LMFDB - Embedded newform 88.2.c.a.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(45,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("88.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.578281160704.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 2x^{8} - 2x^{7} - 3x^{6} - 6x^{5} - 6x^{4} - 8x^{3} + 16x^{2} + 32 $ x^10 + 2x^8 - 2x^7 - 3x^6 - 6x^5 - 6x^4 - 8x^3 + 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			45.1
Root			$1.41363 + 0.0406696i$ of defining polynomial
Character	$\chi$	$=$	88.45
Dual form			88.2.c.a.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29865 - 0.559929i) q^{2} +0.229967i q^{3} +(1.37296 + 1.45430i) q^{4} +2.51595i q^{5} +(0.128765 - 0.298645i) q^{6} +1.47743 q^{7} +(-0.968683 - 2.65738i) q^{8} +2.94712 q^{9} +O(q^{10})$	\(q+(-1.29865 - 0.559929i) q^{2} +0.229967i q^{3} +(1.37296 + 1.45430i) q^{4} +2.51595i q^{5} +(0.128765 - 0.298645i) q^{6} +1.47743 q^{7} +(-0.968683 - 2.65738i) q^{8} +2.94712 q^{9} +(1.40875 - 3.26733i) q^{10} -1.00000i q^{11} +(-0.334440 + 0.315735i) q^{12} +3.47743i q^{13} +(-1.91866 - 0.827257i) q^{14} -0.578585 q^{15} +(-0.229967 + 3.99338i) q^{16} -3.31475 q^{17} +(-3.82726 - 1.65018i) q^{18} -7.13195i q^{19} +(-3.65894 + 3.45430i) q^{20} +0.339760i q^{21} +(-0.559929 + 1.29865i) q^{22} -6.45332 q^{23} +(0.611108 - 0.222765i) q^{24} -1.33001 q^{25} +(1.94712 - 4.51595i) q^{26} +1.36764i q^{27} +(2.02845 + 2.14863i) q^{28} -1.41480i q^{29} +(0.751377 + 0.323967i) q^{30} +0.636125 q^{31} +(2.53466 - 5.05722i) q^{32} +0.229967 q^{33} +(4.30469 + 1.85603i) q^{34} +3.71715i q^{35} +(4.04627 + 4.28598i) q^{36} -6.97588i q^{37} +(-3.99338 + 9.26187i) q^{38} -0.799694 q^{39} +(6.68583 - 2.43716i) q^{40} +6.72955 q^{41} +(0.190242 - 0.441228i) q^{42} -3.21471i q^{43} +(1.45430 - 1.37296i) q^{44} +7.41480i q^{45} +(8.38057 + 3.61340i) q^{46} +0.862328 q^{47} +(-0.918346 - 0.0528847i) q^{48} -4.81719 q^{49} +(1.72721 + 0.744712i) q^{50} -0.762283i q^{51} +(-5.05722 + 4.77437i) q^{52} -13.2515i q^{53} +(0.765781 - 1.77608i) q^{54} +2.51595 q^{55} +(-1.43116 - 3.92610i) q^{56} +1.64011 q^{57} +(-0.792187 + 1.83732i) q^{58} +2.63236i q^{59} +(-0.794374 - 0.841435i) q^{60} +6.45993i q^{61} +(-0.826100 - 0.356185i) q^{62} +4.35416 q^{63} +(-6.12331 + 5.14831i) q^{64} -8.74905 q^{65} +(-0.298645 - 0.128765i) q^{66} +7.66426i q^{67} +(-4.55102 - 4.82064i) q^{68} -1.48405i q^{69} +(2.08134 - 4.82726i) q^{70} +12.2900 q^{71} +(-2.85482 - 7.83160i) q^{72} -13.2440 q^{73} +(-3.90600 + 9.05920i) q^{74} -0.305858i q^{75} +(10.3720 - 9.79187i) q^{76} -1.47743i q^{77} +(1.03852 + 0.447772i) q^{78} -16.3409 q^{79} +(-10.0472 - 0.578585i) q^{80} +8.52683 q^{81} +(-8.73930 - 3.76807i) q^{82} +13.8040i q^{83} +(-0.494113 + 0.466477i) q^{84} -8.33976i q^{85} +(-1.80001 + 4.17477i) q^{86} +0.325357 q^{87} +(-2.65738 + 0.968683i) q^{88} -1.04979 q^{89} +(4.15176 - 9.62919i) q^{90} +5.13767i q^{91} +(-8.86014 - 9.38505i) q^{92} +0.146288i q^{93} +(-1.11986 - 0.482842i) q^{94} +17.9436 q^{95} +(1.16299 + 0.582887i) q^{96} +16.2110 q^{97} +(6.25582 + 2.69729i) q^{98} -2.94712i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) $ 10 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	$ 10 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 10 q^{10} - 4 q^{12} - 12 q^{14} + 8 q^{15} - 4 q^{17} - 10 q^{18} + 12 q^{20} - 12 q^{23} - 6 q^{25} - 20 q^{26} - 12 q^{28} + 18 q^{30} - 4 q^{31} - 20 q^{32} + 32 q^{36} + 8 q^{38} + 24 q^{39} + 20 q^{40} + 4 q^{41} + 20 q^{42} + 4 q^{44} + 2 q^{46} - 4 q^{47} + 32 q^{48} - 6 q^{49} - 6 q^{50} - 20 q^{52} - 38 q^{54} - 8 q^{55} - 8 q^{56} + 16 q^{57} + 36 q^{58} - 4 q^{60} + 22 q^{62} - 40 q^{63} - 16 q^{64} + 16 q^{65} + 10 q^{66} - 28 q^{68} + 28 q^{70} - 12 q^{71} - 4 q^{72} - 4 q^{73} - 14 q^{74} + 44 q^{76} - 8 q^{78} + 16 q^{79} - 56 q^{80} - 6 q^{81} - 4 q^{82} - 52 q^{84} - 20 q^{86} + 32 q^{87} - 12 q^{88} - 4 q^{89} - 36 q^{90} - 36 q^{92} + 24 q^{95} + 60 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 10 * q^10 - 4 * q^12 - 12 * q^14 + 8 * q^15 - 4 * q^17 - 10 * q^18 + 12 * q^20 - 12 * q^23 - 6 * q^25 - 20 * q^26 - 12 * q^28 + 18 * q^30 - 4 * q^31 - 20 * q^32 + 32 * q^36 + 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 + 20 * q^42 + 4 * q^44 + 2 * q^46 - 4 * q^47 + 32 * q^48 - 6 * q^49 - 6 * q^50 - 20 * q^52 - 38 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^57 + 36 * q^58 - 4 * q^60 + 22 * q^62 - 40 * q^63 - 16 * q^64 + 16 * q^65 + 10 * q^66 - 28 * q^68 + 28 * q^70 - 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 + 44 * q^76 - 8 * q^78 + 16 * q^79 - 56 * q^80 - 6 * q^81 - 4 * q^82 - 52 * q^84 - 20 * q^86 + 32 * q^87 - 12 * q^88 - 4 * q^89 - 36 * q^90 - 36 * q^92 + 24 * q^95 + 60 * q^96 - 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.29865	−	0.559929i	−0.918281	−	0.395930i
$2$	−1.29865	−	0.559929i	−0.918281	−	0.395930i
$3$			0.229967i			0.132771i	0.997794	+	0.0663857i	$0.0211468\pi$
$3$			0.229967i			0.132771i	−0.997794	+	0.0663857i	$0.978853\pi$
$4$	1.37296	+	1.45430i	0.686480	+	0.727149i
$5$			2.51595i			1.12517i	0.826740	+	0.562584i	$0.190193\pi$
$5$			2.51595i			1.12517i	−0.826740	+	0.562584i	$0.809807\pi$
$6$	0.128765	−	0.298645i	0.0525681	−	0.121921i
$7$	1.47743			0.558417			0.279209	−	0.960230i	$-0.409928\pi$
$7$	1.47743			0.558417			0.279209	+	0.960230i	$0.409928\pi$
$8$	−0.968683	−	2.65738i	−0.342481	−	0.939525i
$9$	2.94712			0.982372
$10$	1.40875	−	3.26733i	0.445487	−	1.03322i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.334440	+	0.315735i	−0.0965446	+	0.0911448i
$13$			3.47743i			0.964466i	0.876043	+	0.482233i	$0.160174\pi$
$13$			3.47743i			0.964466i	−0.876043	+	0.482233i	$0.839826\pi$
$14$	−1.91866	−	0.827257i	−0.512784	−	0.221094i
$15$	−0.578585			−0.149390
$16$	−0.229967	+	3.99338i	−0.0574917	+	0.998346i
$17$	−3.31475			−0.803946			−0.401973	−	0.915652i	$-0.631675\pi$
$17$	−3.31475			−0.803946			−0.401973	+	0.915652i	$0.631675\pi$
$18$	−3.82726	−	1.65018i	−0.902093	−	0.388950i
$19$		−	7.13195i		−	1.63618i	−0.575090	−	0.818090i	$-0.695033\pi$
$19$		−	7.13195i		−	1.63618i	0.575090	−	0.818090i	$-0.304967\pi$
$20$	−3.65894	+	3.45430i	−0.818165	+	0.772405i
$21$			0.339760i			0.0741418i
$22$	−0.559929	+	1.29865i	−0.119377	+	0.276872i
$23$	−6.45332			−1.34561			−0.672805	−	0.739820i	$-0.734911\pi$
$23$	−6.45332			−1.34561			−0.672805	+	0.739820i	$0.734911\pi$
$24$	0.611108	−	0.222765i	0.124742	−	0.0454717i
$25$	−1.33001			−0.266002
$26$	1.94712	−	4.51595i	0.381861	−	0.885651i
$27$			1.36764i			0.263202i
$28$	2.02845	+	2.14863i	0.383342	+	0.406052i
$29$		−	1.41480i		−	0.262722i	−0.991335	−	0.131361i	$-0.958065\pi$
$29$		−	1.41480i		−	0.262722i	0.991335	−	0.131361i	$-0.0419346\pi$
$30$	0.751377	+	0.323967i	0.137182	+	0.0591479i
$31$	0.636125			0.114251			0.0571257	−	0.998367i	$-0.481806\pi$
$31$	0.636125			0.114251			0.0571257	+	0.998367i	$0.481806\pi$
$32$	2.53466	−	5.05722i	0.448068	−	0.893999i
$33$	0.229967			0.0400321
$34$	4.30469	+	1.85603i	0.738248	+	0.318306i
$35$			3.71715i			0.628313i
$36$	4.04627	+	4.28598i	0.674378	+	0.714331i
$37$		−	6.97588i		−	1.14683i	−0.819266	−	0.573414i	$-0.805619\pi$
$37$		−	6.97588i		−	1.14683i	0.819266	−	0.573414i	$-0.194381\pi$
$38$	−3.99338	+	9.26187i	−0.647812	+	1.50247i
$39$	−0.799694			−0.128054
$40$	6.68583	−	2.43716i	1.05712	−	0.385349i
$41$	6.72955			1.05098			0.525490	−	0.850800i	$-0.323882\pi$
$41$	6.72955			1.05098			0.525490	+	0.850800i	$0.323882\pi$
$42$	0.190242	−	0.441228i	0.0293549	−	0.0680830i
$43$		−	3.21471i		−	0.490239i	−0.969493	−	0.245119i	$-0.921173\pi$
$43$		−	3.21471i		−	0.490239i	0.969493	−	0.245119i	$-0.0788271\pi$
$44$	1.45430	−	1.37296i	0.219244	−	0.206981i
$45$			7.41480i			1.10533i
$46$	8.38057	+	3.61340i	1.23565	+	0.532767i
$47$	0.862328			0.125783			0.0628917	−	0.998020i	$-0.479968\pi$
$47$	0.862328			0.125783			0.0628917	+	0.998020i	$0.479968\pi$
$48$	−0.918346	−	0.0528847i	−0.132552	−	0.00763325i
$49$	−4.81719			−0.688170
$50$	1.72721	+	0.744712i	0.244265	+	0.105318i
$51$		−	0.762283i		−	0.106741i
$52$	−5.05722	+	4.77437i	−0.701311	+	0.662086i
$53$		−	13.2515i		−	1.82023i	−0.414353	−	0.910116i	$-0.635992\pi$
$53$		−	13.2515i		−	1.82023i	0.414353	−	0.910116i	$-0.364008\pi$
