0.868022\pi$
$809$	−23.1803	+	16.8415i	−0.814977	+	0.592116i	0.100292	+	0.994958i	$0.468022\pi$
$810$		0			0
$811$	−5.05573	+	15.5599i	−0.177531	+	0.546383i	−0.999740	−	0.0228021i	$-0.992741\pi$
$811$	−5.05573	+	15.5599i	−0.177531	+	0.546383i	0.822209	+	0.569185i	$0.192741\pi$
$812$	1.61803	+	1.17557i	0.0567819	+	0.0412544i
$813$		0			0
$814$	26.4894	−	30.1033i	0.928451	−	1.05512i
$815$	−15.4590			−0.541504
$816$		0			0
$817$	−1.00000	+	3.07768i	−0.0349856	+	0.107675i
$818$	8.88854	+	27.3561i	0.310781	+	0.956484i
$819$		0			0
$820$	25.0623	−	18.2088i	0.875214	−	0.635880i
$821$	−9.38197	−	28.8747i	−0.327433	−	1.00773i	−0.970330	−	0.241783i	$-0.922268\pi$
$821$	−9.38197	−	28.8747i	−0.327433	−	1.00773i	0.642898	−	0.765952i	$-0.277732\pi$
$822$		0			0
$823$	−19.7984	−	14.3844i	−0.690128	−	0.501407i	0.186574	−	0.982441i	$-0.440262\pi$
$823$	−19.7984	−	14.3844i	−0.690128	−	0.501407i	−0.876702	+	0.481034i	$0.840262\pi$
$824$	30.9787			1.07919
$825$		0			0
$826$	−6.76393			−0.235347
$827$	−3.50000	−	2.54290i	−0.121707	−	0.0884253i	0.525267	−	0.850938i	$-0.323966\pi$
$827$	−3.50000	−	2.54290i	−0.121707	−	0.0884253i	−0.646974	+	0.762512i	$0.723966\pi$
$828$		0			0
$829$	8.94427	+	27.5276i	0.310647	+	0.956074i	0.977509	+	0.210893i	$0.0676371\pi$
$829$	8.94427	+	27.5276i	0.310647	+	0.956074i	−0.666862	+	0.745181i	$0.732363\pi$
$830$	6.79837	−	4.93931i	0.235975	−	0.171446i
$831$		0			0
$832$	−2.67376	−	8.22899i	−0.0926960	−	0.285289i
$833$	−2.42705	+	7.46969i	−0.0840923	+	0.258810i
$834$		0			0
$835$	−23.3475			−0.807974
$836$	7.97214	+	3.44095i	0.275722	+	0.119008i
$837$		0			0
$838$	11.9443	+	8.67802i	0.412608	+	0.299777i
$839$	−10.3262	+	31.7809i	−0.356501	+	1.09720i	0.598633	+	0.801024i	$0.295711\pi$
$839$	−10.3262	+	31.7809i	−0.356501	+	1.09720i	−0.955134	+	0.296174i	$0.904289\pi$
$840$		0			0
$841$	20.2254	−	14.6946i	0.697428	−	0.506711i
$842$	3.50000	−	2.54290i	0.120618	−	0.0876341i
$843$		0			0
$844$	0.618034	−	1.90211i	0.0212736	−	0.0654734i
$845$	26.4894	+	19.2456i	0.911262	+	0.662070i
$846$		0			0
$847$	−5.28115	+	9.64932i	−0.181463	+	0.331555i
$848$	12.1803			0.418275
$849$		0			0
$850$	−7.63525	+	23.4989i	−0.261887	+	0.806006i
$851$	−11.5451	−	35.5321i	−0.395760	−	1.21803i
$852$		0			0
$853$	12.7082	−	9.23305i	0.435121	−	0.316134i	−0.348573	−	0.937282i	$-0.613333\pi$
$853$	12.7082	−	9.23305i	0.435121	−	0.316134i	0.783693	+	0.621148i	$0.213333\pi$
$854$	2.76393	+	8.50651i	0.0945798	+	0.291087i