$54$	0.765781	−	1.77608i	0.104210	−	0.241694i
$55$	2.51595			0.339251
$56$	−1.43116	−	3.92610i	−0.191247	−	0.524647i
$57$	1.64011			0.217238
$58$	−0.792187	+	1.83732i	−0.104019	+	0.241252i
$59$			2.63236i			0.342704i	0.985210	+	0.171352i	$0.0548136\pi$
$59$			2.63236i			0.342704i	−0.985210	+	0.171352i	$0.945186\pi$
$60$	−0.794374	−	0.841435i	−0.102553	−	0.108629i
$61$			6.45993i			0.827110i	0.910479	+	0.413555i	$0.135713\pi$
$61$			6.45993i			0.827110i	−0.910479	+	0.413555i	$0.864287\pi$
$62$	−0.826100	−	0.356185i	−0.104915	−	0.0452355i
$63$	4.35416			0.548573
$64$	−6.12331	+	5.14831i	−0.765413	+	0.643539i
$65$	−8.74905			−1.08519
$66$	−0.298645	−	0.128765i	−0.0367607	−	0.0158499i
$67$			7.66426i			0.936339i	0.883639	+	0.468169i	$0.155086\pi$
$67$			7.66426i			0.936339i	−0.883639	+	0.468169i	$0.844914\pi$
$68$	−4.55102	−	4.82064i	−0.551892	−	0.584589i
$69$		−	1.48405i		−	0.178658i
$70$	2.08134	−	4.82726i	0.248768	−	0.576968i
$71$	12.2900			1.45856			0.729278	−	0.684218i	$-0.239856\pi$
$71$	12.2900			1.45856			0.729278	+	0.684218i	$0.239856\pi$
$72$	−2.85482	−	7.83160i	−0.336444	−	0.922963i
$73$	−13.2440			−1.55009			−0.775045	−	0.631905i	$-0.782273\pi$
$73$	−13.2440			−1.55009			−0.775045	+	0.631905i	$0.782273\pi$
$74$	−3.90600	+	9.05920i	−0.454063	+	1.05311i
$75$		−	0.305858i		−	0.0353175i
$76$	10.3720	−	9.79187i	1.18975	−	1.12320i
$77$		−	1.47743i		−	0.168369i
$78$	1.03852	+	0.447772i	0.117589	+	0.0507002i
$79$	−16.3409			−1.83850			−0.919249	−	0.393676i	$-0.871203\pi$
$79$	−16.3409			−1.83850			−0.919249	+	0.393676i	$0.871203\pi$
$80$	−10.0472	−	0.578585i	−1.12331	−	0.0646878i
$81$	8.52683			0.947426
$82$	−8.73930	−	3.76807i	−0.965094	−	0.416114i
$83$			13.8040i			1.51518i	0.652730	+	0.757591i	$0.273624\pi$
$83$			13.8040i			1.51518i	−0.652730	+	0.757591i	$0.726376\pi$
$84$	−0.494113	+	0.466477i	−0.0539121	+	0.0508968i
$85$		−	8.33976i		−	0.904574i
$86$	−1.80001	+	4.17477i	−0.194100	+	0.450177i
$87$	0.325357			0.0348819
$88$	−2.65738	+	0.968683i	−0.283277	+	0.103262i
$89$	−1.04979			−0.111277			−0.0556387	−	0.998451i	$-0.517720\pi$
$89$	−1.04979			−0.111277			−0.0556387	+	0.998451i	$0.517720\pi$
$90$	4.15176	−	9.62919i	0.437634	−	1.01501i
$91$			5.13767i			0.538574i
$92$	−8.86014	−	9.38505i	−0.923734	−	0.978459i
$93$			0.146288i			0.0151693i
$94$	−1.11986	−	0.482842i	−0.115505	−	0.0498014i
$95$	17.9436			1.84098
$96$	1.16299	+	0.582887i	0.118698	+	0.0594906i
$97$	16.2110			1.64598			0.822989	−	0.568057i	$-0.192305\pi$
$97$	16.2110			1.64598			0.822989	+	0.568057i	$0.192305\pi$
$98$	6.25582	+	2.69729i	0.631934	+	0.272467i
$99$		−	2.94712i		−	0.296196i
$100$	−1.82605	−	1.93423i	−0.182605	−	0.193423i
$101$		−	8.63460i		−	0.859175i	−0.903025	−	0.429588i	$-0.858659\pi$
$101$		−	8.63460i		−	0.859175i	0.903025	−	0.429588i	$-0.141341\pi$
$102$	−0.426825	+	0.989936i	−0.0422619	+	0.0980182i
$103$	−4.95487			−0.488217			−0.244109	−	0.969748i	$-0.578495\pi$
$103$	−4.95487			−0.488217			−0.244109	+	0.969748i	$0.578495\pi$
$104$	9.24085	−	3.36853i	0.906140	−	0.330312i
$105$	−0.854821			−0.0834220
$106$	−7.41989	+	17.2090i	−0.720684	+	1.67148i
$107$			6.34666i			0.613554i	0.951781	+	0.306777i	$0.0992507\pi$
$107$			6.34666i			0.613554i	−0.951781	+	0.306777i	$0.900749\pi$
$108$	−1.98895	+	1.87771i	−0.191387	+	0.180683i
$109$			7.94246i			0.760750i	0.924832	+	0.380375i	$0.124205\pi$
$109$			7.94246i			0.760750i	−0.924832	+	0.380375i	$0.875795\pi$
$110$	−3.26733	−	1.40875i	−0.311528	−	0.134319i
$111$	1.60422			0.152266
$112$	−0.339760	+	5.89996i	−0.0321043	+	0.557493i
$113$	4.88248			0.459305			0.229653	−	0.973273i	$-0.426241\pi$
$113$	4.88248			0.459305			0.229653	+	0.973273i	$0.426241\pi$
$114$	−2.12992	−	0.918346i	−0.199486	−	0.0860109i
$115$		−	16.2362i		−	1.51404i
$116$	2.05754	−	1.94246i	0.191038	−	0.180353i
$117$			10.2484i			0.947464i
$118$	1.47394	−	3.41850i	0.135687	−	0.314699i
$119$	−4.89733			−0.448937
$120$	0.560466	+	1.53752i	0.0511633	+	0.140356i
$121$	−1.00000			−0.0909091
$122$	3.61710	−	8.38916i	0.327477	−	0.759519i
$123$			1.54757i			0.139540i
$124$	0.873373	+	0.925115i	0.0784312	+	0.0830778i
$125$			9.23351i			0.825871i
$126$	−5.65451	−	2.43802i	−0.503744	−	0.217196i
$127$	−4.12017			−0.365606			−0.182803	−	0.983150i	$-0.558517\pi$
$127$	−4.12017			−0.365606			−0.182803	+	0.983150i	$0.558517\pi$
$128$	10.8347	−	3.25721i	0.957661	−	0.287900i
$129$	0.739276			0.0650897
$130$	11.3619	+	4.89885i	0.996506	+	0.429657i
$131$			13.3015i			1.16216i	0.813847	+	0.581080i	$0.197370\pi$
$131$			13.3015i			1.16216i	−0.813847	+	0.581080i	$0.802630\pi$
$132$	0.315735	+	0.334440i	0.0274812	+	0.0291093i
$133$		−	10.5370i		−	0.913671i
$134$	4.29144	−	9.95316i	0.370724	−	0.859822i
$135$	−3.44091			−0.296147
$136$	3.21095	+	8.80855i	0.275336	+	0.755327i
$137$	−6.84444			−0.584760			−0.292380	−	0.956302i	$-0.594447\pi$
$137$	−6.84444			−0.584760			−0.292380	+	0.956302i	$0.594447\pi$
$138$	−0.830962	+	1.92725i	−0.0707362	+	0.164059i
$139$		−	12.1966i		−	1.03450i	−0.855834	−	0.517250i	$-0.826956\pi$
$139$		−	12.1966i		−	1.03450i	0.855834	−	0.517250i	$-0.173044\pi$
$140$	−5.40584	+	5.10349i	−0.456877	+	0.431324i
$141$			0.198307i			0.0167004i
$142$	−15.9604	−	6.88153i	−1.33936	−	0.577485i
$143$	3.47743			0.290798
$144$	−0.677739	+	11.7690i	−0.0564782	+	0.980747i
$145$	3.55956			0.295606
$146$	17.1992	+	7.41569i	1.42342	+	0.613727i
$147$		−	1.10779i		−	0.0913693i
$148$	10.1450	−	9.57760i	0.833915	−	0.787274i
$149$		−	3.04004i		−	0.249050i	−0.992216	−	0.124525i	$-0.960259\pi$
$149$		−	3.04004i		−	0.249050i	0.992216	−	0.124525i	$-0.0397407\pi$
$150$	−0.171259	+	0.397202i	−0.0139832	+	0.0324314i
$151$	−1.83669			−0.149468			−0.0747339	−	0.997204i	$-0.523811\pi$
$151$	−1.83669			−0.149468			−0.0747339	+	0.997204i	$0.523811\pi$
$152$	−18.9523	+	6.90860i	−1.53723	+	0.560361i
$153$	−9.76896			−0.789774
$154$	−0.827257	+	1.91866i	−0.0666623	+	0.154610i
$155$			1.60046i			0.128552i
$156$	−1.09795	−	1.16299i	−0.0879061	−	0.0931140i
$157$			10.0560i			0.802558i	0.915956	+	0.401279i	$0.131434\pi$
$157$			10.0560i			0.802558i	−0.915956	+	0.401279i	$0.868566\pi$
$158$	21.2211	+	9.14976i	1.68826	+	0.727916i
$159$	3.04740			0.241675
$160$	12.7237	+	6.37707i	1.00590	+	0.504152i
$161$	−9.53434			−0.751411
$162$	−11.0733	−	4.77442i	−0.870003	−	0.375114i
$163$		−	12.8934i		−	1.00989i	−0.863152	−	0.504945i	$-0.831513\pi$
$163$		−	12.8934i		−	1.00989i	0.863152	−	0.504945i	$-0.168487\pi$
$164$	9.23940	+	9.78678i	0.721476	+	0.764219i
$165$			0.578585i			0.0450428i
$166$	7.72924	−	17.9264i	0.599905	−	1.39136i
$167$	4.47434			0.346235			0.173117	−	0.984901i	$-0.444616\pi$
$167$	4.47434			0.346235			0.173117	+	0.984901i	$0.444616\pi$
$168$	0.902872	−	0.329120i	0.0696581	−	0.0253922i
$169$	0.907463			0.0698048
$170$	−4.66967	+	10.8304i	−0.358148	+	0.830653i
$171$		−	21.0187i		−	1.60734i
$172$	4.67515	−	4.41366i	0.356477	−	0.336539i
$173$			0.182807i			0.0138986i	0.999976	+	0.00694928i	$0.00221204\pi$
$173$			0.182807i			0.0138986i	−0.999976	+	0.00694928i	$0.997788\pi$
$174$	−0.422523	−	0.182177i	−0.0320314	−	0.0138108i
$175$	−1.96500			−0.148540
$176$	3.99338	+	0.229967i	0.301013	+	0.0173344i
$177$	−0.605356			−0.0455013
$178$	1.36330	+	0.587808i	0.102184	+	0.0440580i
$179$		−	20.0915i		−	1.50171i	−0.660469	−	0.750853i	$-0.729642\pi$
$179$		−	20.0915i		−	1.50171i	0.660469	−	0.750853i	$-0.270358\pi$
$180$	−10.7833	+	10.1802i	−0.803742	+	0.758788i
$181$		−	7.63413i		−	0.567440i	−0.958907	−	0.283720i	$-0.908431\pi$
$181$		−	7.63413i		−	0.567440i	0.958907	−	0.283720i	$-0.0915686\pi$
$182$	2.87673	−	6.67201i	0.213238	−	0.494563i
$183$	−1.48557			−0.109817
$184$	6.25122	+	17.1489i	0.460846	+	1.26423i
$185$	17.5510			1.29037
$186$	0.0819106	−	0.189976i	0.00600598	−	0.0139297i
$187$			3.31475i			0.242399i
$188$	1.18394	+	1.25408i	0.0863478	+	0.0914633i
$189$			2.02059i			0.146977i
$190$	−23.3024	−	10.0472i	−1.69053	−	0.728898i
$191$	−22.9943			−1.66381			−0.831906	−	0.554917i	$-0.812750\pi$
$191$	−22.9943			−1.66381			−0.831906	+	0.554917i	$0.812750\pi$
$192$	−1.18394	−	1.40816i	−0.0854436	−	0.101625i
$193$	0.735278			0.0529265			0.0264632	−	0.999650i	$-0.491576\pi$
$193$	0.735278			0.0529265			0.0264632	+	0.999650i	$0.491576\pi$
$194$	−21.0524	−	9.07701i	−1.51147	−	0.651692i
$195$		−	2.01199i		−	0.144082i
$196$	−6.61381	−	7.00564i	−0.472415	−	0.500403i
$197$			11.1665i			0.795579i	0.917477	+	0.397789i	$0.130223\pi$
$197$			11.1665i			0.795579i	−0.917477	+	0.397789i	$0.869777\pi$
$198$	−1.65018	+	3.82726i	−0.117273	+	0.271991i
$199$	−18.1315			−1.28531			−0.642655	−	0.766156i	$-0.722167\pi$
$199$	−18.1315			−1.28531			−0.642655	+	0.766156i	$0.722167\pi$
$200$	1.28836	+	3.53434i	0.0911008	+	0.249916i
$201$	−1.76253			−0.124319
$202$	−4.83476	+	11.2133i	−0.340173	+	0.788964i
$203$		−	2.09027i		−	0.146708i
$204$	1.10859	−	1.04658i	0.0776166	−	0.0732755i
$205$			16.9312i			1.18253i
$206$	6.43461	+	2.77437i	0.448321	+	0.193300i
$207$	−19.0187			−1.32189
$208$	−13.8867	−	0.799694i	−0.962871	−	0.0554488i
$209$	−7.13195			−0.493327
$210$	1.11011	+	0.478639i	0.0766048	+	0.0330292i
$211$			18.4180i			1.26795i	0.773355	+	0.633973i	$0.218577\pi$
$211$			18.4180i			1.26795i	−0.773355	+	0.633973i	$0.781423\pi$
$212$	19.2716	−	18.1938i	1.32358	−	1.24955i
$213$			2.82629i			0.193654i
$214$	3.55368	−	8.24206i	0.242924	−	0.563415i
$215$	8.08805			0.551601
$216$	3.63433	−	1.32481i	0.247285	−	0.0901418i
$217$	0.939831			0.0637999
$218$	4.44721	−	10.3144i	0.301203	−	0.698582i
$219$		−	3.04568i		−	0.205808i
$220$	3.45430	+	3.65894i	0.232889	+	0.246686i
$221$		−	11.5268i		−	0.775379i
$222$	−2.08332	−	0.898250i	−0.139823	−	0.0602866i
$223$	14.5654			0.975368			0.487684	−	0.873020i	$-0.337842\pi$
$223$	14.5654			0.975368			0.487684	+	0.873020i	$0.337842\pi$
$224$	3.74478	−	7.47171i	0.250209	−	0.499224i
$225$	−3.91970			−0.261313
$226$	−6.34061	−	2.73384i	−0.421771	−	0.181853i
$227$		−	7.15145i		−	0.474658i	−0.971429	−	0.237329i	$-0.923728\pi$
$227$		−	7.15145i		−	0.474658i	0.971429	−	0.237329i	$-0.0762720\pi$
$228$	2.25181	+	2.38521i	0.149129	+	0.157964i
$229$			6.48500i			0.428541i	0.976774	+	0.214271i	$0.0687374\pi$
$229$			6.48500i			0.428541i	−0.976774	+	0.214271i	$0.931263\pi$
$230$	−9.09114	+	21.0851i	−0.599452	+	1.39031i
$231$	0.339760			0.0223546
$232$	−3.75965	+	1.37049i	−0.246833	+	0.0899772i
$233$	11.4786			0.751988			0.375994	−	0.926622i	$-0.377301\pi$
$233$	11.4786			0.751988			0.375994	+	0.926622i	$0.377301\pi$
$234$	5.73837	−	13.3090i	0.375129	−	0.870038i
$235$			2.16957i			0.141527i
$236$	−3.82824	+	3.61412i	−0.249197	+	0.235259i
$237$		−	3.75787i		−	0.244100i
$238$	6.35989	+	2.74215i	0.412250	+	0.177747i
$239$	0.112036			0.00724698			0.00362349	−	0.999993i	$-0.498847\pi$
$239$	0.112036			0.00724698			0.00362349	+	0.999993i	$0.498847\pi$
$240$	0.133055	−	2.31051i	0.00858869	−	0.149143i
$241$	2.93937			0.189341			0.0946706	−	0.995509i	$-0.469820\pi$
$241$	2.93937			0.189341			0.0946706	+	0.995509i	$0.469820\pi$
$242$	1.29865	+	0.559929i	0.0834801	+	0.0359936i
$243$			6.06381i			0.388993i
$244$	−9.39467	+	8.86922i	−0.601432	+	0.567794i
$245$		−	12.1198i		−	0.774307i
$246$	0.866531	−	2.00975i	0.0552480	−	0.128137i
$247$	24.8009			1.57804
$248$	−0.616203	−	1.69042i	−0.0391289	−	0.107342i
$249$	−3.17445			−0.201173
$250$	5.17011	−	11.9911i	0.326987	−	0.758381i
$251$			31.2199i			1.97058i	0.170882	+	0.985291i	$0.445338\pi$
$251$			31.2199i			1.97058i	−0.170882	+	0.985291i	$0.554662\pi$
$252$	5.97809	+	6.33225i	0.376584	+	0.398894i
$253$			6.45332i			0.405717i
$254$	5.35064	+	2.30700i	0.335729	+	0.144754i
$255$	1.91787			0.120102
$256$	−15.8942	−	1.83669i	−0.993389	−	0.114793i
$257$	7.09741			0.442725			0.221362	−	0.975192i	$-0.428950\pi$
$257$	7.09741			0.442725			0.221362	+	0.975192i	$0.428950\pi$
$258$	−0.960058	−	0.413942i	−0.0597706	−	0.0257709i
$259$		−	10.3064i		−	0.640409i
$260$	−12.0121	−	12.7237i	−0.744958	−	0.789092i
$261$		−	4.16957i		−	0.258090i
$262$	7.44791	−	17.2740i	0.460133	−	1.06719i
$263$	16.3863			1.01042			0.505211	−	0.862996i	$-0.331415\pi$
$263$	16.3863			1.01042			0.505211	+	0.862996i	$0.331415\pi$
$264$	−0.222765	−	0.611108i	−0.0137102	−	0.0376111i
$265$	33.3401			2.04807
$266$	−5.89996	+	13.6838i	−0.361749	+	0.839007i
$267$		−	0.241417i		−	0.0147745i
$268$	−11.1461	+	10.5227i	−0.680858	+	0.642777i
$269$			17.1262i			1.04420i	0.852883	+	0.522102i	$0.174852\pi$
$269$			17.1262i			1.04420i	−0.852883	+	0.522102i	$0.825148\pi$
$270$	4.46853	+	1.92667i	0.271946	+	0.117253i
$271$	19.5142			1.18540			0.592702	−	0.805422i	$-0.298061\pi$
$271$	19.5142			1.18540			0.592702	+	0.805422i	$0.298061\pi$
$272$	0.762283	−	13.2371i	0.0462202	−	0.802616i
$273$	−1.18149			−0.0715073
$274$	8.88850	+	3.83240i	0.536974	+	0.231524i
$275$			1.33001i			0.0802027i
$276$	2.15825	−	2.03754i	0.129911	−	0.122645i
$277$			10.5618i			0.634596i	0.948326	+	0.317298i	$0.102776\pi$
$277$			10.5618i			0.634596i	−0.948326	+	0.317298i	$0.897224\pi$
$278$	−6.82922	+	15.8390i	−0.409589	+	0.949962i
$279$	1.87473			0.112237
$280$	9.87787	−	3.60074i	0.590315	−	0.215185i
$281$	−11.5994			−0.691961			−0.345981	−	0.938242i	$-0.612454\pi$
$281$	−11.5994			−0.691961			−0.345981	+	0.938242i	$0.612454\pi$
$282$	0.111038	−	0.257530i	0.00661220	−	0.0153357i
$283$			21.6234i			1.28538i	0.766128	+	0.642688i	$0.222181\pi$
$283$			21.6234i			1.28538i	−0.766128	+	0.642688i	$0.777819\pi$
$284$	16.8737	+	17.8733i	1.00127	+	1.06059i
$285$			4.12644i			0.244429i
$286$	−4.51595	−	1.94712i	−0.267034	−	0.115135i
$287$	9.94246			0.586885
$288$	7.46993	−	14.9042i	0.440170	−	0.878240i
$289$	−6.01240			−0.353671
$290$	−4.62261	−	1.99310i	−0.271449	−	0.117039i
$291$			3.72799i			0.218539i
$292$	−18.1834	−	19.2607i	−1.06411	−	1.12715i
$293$		−	20.1305i		−	1.17604i	−0.808848	−	0.588018i	$-0.799908\pi$
$293$		−	20.1305i		−	1.17604i	0.808848	−	0.588018i	$-0.200092\pi$
$294$	−0.620286	+	1.43863i	−0.0361758	+	0.0839027i
$295$	−6.62289			−0.385600
$296$	−18.5376	+	6.75742i	−1.07747	+	0.392767i
$297$	1.36764			0.0793585
$298$	−1.70221	+	3.94793i	−0.0986062	+	0.228698i
$299$		−	22.4410i		−	1.29780i
$300$	0.444809	−	0.419931i	0.0256811	−	0.0242447i
$301$		−	4.74952i		−	0.273758i
$302$	2.38521	+	1.02842i	0.137253	+	0.0591787i
$303$	1.98567			0.114074
$304$	28.4806	+	1.64011i	1.63347	+	0.0940668i
$305$	−16.2529			−0.930637
$306$	12.6864	+	5.46993i	0.725234	+	0.312695i
$307$			2.24089i			0.127894i	0.997953	+	0.0639471i	$0.0203689\pi$
$307$			2.24089i			0.127894i	−0.997953	+	0.0639471i	$0.979631\pi$
$308$	2.14863	−	2.02845i	0.122429	−	0.115582i
$309$		−	1.13945i		−	0.0648213i
$310$	0.896143	−	2.07843i	0.0508975	−	0.118047i
$311$	−15.6919			−0.889807			−0.444904	−	0.895578i	$-0.646762\pi$
$311$	−15.6919			−0.889807			−0.444904	+	0.895578i	$0.646762\pi$
$312$	0.774650	+	2.12509i	0.0438559	+	0.120309i
$313$	−12.1167			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$313$	−12.1167			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$314$	5.63066	−	13.0592i	0.317756	−	0.736973i
$315$			10.9549i			0.617237i
$316$	−22.4354	−	23.7646i	−1.26209	−	1.33686i
$317$		−	11.8958i		−	0.668132i	−0.942550	−	0.334066i	$-0.891579\pi$
$317$		−	11.8958i		−	0.668132i	0.942550	−	0.334066i	$-0.108421\pi$
$318$	−3.95749	−	1.70633i	−0.221925	−	0.0956862i
$319$	−1.41480			−0.0792135
$320$	−12.9529	−	15.4059i	−0.724089	−	0.861218i
$321$	−1.45952			−0.0814625
$322$	12.3817	+	5.33855i	0.690007	+	0.297506i
$323$			23.6407i			1.31540i
$324$	11.7070	+	12.4006i	0.650389	+	0.688920i
$325$		−	4.62502i		−	0.256550i
$326$	−7.21939	+	16.7440i	−0.399845	+	0.927362i
$327$	−1.82650			−0.101006
$328$	−6.51880	−	17.8830i	−0.359941	−	0.987421i
$329$	1.27403			0.0702396
$330$	0.323967	−	0.751377i	0.0178338	−	0.0413619i
$331$		−	24.7692i		−	1.36144i	−0.732544	−	0.680719i	$-0.761667\pi$
$331$		−	24.7692i		−	1.36144i	0.732544	−	0.680719i	$-0.238333\pi$
$332$	−20.0751	+	18.9523i	−1.10176	+	1.04014i
$333$		−	20.5587i		−	1.12661i
$334$	−5.81058	−	2.50531i	−0.317941	−	0.137085i
$335$	−19.2829			−1.05354
$336$	−1.35679	−	0.0781336i	−0.0740192	−	0.00426254i
$337$	−11.2285			−0.611654			−0.305827	−	0.952087i	$-0.598933\pi$
$337$	−11.2285			−0.611654			−0.305827	+	0.952087i	$0.598933\pi$
$338$	−1.17847	−	0.508115i	−0.0641004	−	0.0276378i
$339$			1.12281i			0.0609826i
$340$	12.1285	−	11.4501i	0.657760	−	0.620972i
$341$		−	0.636125i		−	0.0344481i
$342$	−11.7690	+	27.2958i	−0.636393	+	1.47599i