$855$		0			0
$856$	−11.9164	−	8.65778i	−0.407294	−	0.295917i
$857$	18.9443			0.647124			0.323562	−	0.946207i	$-0.395120\pi$
$857$	18.9443			0.647124			0.323562	+	0.946207i	$0.395120\pi$
$858$		0			0
$859$	−5.88854			−0.200915			−0.100457	−	0.994941i	$-0.532031\pi$
$859$	−5.88854			−0.200915			−0.100457	+	0.994941i	$0.532031\pi$
$860$	−2.85410	−	2.07363i	−0.0973241	−	0.0707101i
$861$		0			0
$862$	0.645898	+	1.98787i	0.0219994	+	0.0677071i
$863$	30.4894	−	22.1518i	1.03787	−	0.754057i	0.0680012	−	0.997685i	$-0.478338\pi$
$863$	30.4894	−	22.1518i	1.03787	−	0.754057i	0.969869	+	0.243629i	$0.0783378\pi$
$864$		0			0
$865$	−17.5106	−	53.8922i	−0.595380	−	1.83239i
$866$	−5.32624	+	16.3925i	−0.180993	+	0.557039i
$867$		0			0
$868$	7.32624			0.248669
$869$	−23.6738	−	39.9444i	−0.803077	−	1.35502i
$870$		0			0
$871$	8.00000	+	5.81234i	0.271070	+	0.196944i
$872$	−9.79180	+	30.1360i	−0.331592	+	1.02054i
$873$		0			0
$874$	−6.54508	+	4.75528i	−0.221391	+	0.160850i
$875$	4.28115	−	3.11044i	0.144729	−	0.105152i
$876$		0			0
$877$	−14.3262	+	44.0916i	−0.483763	+	1.48887i	0.350002	+	0.936749i	$0.386181\pi$
$877$	−14.3262	+	44.0916i	−0.483763	+	1.48887i	−0.833765	+	0.552120i	$0.813819\pi$
$878$	17.6353	+	12.8128i	0.595161	+	0.432410i
$879$		0			0
$880$	6.25329	−	7.10642i	0.210798	−	0.239557i
$881$	33.4508			1.12699			0.563494	−	0.826120i	$-0.309457\pi$
$881$	33.4508			1.12699			0.563494	+	0.826120i	$0.309457\pi$
$882$		0			0
$883$	2.38197	−	7.33094i	0.0801595	−	0.246706i	−0.902943	−	0.429760i	$-0.858598\pi$
$883$	2.38197	−	7.33094i	0.0801595	−	0.246706i	0.983103	+	0.183054i	$0.0585983\pi$
$884$	−3.00000	−	9.23305i	−0.100901	−	0.310541i
$885$		0			0
$886$	3.97214	−	2.88593i	0.133447	−	0.0969546i
$887$	14.3820	+	44.2631i	0.482899	+	1.48621i	0.835001	+	0.550249i	$0.185467\pi$
$887$	14.3820	+	44.2631i	0.482899	+	1.48621i	−0.352101	+	0.935962i	$0.614533\pi$
$888$		0			0
$889$	2.61803	+	1.90211i	0.0878060	+	0.0637948i
$890$	−3.11146			−0.104296
$891$		0			0
$892$	−20.7984			−0.696381
$893$	4.23607	+	3.07768i	0.141755	+	0.102991i
$894$		0			0
$895$	−7.39261	−	22.7521i	−0.247108	−	0.760519i
$896$	2.42705	−	1.76336i	0.0810821	−	0.0589096i
$897$		0			0
$898$	−12.9443	−	39.8384i	−0.431956	−	1.32942i
$899$	−4.52786	+	13.9353i	−0.151013	+	0.464769i
$900$		0			0
$901$	95.6656			3.18708
$902$	35.1246	−	7.88597i	1.16952	−	0.262574i
$903$		0			0
$904$	−1.85410	−	1.34708i	−0.0616665	−	0.0448033i
$905$	−16.7082	+	51.4226i	−0.555399	+	1.70934i