$343$	−17.4591			−0.942703
$344$	−8.54270	+	3.11403i	−0.460591	+	0.167898i
$345$	3.73379			0.201021
$346$	0.102359	−	0.237401i	0.00550285	−	0.0127628i
$347$			16.0230i			0.860160i	0.902791	+	0.430080i	$0.141515\pi$
$347$			16.0230i			0.860160i	−0.902791	+	0.430080i	$0.858485\pi$
$348$	0.446701	+	0.473166i	0.0239457	+	0.0253643i
$349$			9.27513i			0.496486i	0.968698	+	0.248243i	$0.0798532\pi$
$349$			9.27513i			0.496486i	−0.968698	+	0.248243i	$0.920147\pi$
$350$	2.55184	+	1.10026i	0.136402	+	0.0588115i
$351$	−4.75587			−0.253850
$352$	−5.05722	−	2.53466i	−0.269551	−	0.135098i
$353$	−9.58150			−0.509972			−0.254986	−	0.966945i	$-0.582071\pi$
$353$	−9.58150			−0.509972			−0.254986	+	0.966945i	$0.582071\pi$
$354$	0.786142	+	0.338956i	0.0417830	+	0.0180153i
$355$			30.9211i			1.64112i
$356$	−1.44132	−	1.52671i	−0.0763897	−	0.0809153i
$357$		−	1.12622i		−	0.0596060i
$358$	−11.2498	+	26.0917i	−0.594570	+	1.37899i
$359$	−7.80501			−0.411932			−0.205966	−	0.978559i	$-0.566034\pi$
$359$	−7.80501			−0.411932			−0.205966	+	0.978559i	$0.566034\pi$
$360$	19.7039	−	7.18259i	1.03849	−	0.378556i
$361$	−31.8647			−1.67709
$362$	−4.27457	+	9.91402i	−0.224666	+	0.521069i
$363$		−	0.229967i		−	0.0120701i
$364$	−7.47171	+	7.05381i	−0.391624	+	0.369720i
$365$		−	33.3212i		−	1.74411i
$366$	1.92923	+	0.831814i	0.100842	+	0.0434796i
$367$	31.4393			1.64112			0.820558	−	0.571563i	$-0.193663\pi$
$367$	31.4393			1.64112			0.820558	+	0.571563i	$0.193663\pi$
$368$	1.48405	−	25.7706i	0.0773614	−	1.34338i
$369$	19.8328			1.03245
$370$	−22.7925	−	9.82731i	−1.18493	−	0.510897i
$371$		−	19.5782i		−	1.01645i
$372$	−0.212746	+	0.200847i	−0.0110303	+	0.0104134i
$373$		−	32.0424i		−	1.65909i	−0.558437	−	0.829547i	$-0.688599\pi$
$373$		−	32.0424i		−	1.65909i	0.558437	−	0.829547i	$-0.311401\pi$
$374$	1.85603	−	4.30469i	0.0959729	−	0.222590i
$375$	−2.12340			−0.109652
$376$	−0.835322	−	2.29153i	−0.0430785	−	0.118177i
$377$	4.91987			0.253386
$378$	1.13139	−	2.62404i	0.0581924	−	0.134966i
$379$			11.4465i			0.587965i	0.955811	+	0.293983i	$0.0949808\pi$
$379$			11.4465i			0.587965i	−0.955811	+	0.293983i	$0.905019\pi$
$380$	24.6359	+	26.0954i	1.26379	+	1.33867i
$381$		−	0.947503i		−	0.0485420i
$382$	29.8615	+	12.8752i	1.52785	+	0.658752i
$383$	−6.82520			−0.348751			−0.174376	−	0.984679i	$-0.555791\pi$
$383$	−6.82520			−0.348751			−0.174376	+	0.984679i	$0.555791\pi$
$384$	0.749051	+	2.49162i	0.0382249	+	0.127150i
$385$	3.71715			0.189443
$386$	−0.954865	−	0.411703i	−0.0486014	−	0.0209552i
$387$		−	9.47412i		−	0.481597i
$388$	22.2571	+	23.5756i	1.12993	+	1.19687i
$389$		−	6.65984i		−	0.337667i	−0.985645	−	0.168834i	$-0.946000\pi$
$389$		−	6.65984i		−	0.337667i	0.985645	−	0.168834i	$-0.0540000\pi$
$390$	−1.12657	+	2.61286i	−0.0570462	+	0.132307i
$391$	21.3912			1.08180
$392$	4.66633	+	12.8011i	0.235685	+	0.646553i
$393$	−3.05891			−0.154302
$394$	6.25244	−	14.5013i	0.314993	−	0.730565i
$395$		−	41.1130i		−	2.06862i
$396$	4.28598	−	4.04627i	0.215379	−	0.203333i
$397$		−	2.42189i		−	0.121551i	−0.998151	−	0.0607757i	$-0.980643\pi$
$397$		−	2.42189i		−	0.121551i	0.998151	−	0.0607757i	$-0.0193574\pi$
$398$	23.5464	+	10.1524i	1.18028	+	0.508892i
$399$	2.42315			0.121309
$400$	0.305858	−	5.31125i	0.0152929	−	0.265562i
$401$	−9.09122			−0.453994			−0.226997	−	0.973895i	$-0.572891\pi$
$401$	−9.09122			−0.453994			−0.226997	+	0.973895i	$0.572891\pi$
$402$	2.28890	+	0.986889i	0.114160	+	0.0492216i
$403$			2.21208i			0.110192i
$404$	12.5573	−	11.8550i	0.624748	−	0.589806i
$405$			21.4531i			1.06601i
$406$	−1.17040	+	2.71452i	−0.0580861	+	0.134719i
$407$	−6.97588			−0.345782
$408$	−2.02567	+	0.738411i	−0.100286	+	0.0365568i
$409$	9.08013			0.448984			0.224492	−	0.974476i	$-0.427928\pi$
$409$	9.08013			0.448984			0.224492	+	0.974476i	$0.427928\pi$
$410$	9.48029	−	21.9877i	0.468198	−	1.08589i
$411$		−	1.57399i		−	0.0776394i
$412$	−6.80283	−	7.20585i	−0.335151	−	0.355007i
$413$			3.88914i			0.191372i
$414$	24.6985	+	10.6491i	1.21387	+	0.523375i
$415$	−34.7301			−1.70483
$416$	17.5862	+	8.81410i	0.862232	+	0.432147i
$417$	2.80481			0.137352
$418$	9.26187	+	3.99338i	0.453013	+	0.195323i
$419$			2.99512i			0.146321i	0.997320	+	0.0731607i	$0.0233086\pi$
$419$			2.99512i			0.146321i	−0.997320	+	0.0731607i	$0.976691\pi$
$420$	−1.17363	−	1.24316i	−0.0572675	−	0.0606602i
$421$			26.6646i			1.29955i	0.760126	+	0.649776i	$0.225137\pi$
$421$			26.6646i			1.29955i	−0.760126	+	0.649776i	$0.774863\pi$
$422$	10.3128	−	23.9184i	0.502017	−	1.16433i
$423$	2.54138			0.123566
$424$	−35.2142	+	12.8365i	−1.71015	+	0.623395i
$425$	4.40866			0.213851
$426$	1.58252	−	3.67035i	0.0766735	−	0.177829i
$427$			9.54412i			0.461872i
$428$	−9.22993	+	8.71370i	−0.446146	+	0.421193i
$429$			0.799694i			0.0386096i
$430$	−10.5035	−	4.52874i	−0.506524	−	0.218395i
$431$	19.5700			0.942656			0.471328	−	0.881958i	$-0.343775\pi$
$431$	19.5700			0.942656			0.471328	+	0.881958i	$0.343775\pi$
$432$	−5.46151	−	0.314512i	−0.262767	−	0.0151319i
$433$	−6.49028			−0.311903			−0.155951	−	0.987765i	$-0.549844\pi$
$433$	−6.49028			−0.311903			−0.155951	+	0.987765i	$0.549844\pi$
$434$	−1.22051	−	0.526239i	−0.0585862	−	0.0252603i
$435$			0.818582i			0.0392480i
$436$	−11.5507	+	10.9047i	−0.553179	+	0.522239i
$437$			46.0247i			2.20166i
$438$	−1.70536	+	3.95525i	−0.0814854	+	0.188989i
$439$	25.3338			1.20912			0.604559	−	0.796560i	$-0.293349\pi$
$439$	25.3338			1.20912			0.604559	+	0.796560i	$0.293349\pi$
$440$	−2.43716	−	6.68583i	−0.116187	−	0.318735i
$441$	−14.1968			−0.676039
$442$	−6.45421	+	14.9693i	−0.306995	+	0.712016i
$443$		−	1.46196i		−	0.0694597i	−0.999397	−	0.0347299i	$-0.988943\pi$
$443$		−	1.46196i		−	0.0694597i	0.999397	−	0.0347299i	$-0.0110571\pi$
$444$	2.20253	+	2.33302i	0.104527	+	0.110720i
$445$		−	2.64122i		−	0.125206i
$446$	−18.9152	−	8.15556i	−0.895662	−	0.386177i
$447$	0.699108			0.0330667
$448$	−9.04677	+	7.60628i	−0.427420	+	0.359363i
$449$	−6.00066			−0.283188			−0.141594	−	0.989925i	$-0.545223\pi$
$449$	−6.00066			−0.283188			−0.141594	+	0.989925i	$0.545223\pi$
$450$	5.09030	+	2.19475i	0.239959	+	0.103462i
$451$		−	6.72955i		−	0.316882i
$452$	6.70345	+	7.10059i	0.315304	+	0.333983i
$453$		−	0.422378i		−	0.0198450i
$454$	−4.00430	+	9.28719i	−0.187931	+	0.435869i
$455$	−12.9261			−0.605986
$456$	−1.58875	−	4.35839i	−0.0743999	−	0.204100i
$457$	17.5689			0.821837			0.410919	−	0.911672i	$-0.365208\pi$
$457$	17.5689			0.821837			0.410919	+	0.911672i	$0.365208\pi$
$458$	3.63114	−	8.42172i	0.169672	−	0.393521i
$459$		−	4.53339i		−	0.211600i
$460$	23.6123	−	22.2917i	1.10093	−	1.03936i
$461$		−	26.1231i		−	1.21668i	−0.793678	−	0.608338i	$-0.791837\pi$
$461$		−	26.1231i		−	1.21668i	0.793678	−	0.608338i	$-0.208163\pi$
$462$	−0.441228	−	0.190242i	−0.0205278	−	0.00885084i
$463$	20.3258			0.944619			0.472310	−	0.881433i	$-0.343420\pi$
$463$	20.3258			0.944619			0.472310	+	0.881433i	$0.343420\pi$
$464$	5.64983	+	0.325357i	0.262287	+	0.0151043i
$465$	−0.368052			−0.0170680
$466$	−14.9066	−	6.42720i	−0.690537	−	0.297734i
$467$			1.29764i			0.0600478i	0.999549	+	0.0300239i	$0.00955833\pi$
$467$			1.29764i			0.0600478i	−0.999549	+	0.0300239i	$0.990442\pi$
$468$	−14.9042	+	14.0706i	−0.688948	+	0.650415i
$469$			11.3234i			0.522868i
$470$	1.21481	−	2.81751i	0.0560349	−	0.129962i
$471$	−2.31255			−0.106557
$472$	6.99518	−	2.54992i	0.321979	−	0.117370i
$473$	−3.21471			−0.147813
$474$	−2.10414	+	4.88014i	−0.0966464	+	0.224152i
$475$			9.48557i			0.435228i
$476$	−6.72383	−	7.12217i	−0.308186	−	0.326444i
$477$		−	39.0537i		−	1.78814i
$478$	−0.145495	−	0.0627320i	−0.00665476	−	0.00286929i
$479$	−28.5133			−1.30281			−0.651404	−	0.758731i	$-0.725820\pi$
$479$	−28.5133			−1.30281			−0.651404	+	0.758731i	$0.725820\pi$
$480$	−1.46651	+	2.92604i	−0.0669369	+	0.133555i
$481$	24.2582			1.10608
$482$	−3.81719	−	1.64584i	−0.173868	−	0.0749658i
$483$		−	2.19258i		−	0.0997659i
$484$	−1.37296	−	1.45430i	−0.0624072	−	0.0661045i
$485$			40.7861i			1.85200i
$486$	3.39530	−	7.87473i	0.154014	−	0.357205i
$487$	−6.03364			−0.273410			−0.136705	−	0.990612i	$-0.543651\pi$
$487$	−6.03364			−0.273410			−0.136705	+	0.990612i	$0.543651\pi$
$488$	17.1665	−	6.25763i	0.777090	−	0.283270i
$489$	2.96505			0.134084
$490$	−6.78624	+	15.7394i	−0.306571	+	0.711031i
$491$			4.15408i			0.187471i	0.995597	+	0.0937354i	$0.0298808\pi$
$491$			4.15408i			0.187471i	−0.995597	+	0.0937354i	$0.970119\pi$
$492$	−2.25063	+	2.12476i	−0.101466	+	0.0957914i
$493$			4.68971i			0.211214i
$494$	−32.2075	−	13.8867i	−1.44909	−	0.624793i
$495$	7.41480			0.333270
$496$	−0.146288	+	2.54029i	−0.00656850	+	0.114062i
$497$	18.1577			0.814482
$498$	4.12249	+	1.77747i	0.184733	+	0.0796502i
$499$		−	30.1028i		−	1.34759i	−0.738920	−	0.673793i	$-0.764664\pi$
$499$		−	30.1028i		−	1.34759i	0.738920	−	0.673793i	$-0.235336\pi$
$500$	−13.4283	+	12.6772i	−0.600531	+	0.566943i
$501$			1.02895i			0.0459700i
$502$	17.4809	−	40.5436i	0.780212	−	1.80955i
$503$	14.0368			0.625869			0.312935	−	0.949775i	$-0.398688\pi$
$503$	14.0368			0.625869			0.312935	+	0.949775i	$0.398688\pi$
$504$	−4.21781	−	11.5707i	−0.187876	−	0.515398i
$505$	21.7242			0.966716
$506$	3.61340	−	8.38057i	0.160635	−	0.372562i
$507$			0.208686i			0.00926808i
$508$	−5.65683	−	5.99196i	−0.250981	−	0.265850i
$509$			16.9844i			0.752821i	0.926453	+	0.376411i	$0.122842\pi$
$509$			16.9844i			0.752821i	−0.926453	+	0.376411i	$0.877158\pi$
$510$	−2.49063	−	1.07387i	−0.110287	−	0.0475518i
$511$	−19.5671			−0.865597
$512$	19.6126	+	11.2849i	0.866760	+	0.498725i
$513$	9.75393			0.430646
$514$	−9.21702	−	3.97405i	−0.406546	−	0.175288i
$515$		−	12.4662i		−	0.549326i
$516$	1.01500	+	1.07513i	0.0446827	+	0.0473299i
$517$		−	0.862328i		−	0.0379251i
$518$	−5.77085	+	13.3844i	−0.253557	+	0.588075i
$519$	−0.0420395			−0.00184533
$520$	8.47506	+	23.2495i	0.371656	+	1.01956i
$521$	−3.66607			−0.160613			−0.0803066	−	0.996770i	$-0.525590\pi$
$521$	−3.66607			−0.160613			−0.0803066	+	0.996770i	$0.525590\pi$
$522$	−2.33467	+	5.41480i	−0.102186	+	0.236999i
$523$		−	2.91807i		−	0.127598i	−0.997963	−	0.0637990i	$-0.979678\pi$
$523$		−	2.91807i		−	0.127598i	0.997963	−	0.0637990i	$-0.0203217\pi$
$524$	−19.3444	+	18.2624i	−0.845063	+	0.797799i
$525$		−	0.451885i		−	0.0197219i
$526$	−21.2800	−	9.17516i	−0.927851	−	0.400056i
$527$	−2.10860			−0.0918519
$528$	−0.0528847	+	0.918346i	−0.00230151	+	0.0399659i
$529$	18.6453			0.810666
$530$	−43.2970	−	18.6681i	−1.88070	−	0.810890i
$531$			7.75787i			0.336663i
$532$	15.3239	−	14.4668i	0.664375	−	0.627217i
$533$			23.4016i			1.01363i
$534$	−0.135176	+	0.313515i	−0.00584965	+	0.0135671i
$535$	−15.9679			−0.690352
$536$	20.3668	−	7.42424i	0.879713	−	0.320678i
$537$	4.62037			0.199384
$538$	9.58947	−	22.2409i	0.413431	−	0.958873i
$539$			4.81719i			0.207491i
$540$	−4.72423	−	5.00411i	−0.203299	−	0.215343i
$541$			16.4673i			0.707984i	0.935248	+	0.353992i	$0.115176\pi$
$541$			16.4673i			0.707984i	−0.935248	+	0.353992i	$0.884824\pi$
$542$	−25.3420	−	10.9266i	−1.08853	−	0.469337i
$543$	1.75560			0.0753398
$544$	−8.40176	+	16.7635i	−0.360223	+	0.718727i
$545$	−19.9828			−0.855971
$546$	1.53434	+	0.661553i	0.0656638	+	0.0283118i
$547$			25.9536i			1.10969i	0.831952	+	0.554847i	$0.187223\pi$
$547$			25.9536i			1.10969i	−0.831952	+	0.554847i	$0.812777\pi$
$548$	−9.39714	−	9.95386i	−0.401426	−	0.425208i
$549$			19.0382i			0.812529i
$550$	0.744712	−	1.72721i	0.0317546	−	0.0736486i
$551$	−10.0903			−0.429860
$552$	−3.94368	+	1.43757i	−0.167854	+	0.0611872i
$553$	−24.1426			−1.02665
$554$	5.91385	−	13.7160i	0.251255	−	0.582737i
$555$			4.03614i			0.171325i
$556$	17.7375	−	16.7454i	0.752236	−	0.710163i
$557$		−	13.0152i		−	0.551473i	−0.961233	−	0.275737i	$-0.911078\pi$
$557$		−	13.0152i		−	0.551473i	0.961233	−	0.275737i	$-0.0889217\pi$
$558$	−2.43461	−	1.04972i	−0.103065	−	0.0444381i
$559$	11.1789			0.472819
$560$	−14.8440	−	0.854821i	−0.627274	−	0.0361228i
$561$	−0.762283			−0.0321836
$562$	15.0635	+	6.49483i	0.635415	+	0.273968i
$563$		−	27.9837i		−	1.17937i	−0.807632	−	0.589687i	$-0.799251\pi$
$563$		−	27.9837i		−	1.17937i	0.807632	−	0.589687i	$-0.200749\pi$
$564$	−0.288397	+	0.272267i	−0.0121437	+	0.0114645i
$565$			12.2841i			0.516795i
$566$	12.1076	−	28.0811i	0.508918	−	1.18034i
$567$	12.5978			0.529059
$568$	−11.9051	−	32.6592i	−0.499528	−	1.37035i
$569$	−10.6048			−0.444574			−0.222287	−	0.974981i	$-0.571352\pi$
$569$	−10.6048			−0.444574			−0.222287	+	0.974981i	$0.571352\pi$
$570$	2.31051	−	5.35878i	0.0967767	−	0.224455i
$571$		−	1.82472i		−	0.0763622i	−0.999271	−	0.0381811i	$-0.987844\pi$
$571$		−	1.82472i		−	0.0763622i	0.999271	−	0.0381811i	$-0.0121564\pi$
$572$	4.77437	+	5.05722i	0.199627	+	0.211453i
$573$		−	5.28793i		−	0.220907i
$574$	−12.9117	−	5.56707i	−0.538925	−	0.232365i
$575$	8.58298			0.357935
$576$	−18.0461	+	15.1727i	−0.751920	+	0.632195i
$577$	23.3377			0.971560			0.485780	−	0.874081i	$-0.338536\pi$
$577$	23.3377			0.971560			0.485780	+	0.874081i	$0.338536\pi$
$578$	7.80798	+	3.36652i	0.324769	+	0.140029i
$579$			0.169089i			0.00702712i
$580$	4.88714	+	5.17667i	0.202927	+	0.214949i
$581$			20.3944i			0.846103i
$582$	2.08741	−	4.84134i	0.0865260	−	0.200680i
$583$	−13.2515			−0.548821
$584$	12.8292	+	35.1943i	0.530877	+	1.45635i
$585$	−25.7845			−1.06606
$586$	−11.2716	+	26.1424i	−0.465627	+	1.07993i
$587$		−	30.3967i		−	1.25461i	−0.778775	−	0.627303i	$-0.784159\pi$
$587$		−	30.3967i		−	1.25461i	0.778775	−	0.627303i	$-0.215841\pi$
$588$	1.61106	−	1.52096i	0.0664391	−	0.0627232i
$589$		−	4.53681i		−	0.186936i
$590$	8.60079	+	3.70835i	0.354089	+	0.152670i
$591$	−2.56792			−0.105630
$592$	27.8574	+	1.60422i	1.14493	+	0.0659331i
$593$	39.3809			1.61718			0.808590	−	0.588373i	$-0.200231\pi$
$593$	39.3809			1.61718			0.808590	+	0.588373i	$0.200231\pi$
$594$	−1.77608	−	0.765781i	−0.0728734	−	0.0314204i
$595$		−	12.3214i		−	0.505130i
$596$	4.42113	−	4.17385i	0.181096	−	0.170968i
$597$		−	4.16965i		−	0.170652i
$598$	−12.5654	+	29.1429i	−0.513835	+	1.19174i
$599$	−35.9183			−1.46758			−0.733792	−	0.679374i	$-0.762251\pi$
$599$	−35.9183			−1.46758			−0.733792	+	0.679374i	$0.762251\pi$
$600$	−0.812781	+	0.296280i	−0.0331817	+	0.0120956i
$601$	13.8292			0.564104			0.282052	−	0.959399i	$-0.408985\pi$
$601$	13.8292			0.564104			0.282052	+	0.959399i	$0.408985\pi$
$602$	−2.65939	+	6.16794i	−0.108389	+	0.251386i
$603$			22.5875i			0.919833i
$604$	−2.52170	−	2.67110i	−0.102607	−	0.108685i
$605$		−	2.51595i		−	0.102288i
$606$	−2.57868	−	1.11184i	−0.104752	−	0.0451652i
$607$	19.7004			0.799615			0.399807	−	0.916599i	$-0.369077\pi$
$607$	19.7004			0.799615			0.399807	+	0.916599i	$0.369077\pi$
$608$	−36.0679	−	18.0770i	−1.46274	−	0.733121i
$609$	0.480693			0.0194786
$610$	21.1067	+	9.10046i	0.854586	+	0.368467i
$611$			2.99869i			0.121314i
$612$	−13.4124	−	14.2070i	−0.542164	−	0.574283i
$613$		−	31.7465i		−	1.28223i	−0.767445	−	0.641114i	$-0.778472\pi$
$613$		−	31.7465i		−	1.28223i	0.767445	−	0.641114i	$-0.221528\pi$
$614$	1.25474	−	2.91012i	0.0506371	−	0.117443i
$615$	−3.89362			−0.157006
$616$	−3.92610	+	1.43116i	−0.158187	+	0.0576632i
$617$	−27.5402			−1.10873			−0.554363	−	0.832275i	$-0.687038\pi$
$617$	−27.5402			−1.10873			−0.554363	+	0.832275i	$0.687038\pi$
$618$	−0.638014	+	1.47975i	−0.0256647	+	0.0595242i
$619$		−	19.6108i		−	0.788224i	−0.919063	−	0.394112i	$-0.871052\pi$
$619$		−	19.6108i		−	0.788224i	0.919063	−	0.394112i	$-0.128948\pi$
$620$	−2.32754	+	2.19736i	−0.0934764	+	0.0882483i
$621$		−	8.82581i		−	0.354167i
$622$	20.3782	+	8.78636i	0.817093	+	0.352301i
$623$	−1.55099			−0.0621392
$624$	0.183903	−	3.19349i	0.00736201	−	0.127842i
$625$	−29.8811			−1.19525
$626$	15.7353	+	6.78449i	0.628908	+	0.271163i
$627$		−	1.64011i		−	0.0654997i
$628$	−14.6244	+	13.8065i	−0.583579	+	0.550939i
$629$			23.1233i			0.921988i
$630$	6.13395	−	14.2265i	0.244382	−	0.566797i
$631$	17.6518			0.702705			0.351353	−	0.936243i	$-0.385722\pi$
$631$	17.6518			0.702705			0.351353	+	0.936243i	$0.385722\pi$
$632$	15.8292	+	43.4240i	0.629651	+	1.72731i
$633$	−4.23552			−0.168347
$634$	−6.66078	+	15.4484i	−0.264533	+	0.613533i
$635$		−	10.3662i		−	0.411368i
$636$	4.18396	+	4.43183i	0.165905	+	0.175734i
$637$		−	16.7515i		−	0.663717i
$638$	1.83732	+	0.792187i	0.0727403	+	0.0313630i
$639$	36.2201			1.43284
$640$	8.19499	+	27.2596i	0.323936	+	1.07753i
$641$	16.7617			0.662047			0.331024	−	0.943622i	$-0.392606\pi$
$641$	16.7617			0.662047			0.331024	+	0.943622i	$0.392606\pi$