$906$		0			0
$907$	38.2148	−	27.7647i	1.26890	−	0.921911i	0.269743	−	0.962932i	$-0.413061\pi$
$907$	38.2148	−	27.7647i	1.26890	−	0.921911i	0.999158	+	0.0410219i	$0.0130613\pi$
$908$	−17.3262	+	12.5882i	−0.574991	+	0.417756i
$909$		0			0
$910$	−1.09017	+	3.35520i	−0.0361388	+	0.111224i
$911$	−8.94427	−	6.49839i	−0.296337	−	0.215301i	0.429675	−	0.902984i	$-0.358628\pi$
$911$	−8.94427	−	6.49839i	−0.296337	−	0.215301i	−0.726012	+	0.687682i	$0.758628\pi$
$912$		0			0
$913$	−9.52786	+	2.13914i	−0.315326	+	0.0707952i
$914$	12.4721			0.412542
$915$		0			0
$916$	−6.56231	+	20.1967i	−0.216825	+	0.667318i
$917$	−0.708204	−	2.17963i	−0.0233870	−	0.0719776i
$918$		0			0
$919$	−6.00000	+	4.35926i	−0.197922	+	0.143799i	−0.682332	−	0.731042i	$-0.739034\pi$
$919$	−6.00000	+	4.35926i	−0.197922	+	0.143799i	0.484410	+	0.874841i	$0.339034\pi$
$920$	−8.17627	−	25.1640i	−0.269564	−	0.829632i
$921$		0			0
$922$	−5.14590	−	3.73871i	−0.169471	−	0.123128i
$923$	11.0557			0.363904
$924$		0			0
$925$	−38.0344			−1.25056
$926$	−9.23607	−	6.71040i	−0.303516	−	0.220517i
$927$		0			0
$928$	3.09017	+	9.51057i	0.101440	+	0.312200i
$929$	−23.2984	+	16.9273i	−0.764395	+	0.555365i	−0.900255	−	0.435363i	$-0.856620\pi$
$929$	−23.2984	+	16.9273i	−0.764395	+	0.555365i	0.135860	+	0.990728i	$0.456620\pi$
$930$		0			0
$931$	0.809017	+	2.48990i	0.0265145	+	0.0816031i
$932$	−1.76393	+	5.42882i	−0.0577795	+	0.177827i
$933$		0			0
$934$	−19.2361			−0.629423
$935$	49.1140	−	55.8146i	1.60620	−	1.82533i
$936$		0			0
$937$	−9.47214	−	6.88191i	−0.309441	−	0.224822i	0.422215	−	0.906495i	$-0.361253\pi$
$937$	−9.47214	−	6.88191i	−0.309441	−	0.224822i	−0.731657	+	0.681673i	$0.761253\pi$
$938$	2.47214	−	7.60845i	0.0807181	−	0.248425i
$939$		0			0
$940$	−4.61803	+	3.35520i	−0.150624	+	0.109434i
$941$	−9.59017	+	6.96767i	−0.312631	+	0.227139i	−0.733024	−	0.680202i	$-0.761892\pi$
$941$	−9.59017	+	6.96767i	−0.312631	+	0.227139i	0.420394	+	0.907342i	$0.361892\pi$
$942$		0			0
$943$	10.3647	−	31.8994i	0.337523	−	1.03879i
$944$	−5.47214	−	3.97574i	−0.178103	−	0.129399i
$945$		0			0
$946$	−2.09017	−	3.52671i	−0.0679573	−	0.114663i
$947$	23.4377			0.761623			0.380811	−	0.924653i	$-0.375645\pi$
$947$	23.4377			0.761623			0.380811	+	0.924653i	$0.375645\pi$
$948$		0			0
$949$	2.00000	−	6.15537i	0.0649227	−	0.199812i
$950$	2.54508	+	7.83297i	0.0825735	+	0.254135i
$951$		0			0
$952$	−19.0623	+	13.8496i	−0.617813	+	0.448867i