$642$	1.89540	+	0.817228i	0.0748054	+	0.0322534i
$643$			22.1367i			0.872984i	0.899708	+	0.436492i	$0.143779\pi$
$643$			22.1367i			0.872984i	−0.899708	+	0.436492i	$0.856221\pi$
$644$	−13.0903	−	13.8658i	−0.515829	−	0.546388i
$645$			1.85998i			0.0732368i
$646$	13.2371	−	30.7008i	0.520806	−	1.20791i
$647$	22.7792			0.895544			0.447772	−	0.894148i	$-0.352218\pi$
$647$	22.7792			0.895544			0.447772	+	0.894148i	$0.352218\pi$
$648$	−8.25980	−	22.6590i	−0.324476	−	0.890130i
$649$	2.63236			0.103329
$650$	−2.58969	+	6.00627i	−0.101576	+	0.235585i
$651$			0.216130i			0.00847080i
$652$	18.7509	−	17.7021i	0.734340	−	0.693268i
$653$			35.9327i			1.40615i	0.711114	+	0.703077i	$0.248191\pi$
$653$			35.9327i			1.40615i	−0.711114	+	0.703077i	$0.751809\pi$
$654$	2.37198	+	1.02271i	0.0927517	+	0.0399912i
$655$	−33.4660			−1.30762
$656$	−1.54757	+	26.8737i	−0.0604226	+	1.04924i
$657$	−39.0315			−1.52277
$658$	−1.65451	−	0.713367i	−0.0644997	−	0.0278099i
$659$		−	1.49362i		−	0.0581831i	−0.999577	−	0.0290916i	$-0.990739\pi$
$659$		−	1.49362i		−	0.0581831i	0.999577	−	0.0290916i	$-0.00926144\pi$
$660$	−0.841435	+	0.794374i	−0.0327528	+	0.0309210i
$661$		−	44.3160i		−	1.72369i	−0.507170	−	0.861846i	$-0.669308\pi$
$661$		−	44.3160i		−	1.72369i	0.507170	−	0.861846i	$-0.330692\pi$
$662$	−13.8690	+	32.1664i	−0.539034	+	1.25018i
$663$	2.65079			0.102948
$664$	36.6823	−	13.3717i	1.42355	−	0.518921i
$665$	26.5105			1.02803
$666$	−11.5114	+	26.6985i	−0.446059	+	1.03455i
$667$			9.13015i			0.353521i
$668$	6.14308	+	6.50702i	0.237683	+	0.251764i
$669$			3.34955i			0.129501i
$670$	25.0417	+	10.7971i	0.967444	+	0.417127i
$671$	6.45993			0.249383
$672$	1.71824	+	0.861176i	0.0662827	+	0.0332206i
$673$	−33.8921			−1.30644			−0.653222	−	0.757166i	$-0.726583\pi$
$673$	−33.8921			−1.30644			−0.653222	+	0.757166i	$0.726583\pi$
$674$	14.5818	+	6.28715i	0.561671	+	0.242172i
$675$		−	1.81898i		−	0.0700124i
$676$	1.24591	+	1.31972i	0.0479196	+	0.0507585i
$677$			7.57568i			0.291157i	0.989347	+	0.145578i	$0.0465043\pi$
$677$			7.57568i			0.291157i	−0.989347	+	0.145578i	$0.953496\pi$
$678$	0.628693	−	1.45813i	0.0241448	−	0.0559992i
$679$	23.9507			0.919143
$680$	−22.1619	+	8.07858i	−0.849870	+	0.309800i
$681$	1.64459			0.0630210
$682$	−0.356185	+	0.826100i	−0.0136390	+	0.0316330i
$683$			16.1346i			0.617374i	0.951164	+	0.308687i	$0.0998896\pi$
$683$			16.1346i			0.617374i	−0.951164	+	0.308687i	$0.900110\pi$
$684$	30.5674	−	28.8578i	1.16877	−	1.10340i
$685$		−	17.2203i		−	0.657953i
$686$	22.6732	+	9.77586i	0.865666	+	0.373244i
$687$	−1.49134			−0.0568980
$688$	12.8376	+	0.739276i	0.489428	+	0.0281847i
$689$	46.0812			1.75555
$690$	−4.84887	−	2.09066i	−0.184593	−	0.0795900i
$691$		−	10.5531i		−	0.401457i	−0.979647	−	0.200729i	$-0.935669\pi$
$691$		−	10.5531i		−	0.401457i	0.979647	−	0.200729i	$-0.0643309\pi$
$692$	−0.265856	+	0.250987i	−0.0101063	+	0.00954108i
$693$		−	4.35416i		−	0.165401i
$694$	8.97175	−	20.8082i	0.340563	−	0.789869i
$695$	30.6860			1.16399
$696$	−0.315168	−	0.864595i	−0.0119464	−	0.0327724i
$697$	−22.3068			−0.844931
$698$	5.19341	−	12.0451i	0.196574	−	0.455914i
$699$			2.63970i			0.0998425i
$700$	−2.69787	−	2.85770i	−0.101970	−	0.108011i
$701$		−	43.8782i		−	1.65726i	−0.559800	−	0.828628i	$-0.689122\pi$
$701$		−	43.8782i		−	1.65726i	0.559800	−	0.828628i	$-0.310878\pi$
$702$	6.17619	+	2.66295i	0.233105	+	0.100507i
$703$	−49.7516			−1.87642
$704$	5.14831	+	6.12331i	0.194034	+	0.230781i
$705$	−0.498930			−0.0187908
$706$	12.4430	+	5.36496i	0.468297	+	0.201913i
$707$		−	12.7570i		−	0.479778i
$708$	−0.831128	−	0.880368i	−0.0312357	−	0.0330862i
$709$		−	4.31359i		−	0.162000i	−0.996714	−	0.0810002i	$-0.974189\pi$
$709$		−	4.31359i		−	0.162000i	0.996714	−	0.0810002i	$-0.0258115\pi$
$710$	17.3136	−	40.1555i	0.649768	−	1.50701i
$711$	−48.1586			−1.80609
$712$	1.01691	+	2.78969i	0.0381104	+	0.104548i
$713$	−4.10511			−0.153738
$714$	−0.630604	+	1.46256i	−0.0235998	+	0.0547351i
$715$			8.74905i			0.327196i
$716$	29.2190	−	27.5848i	1.09196	−	1.03089i
$717$			0.0257645i			0.000962192i
$718$	10.1359	+	4.37025i	0.378270	+	0.163096i
$719$	−0.793243			−0.0295830			−0.0147915	−	0.999891i	$-0.504708\pi$
$719$	−0.793243			−0.0295830			−0.0147915	+	0.999891i	$0.504708\pi$
$720$	−29.6101	−	1.70516i	−1.10350	−	0.0635475i
$721$	−7.32048			−0.272629
$722$	41.3809	+	17.8420i	1.54004	+	0.664009i
$723$			0.675956i			0.0251391i
$724$	11.1023	−	10.4813i	0.412614	−	0.389536i
$725$			1.88170i			0.0698845i
$726$	−0.128765	+	0.298645i	−0.00477892	+	0.0110838i
$727$	−38.5654			−1.43031			−0.715155	−	0.698966i	$-0.753644\pi$
$727$	−38.5654			−1.43031			−0.715155	+	0.698966i	$0.753644\pi$
$728$	13.6527	−	4.97678i	0.506004	−	0.184452i
$729$	24.1860			0.895779
$730$	−18.6575	+	43.2724i	−0.690546	+	1.60158i
$731$			10.6560i			0.394125i
$732$	−2.03963	−	2.16046i	−0.0753868	−	0.0798530i
$733$		−	35.3659i		−	1.30627i	−0.757242	−	0.653134i	$-0.773454\pi$
$733$		−	35.3659i		−	1.30627i	0.757242	−	0.653134i	$-0.226546\pi$
$734$	−40.8284	−	17.6038i	−1.50701	−	0.649766i
$735$	2.78716			0.102806
$736$	−16.3569	+	32.6359i	−0.602925	+	1.20297i
$737$	7.66426			0.282317
$738$	−25.7557	−	11.1049i	−0.948082	−	0.408779i
$739$			41.6624i			1.53258i	0.642497	+	0.766288i	$0.277899\pi$
$739$			41.6624i			1.53258i	−0.642497	+	0.766288i	$0.722101\pi$
$740$	24.0968	+	25.5244i	0.885816	+	0.938294i
$741$			5.70338i			0.209519i
$742$	−10.9624	+	25.4251i	−0.402442	+	0.933385i
$743$	33.2692			1.22053			0.610264	−	0.792198i	$-0.291063\pi$
$743$	33.2692			1.22053			0.610264	+	0.792198i	$0.291063\pi$
$744$	0.388741	−	0.141706i	0.0142519	−	0.00519520i
$745$	7.64859			0.280223
$746$	−17.9415	+	41.6118i	−0.656885	+	1.52351i
$747$			40.6819i			1.48847i
$748$	−4.82064	+	4.55102i	−0.176260	+	0.166402i
$749$			9.37676i			0.342619i
$750$	2.75755	+	1.18895i	0.100691	+	0.0434145i
$751$	−3.69284			−0.134754			−0.0673768	−	0.997728i	$-0.521463\pi$
$751$	−3.69284			−0.134754			−0.0673768	+	0.997728i	$0.521463\pi$
$752$	−0.198307	+	3.44361i	−0.00723150	+	0.125575i
$753$	−7.17954			−0.261637
$754$	−6.38916	−	2.75478i	−0.232680	−	0.100323i
$755$		−	4.62103i		−	0.168176i
$756$	−2.93855	+	2.77419i	−0.106874	+	0.100896i
$757$		−	19.2210i		−	0.698600i	−0.937011	−	0.349300i	$-0.886419\pi$
$757$		−	19.2210i		−	0.698600i	0.937011	−	0.349300i	$-0.113581\pi$
$758$	6.40920	−	14.8649i	0.232793	−	0.539917i
$759$	−1.48405			−0.0538676
$760$	−17.3817	−	47.6830i	−0.630500	−	1.72964i
$761$	−9.79341			−0.355011			−0.177505	−	0.984120i	$-0.556803\pi$
$761$	−9.79341			−0.355011			−0.177505	+	0.984120i	$0.556803\pi$
$762$	−0.530534	+	1.23047i	−0.0192192	+	0.0445752i
$763$			11.7345i			0.424816i
$764$	−31.5703	−	33.4406i	−1.14217	−	1.20984i
$765$		−	24.5782i		−	0.888628i
$766$	8.86351	+	3.82163i	0.320252	+	0.138081i
$767$	−9.15386			−0.330527
$768$	0.422378	−	3.65515i	0.0152413	−	0.131894i
$769$	−48.2853			−1.74121			−0.870606	−	0.491981i	$-0.836273\pi$
$769$	−48.2853			−1.74121			−0.870606	+	0.491981i	$0.836273\pi$
$770$	−4.82726	−	2.08134i	−0.173962	−	0.0750063i
$771$			1.63217i			0.0587812i
$772$	1.00951	+	1.06931i	0.0363329	+	0.0384854i
$773$			21.0475i			0.757025i	0.925596	+	0.378513i	$0.123564\pi$
$773$			21.0475i			0.757025i	−0.925596	+	0.378513i	$0.876436\pi$
$774$	−5.30483	+	12.3035i	−0.190678	+	0.442241i
$775$	−0.846053			−0.0303911
$776$	−15.7033	−	43.0788i	−0.563717	−	1.54644i
$777$	2.37013			0.0850279
$778$	−3.72904	+	8.64877i	−0.133692	+	0.310073i
$779$		−	47.9948i		−	1.71959i
$780$	2.92604	−	2.76238i	0.104769	−	0.0989091i
$781$		−	12.2900i		−	0.439771i
$782$	−27.7795	−	11.9775i	−0.993394	−	0.428316i
$783$	1.93493			0.0691489
$784$	1.10779	−	19.2369i	0.0395641	−	0.687032i
$785$	−25.3005			−0.903012
$786$	3.97244	+	1.71277i	0.141692	+	0.0610925i
$787$		−	18.2077i		−	0.649034i	−0.945880	−	0.324517i	$-0.894798\pi$
$787$		−	18.2077i		−	0.649034i	0.945880	−	0.324517i	$-0.105202\pi$
$788$	−16.2394	+	15.3311i	−0.578504	+	0.546149i
$789$			3.76830i			0.134155i
$790$	−23.0204	+	53.3912i	−0.819027	+	1.89957i
$791$	7.21354			0.256484
$792$	−7.83160	+	2.85482i	−0.278284	+	0.101442i
$793$	−22.4640			−0.797719
$794$	−1.35609	+	3.14518i	−0.0481258	+	0.111618i
$795$			7.66712i			0.271925i