$953$	−1.49342	−	4.59628i	−0.0483767	−	0.148888i	0.923950	−	0.382513i	$-0.124941\pi$
$953$	−1.49342	−	4.59628i	−0.0483767	−	0.148888i	−0.972327	+	0.233625i	$0.924941\pi$
$954$		0			0
$955$	−42.1869	−	30.6506i	−1.36514	−	0.991830i
$956$	−1.56231			−0.0505286
$957$		0			0
$958$	11.0557			0.357194
$959$	5.47214	+	3.97574i	0.176704	+	0.128383i
$960$		0			0
$961$	7.00658	+	21.5640i	0.226019	+	0.695614i
$962$	−12.0902	+	8.78402i	−0.389803	+	0.283208i
$963$		0			0
$964$	−1.52786	−	4.70228i	−0.0492092	−	0.151450i
$965$	16.2123	−	49.8962i	0.521891	−	1.60622i
$966$		0			0
$967$	49.3050			1.58554			0.792770	−	0.609521i	$-0.208638\pi$
$967$	49.3050			1.58554			0.792770	+	0.609521i	$0.208638\pi$
$968$	−29.8328	+	14.1068i	−0.958863	+	0.453411i
$969$		0			0
$970$	8.14590	+	5.91834i	0.261549	+	0.190026i
$971$	−13.0000	+	40.0099i	−0.417190	+	1.28398i	0.493088	+	0.869980i	$0.335868\pi$
$971$	−13.0000	+	40.0099i	−0.417190	+	1.28398i	−0.910277	+	0.413999i	$0.864132\pi$
$972$		0			0
$973$	−3.88197	+	2.82041i	−0.124450	+	0.0904183i
$974$	31.7426	−	23.0624i	1.01710	−	0.738966i
$975$		0			0
$976$	−2.76393	+	8.50651i	−0.0884713	+	0.272287i
$977$	−21.5066	−	15.6254i	−0.688056	−	0.499902i	0.187964	−	0.982176i	$-0.439811\pi$
$977$	−21.5066	−	15.6254i	−0.688056	−	0.499902i	−0.876021	+	0.482274i	$0.839811\pi$
$978$		0			0
$979$	3.31966	+	1.43284i	0.106097	+	0.0457938i
$980$	−2.85410			−0.0911709
$981$		0			0
$982$	0.100813	−	0.310271i	0.00321707	−	0.00990114i
$983$	−14.9787	−	46.0997i	−0.477747	−	1.47035i	−0.842217	−	0.539138i	$-0.818750\pi$
$983$	−14.9787	−	46.0997i	−0.477747	−	1.47035i	0.364470	−	0.931215i	$-0.381250\pi$
$984$		0			0
$985$	9.23607	−	6.71040i	0.294286	−	0.213811i
$986$	−4.85410	−	14.9394i	−0.154586	−	0.475767i
$987$		0			0
$988$	−2.61803	−	1.90211i	−0.0832908	−	0.0605143i
$989$	−3.81966			−0.121458
$990$		0			0
$991$	18.6525			0.592515			0.296258	−	0.955108i	$-0.404261\pi$
$991$	18.6525			0.592515			0.296258	+	0.955108i	$0.404261\pi$
$992$	29.6353	+	21.5313i	0.940920	+	0.683619i
$993$		0			0
$994$	−2.76393	−	8.50651i	−0.0876666	−	0.269810i
$995$	6.04508	−	4.39201i	0.191642	−	0.139236i
$996$		0			0
$997$	−16.2361	−	49.9695i	−0.514201	−	1.58255i	−0.784730	−	0.619837i	$-0.787199\pi$
$997$	−16.2361	−	49.9695i	−0.514201	−	1.58255i	0.270529	−	0.962712i	$-0.412801\pi$
$998$	8.09017	−	24.8990i	0.256090	−	0.788164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.c.631.1		4
3.2	odd	2		231.2.j.c.169.1	✓	4
11.3	even	5	inner	693.2.m.c.190.1		4