$796$	−24.8939	−	26.3687i	−0.882339	−	0.934612i
$797$		−	40.2274i		−	1.42493i	−0.701709	−	0.712463i	$-0.747579\pi$
$797$		−	40.2274i		−	1.42493i	0.701709	−	0.712463i	$-0.252421\pi$
$798$	−3.14682	−	1.35679i	−0.111396	−	0.0480300i
$799$	−2.85840			−0.101123
$800$	−3.37112	+	6.72617i	−0.119187	+	0.237806i
$801$	−3.09385			−0.109316
$802$	11.8063	+	5.09044i	0.416894	+	0.179750i
$803$			13.2440i			0.467370i
$804$	−2.41988	−	2.56324i	−0.0853425	−	0.0903985i
$805$		−	23.9879i		−	0.845464i
$806$	1.23861	−	2.87271i	0.0436281	−	0.101187i
$807$	−3.93846			−0.138640
$808$	−22.9454	+	8.36419i	−0.807216	+	0.294251i
$809$	27.8044			0.977552			0.488776	−	0.872409i	$-0.337444\pi$
$809$	27.8044			0.977552			0.488776	+	0.872409i	$0.337444\pi$
$810$	12.0122	−	27.8600i	0.422066	−	0.978899i
$811$		−	7.59987i		−	0.266868i	−0.991058	−	0.133434i	$-0.957400\pi$
$811$		−	7.59987i		−	0.266868i	0.991058	−	0.133434i	$-0.0426004\pi$
$812$	3.03988	−	2.86985i	0.106679	−	0.100712i
$813$			4.48762i			0.157388i
$814$	9.05920	+	3.90600i	0.317525	+	0.136905i
$815$	32.4392			1.13629
$816$	3.04409	+	0.175300i	0.106564	+	0.00613672i
$817$	−22.9271			−0.802119
$818$	−11.7919	−	5.08423i	−0.412293	−	0.177766i
$819$			15.1413i			0.529080i
$820$	−24.6231	+	23.2459i	−0.859874	+	0.811781i
$821$			26.6456i			0.929937i	0.885327	+	0.464968i	$0.153934\pi$
$821$			26.6456i			0.929937i	−0.885327	+	0.464968i	$0.846066\pi$
$822$	−0.881325	+	2.04406i	−0.0307397	+	0.0712948i
$823$	35.5588			1.23950			0.619751	−	0.784799i	$-0.287234\pi$
$823$	35.5588			1.23950			0.619751	+	0.784799i	$0.287234\pi$
$824$	4.79969	+	13.1669i	0.167205	+	0.458692i
$825$	−0.305858			−0.0106486
$826$	2.17764	−	5.05061i	0.0757698	−	0.175733i
$827$		−	3.03188i		−	0.105429i	−0.998610	−	0.0527145i	$-0.983213\pi$
$827$		−	3.03188i		−	0.105429i	0.998610	−	0.0527145i	$-0.0167873\pi$
$828$	−26.1119	−	27.6588i	−0.907450	−	0.961210i
$829$			35.0569i			1.21758i	0.793332	+	0.608789i	$0.208344\pi$
$829$			35.0569i			1.21758i	−0.793332	+	0.608789i	$0.791656\pi$
$830$	45.1021	+	19.4464i	1.56552	+	0.674994i
$831$	−2.42886			−0.0842562
$832$	−17.9029	−	21.2934i	−0.620672	−	0.738215i
$833$	15.9678			0.553252
$834$	−3.64245	−	1.57049i	−0.126128	−	0.0543817i
$835$			11.2572i			0.389572i
$836$	−9.79187	−	10.3720i	−0.338659	−	0.358722i
$837$			0.869989i			0.0300712i
$838$	1.67706	−	3.88960i	0.0579329	−	0.134364i
$839$	−6.41520			−0.221477			−0.110739	−	0.993850i	$-0.535322\pi$
$839$	−6.41520			−0.221477			−0.110739	+	0.993850i	$0.535322\pi$
$840$	0.828050	+	2.27158i	0.0285704	+	0.0783770i
$841$	26.9983			0.930977
$842$	14.9303	−	34.6278i	0.514531	−	1.19335i
$843$		−	2.66747i		−	0.0918727i
$844$	−26.7852	+	25.2871i	−0.921985	+	0.870419i
$845$			2.28313i			0.0785421i
$846$	−3.30035	−	1.42299i	−0.113468	−	0.0489235i
$847$	−1.47743			−0.0507652
$848$	52.9183	+	3.04740i	1.81722	+	0.104648i
$849$	−4.97266			−0.170661
$850$	−5.72529	−	2.46854i	−0.196376	−	0.0846701i
$851$			45.0176i			1.54318i
$852$	−4.11027	+	3.88039i	−0.140816	+	0.132940i
$853$			10.5605i			0.361585i	0.983521	+	0.180793i	$0.0578663\pi$
$853$			10.5605i			0.361585i	−0.983521	+	0.180793i	$0.942134\pi$
$854$	5.34403	−	12.3944i	0.182869	−	0.424128i
$855$	52.8820			1.80852
$856$	16.8655	−	6.14790i	0.576450	−	0.210131i
$857$	−5.03900			−0.172129			−0.0860644	−	0.996290i	$-0.527429\pi$
$857$	−5.03900			−0.172129			−0.0860644	+	0.996290i	$0.527429\pi$
$858$	0.447772	−	1.03852i	0.0152867	−	0.0354544i
$859$			24.5174i			0.836521i	0.908327	+	0.418261i	$0.137360\pi$
$859$			24.5174i			0.836521i	−0.908327	+	0.418261i	$0.862640\pi$
$860$	11.1046	+	11.7624i	0.378663	+	0.401096i
$861$			2.28644i			0.0779215i
$862$	−25.4145	−	10.9578i	−0.865623	−	0.373225i
$863$	17.8155			0.606448			0.303224	−	0.952919i	$-0.401937\pi$
$863$	17.8155			0.606448			0.303224	+	0.952919i	$0.401937\pi$
$864$	6.91646	+	3.46650i	0.235303	+	0.117933i
$865$	−0.459934			−0.0156382
$866$	8.42857	+	3.63409i	0.286414	+	0.123492i
$867$		−	1.38265i		−	0.0469574i
$868$	1.29035	+	1.36679i	0.0437973	+	0.0463920i
$869$			16.3409i			0.554328i
$870$	0.458348	−	1.06305i	0.0155394	−	0.0360407i
$871$	−26.6520			−0.903067
$872$	21.1061	−	7.69373i	0.714743	−	0.260542i
$873$	47.7757			1.61696
$874$	25.7706	−	59.7698i	0.871703	−	2.02174i
$875$			13.6419i			0.461180i
$876$	4.42932	−	4.18159i	0.149653	−	0.141283i
$877$			22.4071i			0.756634i	0.925676	+	0.378317i	$0.123497\pi$
$877$			22.4071i			0.756634i	−0.925676	+	0.378317i	$0.876503\pi$
$878$	−32.8997	−	14.1852i	−1.11031	−	0.478726i
$879$	4.62934			0.156144
$880$	−0.578585	+	10.0472i	−0.0195041	+	0.338690i
$881$	−12.0016			−0.404345			−0.202172	−	0.979350i	$-0.564800\pi$
$881$	−12.0016			−0.404345			−0.202172	+	0.979350i	$0.564800\pi$
$882$	18.4366	+	7.94921i	0.620794	+	0.267664i
$883$		−	27.9363i		−	0.940130i	−0.882632	−	0.470065i	$-0.844230\pi$
$883$		−	27.9363i		−	0.940130i	0.882632	−	0.470065i	$-0.155770\pi$
$884$	16.7635	−	15.8259i	0.563816	−	0.532282i
$885$		−	1.52305i		−	0.0511966i
$886$	−0.818593	+	1.89857i	−0.0275012	+	0.0637836i
$887$	−48.6903			−1.63486			−0.817430	−	0.576028i	$-0.804602\pi$
$887$	−48.6903			−1.63486			−0.817430	+	0.576028i	$0.804602\pi$
$888$	−1.55398	−	4.26302i	−0.0521482	−	0.143058i
$889$	−6.08728			−0.204161
$890$	−1.47890	+	3.43001i	−0.0495727	+	0.114974i
$891$		−	8.52683i		−	0.285660i
$892$	19.9976	+	21.1824i	0.669570	+	0.709238i
$893$		−	6.15008i		−	0.205804i
$894$	−0.907894	−	0.391451i	−0.0303645	−	0.0130921i
$895$	50.5492			1.68967
$896$	16.0075	−	4.81232i	0.534774	−	0.160768i
$897$	5.16068			0.172310
$898$	7.79272	+	3.35994i	0.260047	+	0.112123i
$899$		−	0.899988i		−	0.0300163i
$900$	−5.38158	−	5.70041i	−0.179386	−	0.190014i
$901$			43.9254i			1.46337i
$902$	−3.76807	+	8.73930i	−0.125463	+	0.290987i
$903$	1.09223			0.0363472
$904$	−4.72958	−	12.9746i	−0.157303	−	0.431529i
$905$	19.2071			0.638465
$906$	−0.236502	+	0.548519i	−0.00785724	+	0.0182233i
$907$		−	48.2773i		−	1.60302i	−0.597981	−	0.801510i	$-0.704030\pi$
$907$		−	48.2773i		−	1.60302i	0.597981	−	0.801510i	$-0.295970\pi$
$908$	10.4003	−	9.81864i	0.345147	−	0.325843i
$909$		−	25.4472i		−	0.844029i
$910$	16.7865	+	7.23772i	0.556466	+	0.239928i
$911$	43.1688			1.43025			0.715123	−	0.698998i	$-0.246370\pi$
$911$	43.1688			1.43025			0.715123	+	0.698998i	$0.246370\pi$
$912$	−0.377171	+	6.54959i	−0.0124894	+	0.216879i
$913$	13.8040			0.456844
$914$	−22.8157	−	9.83732i	−0.754677	−	0.325390i
$915$		−	3.73762i		−	0.123562i
$916$	−9.43113	+	8.90364i	−0.311613	+	0.294185i
$917$			19.6521i			0.648970i
$918$	−2.53837	+	5.88726i	−0.0837789	+	0.194309i
$919$	36.1457			1.19234			0.596168	−	0.802860i	$-0.296689\pi$
$919$	36.1457			1.19234			0.596168	+	0.802860i	$0.296689\pi$
$920$	−43.1458	+	15.7278i	−1.42247	+	0.518529i
$921$	−0.515330			−0.0169807
$922$	−14.6271	+	33.9247i	−0.481718	+	1.11725i
$923$			42.7377i			1.40673i
$924$	0.466477	+	0.494113i	0.0153460	+	0.0162551i
$925$			9.27801i			0.305059i
$926$	−26.3960	−	11.3810i	−0.867426	−	0.374003i
$927$	−14.6026			−0.479611
$928$	−7.15495	−	3.58603i	−0.234873	−	0.117717i
$929$	26.1901			0.859269			0.429634	−	0.903003i	$-0.358642\pi$
$929$	26.1901			0.859269			0.429634	+	0.903003i	$0.358642\pi$
$930$	0.477969	+	0.206083i	0.0156732	+	0.00675773i
$931$			34.3560i			1.12597i
$932$	15.7597	+	16.6933i	0.516225	+	0.546808i
$933$		−	3.60862i		−	0.118141i
$934$	0.726588	−	1.68518i	0.0237747	−	0.0551407i
$935$	−8.33976			−0.272739
$936$	27.2338	−	9.92745i	0.890166	−	0.324489i
$937$	−14.6547			−0.478749			−0.239375	−	0.970927i	$-0.576942\pi$
$937$	−14.6547			−0.478749			−0.239375	+	0.970927i	$0.576942\pi$
$938$	6.34032	−	14.7051i	0.207019	−	0.480139i
$939$		−	2.78644i		−	0.0909319i
$940$	−3.15521	+	2.97874i	−0.102912	+	0.0971557i
$941$			5.50159i			0.179347i	0.995971	+	0.0896734i	$0.0285823\pi$
$941$			5.50159i			0.179347i	−0.995971	+	0.0896734i	$0.971418\pi$
$942$	3.00318	+	1.29486i	0.0978490	+	0.0421889i
$943$	−43.4279			−1.41421
$944$	−10.5120	−	0.605356i	−0.342137	−	0.0197026i
$945$	−5.08372			−0.165373
$946$	4.17477	+	1.80001i	0.135733	+	0.0585233i
$947$		−	1.00019i		−	0.0325019i	−0.999868	−	0.0162509i	$-0.994827\pi$
$947$		−	1.00019i		−	0.0325019i	0.999868	−	0.0162509i	$-0.00517306\pi$
$948$	5.46507	−	5.15940i	0.177497	−	0.167570i