11.5	even	5		7623.2.a.bu.1.2		2
11.6	odd	10		7623.2.a.w.1.2		2
33.5	odd	10		2541.2.a.n.1.1		2
33.14	odd	10		231.2.j.c.190.1	yes	4
33.17	even	10		2541.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.169.1	✓	4	3.2	odd	2
231.2.j.c.190.1	yes	4	33.14	odd	10
693.2.m.c.190.1		4	11.3	even	5	inner
693.2.m.c.631.1		4	1.1	even	1	trivial
2541.2.a.n.1.1		2	33.5	odd	10
2541.2.a.bd.1.1		2	33.17	even	10
7623.2.a.w.1.2		2	11.6	odd	10
7623.2.a.bu.1.2		2	11.5	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(-2.30902 + 1.67760i) q^{5} +(0.309017 + 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +2.85410 q^{10} +(-3.04508 - 1.31433i) q^{11} +(1.00000 + 0.726543i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.809017 - 0.587785i) q^{16} +(6.35410 - 4.61653i) q^{17} +(0.809017 - 2.48990i) q^{19} +(2.30902 + 1.67760i) q^{20} +(1.69098 + 2.85317i) q^{22} +3.09017 q^{23} +(0.972136 - 2.99193i) q^{25} +(-0.381966 - 1.17557i) q^{26} +(0.809017 - 0.587785i) q^{28} +(0.618034 + 1.90211i) q^{29} +(5.92705 + 4.30625i) q^{31} +5.00000 q^{32} -7.85410 q^{34} +(-2.30902 - 1.67760i) q^{35} +(-3.73607 - 11.4984i) q^{37} +(-2.11803 + 1.53884i) q^{38} +(-2.64590 - 8.14324i) q^{40} +(3.35410 - 10.3229i) q^{41} -1.23607 q^{43} +(-0.309017 + 3.30220i) q^{44} +(-2.50000 - 1.81636i) q^{46} +(-0.618034 + 1.90211i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-2.54508 + 1.84911i) q^{50} +(0.381966 - 1.17557i) q^{52} +(9.85410 + 7.15942i) q^{53} +(9.23607 - 2.07363i) q^{55} -3.00000 q^{56} +(0.618034 - 1.90211i) q^{58} +(-2.09017 - 6.43288i) q^{59} +(-7.23607 + 5.25731i) q^{61} +(-2.26393 - 6.96767i) q^{62} +(-5.66312 - 4.11450i) q^{64} -3.52786 q^{65} +8.00000 q^{67} +(-6.35410 - 4.61653i) q^{68} +(0.881966 + 2.71441i) q^{70} +(7.23607 - 5.25731i) q^{71} +(-1.61803 - 4.97980i) q^{73} +(-3.73607 + 11.4984i) q^{74} -2.61803 q^{76} +(0.309017 - 3.30220i) q^{77} +(11.3262 + 8.22899i) q^{79} +(-0.881966 + 2.71441i) q^{80} +(-8.78115 + 6.37988i) q^{82} +(2.38197 - 1.73060i) q^{83} +(-6.92705 + 21.3193i) q^{85} +(1.00000 + 0.726543i) q^{86} +(6.57295 - 7.46969i) q^{88} -1.09017 q^{89} +(-0.381966 + 1.17557i) q^{91} +(-0.954915 - 2.93893i) q^{92} +(1.61803 - 1.17557i) q^{94} +(2.30902 + 7.10642i) q^{95} +(2.85410 + 2.07363i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} - 7 q^{5} - q^{7} + 3 q^{8}+O(q^{10}) \) 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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