$949$		−	46.0551i		−	1.49501i
$950$	5.31125	−	12.3184i	0.172320	−	0.399661i
$951$	2.73563			0.0887088
$952$	4.74396	+	13.0140i	0.153753	+	0.421788i
$953$	55.6770			1.80356			0.901778	−	0.432200i	$-0.142263\pi$
$953$	55.6770			1.80356			0.901778	+	0.432200i	$0.142263\pi$
$954$	−21.8673	+	50.7169i	−0.707979	+	1.64202i
$955$		−	57.8526i		−	1.87207i
$956$	0.153820	+	0.162933i	0.00497490	+	0.00526964i
$957$		−	0.325357i		−	0.0105173i
$958$	37.0287	+	15.9654i	1.19634	+	0.515820i
$959$	−10.1122			−0.326540
$960$	3.54285	−	2.97874i	0.114345	−	0.0961383i
$961$	−30.5953			−0.986947
$962$	−31.5028	−	13.5829i	−1.01569	−	0.437929i
$963$			18.7043i			0.602739i
$964$	4.03563	+	4.27471i	0.129979	+	0.137679i
$965$			1.84992i			0.0595511i
$966$	−1.22769	+	2.84739i	−0.0395003	+	0.0916131i
$967$	−25.9869			−0.835682			−0.417841	−	0.908520i	$-0.637213\pi$
$967$	−25.9869			−0.835682			−0.417841	+	0.908520i	$0.637213\pi$
$968$	0.968683	+	2.65738i	0.0311347	+	0.0854113i
$969$	−5.43656			−0.174648
$970$	22.8373	−	52.9667i	0.733262	−	1.70066i
$971$			16.0587i			0.515349i	0.966232	+	0.257675i	$0.0829563\pi$
$971$			16.0587i			0.515349i	−0.966232	+	0.257675i	$0.917044\pi$
$972$	−8.81858	+	8.32536i	−0.282856	+	0.267036i
$973$		−	18.0196i		−	0.577683i
$974$	7.83556	+	3.37841i	0.251068	+	0.108251i
$975$	1.06360			0.0340625
$976$	−25.7970	−	1.48557i	−0.825742	−	0.0475519i
$977$	−5.40488			−0.172918			−0.0864588	−	0.996255i	$-0.527555\pi$
$977$	−5.40488			−0.172918			−0.0864588	+	0.996255i	$0.527555\pi$
$978$	−3.85055	−	1.66022i	−0.123127	−	0.0530880i
$979$			1.04979i			0.0335514i
$980$	17.6258	−	16.6400i	0.563037	−	0.531546i
$981$			23.4073i			0.747339i
$982$	2.32599	−	5.39467i	0.0742252	−	0.172151i
$983$	−36.4792			−1.16350			−0.581752	−	0.813366i	$-0.697633\pi$
$983$	−36.4792			−1.16350			−0.581752	+	0.813366i	$0.697633\pi$
$984$	4.11249	−	1.49911i	0.131101	−	0.0477898i
$985$	−28.0943			−0.895159
$986$	2.62590	−	6.09027i	0.0836258	−	0.193954i
$987$			0.292985i			0.00932581i
$988$	34.0506	+	36.0679i	1.08329	+	1.14747i
$989$			20.7455i			0.659670i
$990$	−9.62919	−	4.15176i	−0.306036	−	0.131952i
$991$	48.2714			1.53339			0.766696	−	0.642010i	$-0.221899\pi$
$991$	48.2714			1.53339			0.766696	+	0.642010i	$0.221899\pi$
$992$	1.61236	−	3.21702i	0.0511924	−	0.102141i
$993$	5.69609			0.180760
$994$	−23.5804	−	10.1670i	−0.747924	−	0.322478i
$995$		−	45.6181i		−	1.44619i
$996$	−4.35839	−	4.61660i	−0.138101	−	0.146283i
$997$		−	8.78994i		−	0.278380i	−0.990266	−	0.139190i	$-0.955550\pi$
$997$		−	8.78994i		−	0.278380i	0.990266	−	0.139190i	$-0.0444499\pi$
$998$	−16.8554	+	39.0929i	−0.533549	+	1.23746i
$999$	9.54049			0.301848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.c.a.45.1	✓	10
3.2	odd	2		792.2.f.g.397.10		10
4.3	odd	2		352.2.c.a.177.5		10
8.3	odd	2		352.2.c.a.177.6		10
8.5	even	2	inner	88.2.c.a.45.2	yes	10
11.2	odd	10		968.2.o.h.565.4		40
11.3	even	5		968.2.o.g.493.3		40
11.4	even	5		968.2.o.g.269.6		40
11.5	even	5		968.2.o.g.245.10		40
11.6	odd	10		968.2.o.h.245.1		40
11.7	odd	10		968.2.o.h.269.5		40
11.8	odd	10		968.2.o.h.493.8		40
11.9	even	5		968.2.o.g.565.7		40
11.10	odd	2		968.2.c.d.485.10		10
12.11	even	2		3168.2.f.g.1585.2		10
16.3	odd	4		2816.2.a.p.1.3		5
16.5	even	4		2816.2.a.r.1.3		5
16.11	odd	4		2816.2.a.q.1.3		5
16.13	even	4		2816.2.a.o.1.3		5
24.5	odd	2		792.2.f.g.397.9		10
24.11	even	2		3168.2.f.g.1585.9		10
44.43	even	2		3872.2.c.f.1937.5		10
88.5	even	10		968.2.o.g.245.7		40
88.13	odd	10		968.2.o.h.565.1		40
88.21	odd	2		968.2.c.d.485.9		10
88.29	odd	10		968.2.o.h.269.8		40
88.37	even	10		968.2.o.g.269.3		40
88.43	even	2		3872.2.c.f.1937.6		10
88.53	even	10		968.2.o.g.565.10		40
88.61	odd	10		968.2.o.h.245.4		40
88.69	even	10		968.2.o.g.493.6		40
88.85	odd	10		968.2.o.h.493.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.1	✓	10	1.1	even	1	trivial
88.2.c.a.45.2	yes	10	8.5	even	2	inner
352.2.c.a.177.5		10	4.3	odd	2
352.2.c.a.177.6		10	8.3	odd	2
792.2.f.g.397.9		10	24.5	odd	2
792.2.f.g.397.10		10	3.2	odd	2
968.2.c.d.485.9		10	88.21	odd	2
968.2.c.d.485.10		10	11.10	odd	2
968.2.o.g.245.7		40	88.5	even	10
968.2.o.g.245.10		40	11.5	even	5
968.2.o.g.269.3		40	88.37	even	10
968.2.o.g.269.6		40	11.4	even	5
968.2.o.g.493.3		40	11.3	even	5
968.2.o.g.493.6		40	88.69	even	10
968.2.o.g.565.7		40	11.9	even	5
968.2.o.g.565.10		40	88.53	even	10
968.2.o.h.245.1		40	11.6	odd	10
968.2.o.h.245.4		40	88.61	odd	10
968.2.o.h.269.5		40	11.7	odd	10
968.2.o.h.269.8		40	88.29	odd	10
968.2.o.h.493.5		40	88.85	odd	10
968.2.o.h.493.8		40	11.8	odd	10
968.2.o.h.565.1		40	88.13	odd	10
968.2.o.h.565.4		40	11.2	odd	10
2816.2.a.o.1.3		5	16.13	even	4
2816.2.a.p.1.3		5	16.3	odd	4
2816.2.a.q.1.3		5	16.11	odd	4
2816.2.a.r.1.3		5	16.5	even	4
3168.2.f.g.1585.2		10	12.11	even	2
3168.2.f.g.1585.9		10	24.11	even	2
3872.2.c.f.1937.5		10	44.43	even	2
3872.2.c.f.1937.6		10	88.43	even	2

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29865 - 0.559929i) q^{2} +0.229967i q^{3} +(1.37296 + 1.45430i) q^{4} +2.51595i q^{5} +(0.128765 - 0.298645i) q^{6} +1.47743 q^{7} +(-0.968683 - 2.65738i) q^{8} +2.94712 q^{9} +O(q^{10})\)	\(q+(-1.29865 - 0.559929i) q^{2} +0.229967i q^{3} +(1.37296 + 1.45430i) q^{4} +2.51595i q^{5} +(0.128765 - 0.298645i) q^{6} +1.47743 q^{7} +(-0.968683 - 2.65738i) q^{8} +2.94712 q^{9} +(1.40875 - 3.26733i) q^{10} -1.00000i q^{11} +(-0.334440 + 0.315735i) q^{12} +3.47743i q^{13} +(-1.91866 - 0.827257i) q^{14} -0.578585 q^{15} +(-0.229967 + 3.99338i) q^{16} -3.31475 q^{17} +(-3.82726 - 1.65018i) q^{18} -7.13195i q^{19} +(-3.65894 + 3.45430i) q^{20} +0.339760i q^{21} +(-0.559929 + 1.29865i) q^{22} -6.45332 q^{23} +(0.611108 - 0.222765i) q^{24} -1.33001 q^{25} +(1.94712 - 4.51595i) q^{26} +1.36764i q^{27} +(2.02845 + 2.14863i) q^{28} -1.41480i q^{29} +(0.751377 + 0.323967i) q^{30} +0.636125 q^{31} +(2.53466 - 5.05722i) q^{32} +0.229967 q^{33} +(4.30469 + 1.85603i) q^{34} +3.71715i q^{35} +(4.04627 + 4.28598i) q^{36} -6.97588i q^{37} +(-3.99338 + 9.26187i) q^{38} -0.799694 q^{39} +(6.68583 - 2.43716i) q^{40} +6.72955 q^{41} +(0.190242 - 0.441228i) q^{42} -3.21471i q^{43} +(1.45430 - 1.37296i) q^{44} +7.41480i q^{45} +(8.38057 + 3.61340i) q^{46} +0.862328 q^{47} +(-0.918346 - 0.0528847i) q^{48} -4.81719 q^{49} +(1.72721 + 0.744712i) q^{50} -0.762283i q^{51} +(-5.05722 + 4.77437i) q^{52} -13.2515i q^{53} +(0.765781 - 1.77608i) q^{54} +2.51595 q^{55} +(-1.43116 - 3.92610i) q^{56} +1.64011 q^{57} +(-0.792187 + 1.83732i) q^{58} +2.63236i q^{59} +(-0.794374 - 0.841435i) q^{60} +6.45993i q^{61} +(-0.826100 - 0.356185i) q^{62} +4.35416 q^{63} +(-6.12331 + 5.14831i) q^{64} -8.74905 q^{65} +(-0.298645 - 0.128765i) q^{66} +7.66426i q^{67} +(-4.55102 - 4.82064i) q^{68} -1.48405i q^{69} +(2.08134 - 4.82726i) q^{70} +12.2900 q^{71} +(-2.85482 - 7.83160i) q^{72} -13.2440 q^{73} +(-3.90600 + 9.05920i) q^{74} -0.305858i q^{75} +(10.3720 - 9.79187i) q^{76} -1.47743i q^{77} +(1.03852 + 0.447772i) q^{78} -16.3409 q^{79} +(-10.0472 - 0.578585i) q^{80} +8.52683 q^{81} +(-8.73930 - 3.76807i) q^{82} +13.8040i q^{83} +(-0.494113 + 0.466477i) q^{84} -8.33976i q^{85} +(-1.80001 + 4.17477i) q^{86} +0.325357 q^{87} +(-2.65738 + 0.968683i) q^{88} -1.04979 q^{89} +(4.15176 - 9.62919i) q^{90} +5.13767i q^{91} +(-8.86014 - 9.38505i) q^{92} +0.146288i q^{93} +(-1.11986 - 0.482842i) q^{94} +17.9436 q^{95} +(1.16299 + 0.582887i) q^{96} +16.2110 q^{97} +(6.25582 + 2.69729i) q^{98} -2.94712i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	\( 10 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 10 q^{10} - 4 q^{12} - 12 q^{14} + 8 q^{15} - 4 q^{17} - 10 q^{18} + 12 q^{20} - 12 q^{23} - 6 q^{25} - 20 q^{26} - 12 q^{28} + 18 q^{30} - 4 q^{31} - 20 q^{32} + 32 q^{36} + 8 q^{38} + 24 q^{39} + 20 q^{40} + 4 q^{41} + 20 q^{42} + 4 q^{44} + 2 q^{46} - 4 q^{47} + 32 q^{48} - 6 q^{49} - 6 q^{50} - 20 q^{52} - 38 q^{54} - 8 q^{55} - 8 q^{56} + 16 q^{57} + 36 q^{58} - 4 q^{60} + 22 q^{62} - 40 q^{63} - 16 q^{64} + 16 q^{65} + 10 q^{66} - 28 q^{68} + 28 q^{70} - 12 q^{71} - 4 q^{72} - 4 q^{73} - 14 q^{74} + 44 q^{76} - 8 q^{78} + 16 q^{79} - 56 q^{80} - 6 q^{81} - 4 q^{82} - 52 q^{84} - 20 q^{86} + 32 q^{87} - 12 q^{88} - 4 q^{89} - 36 q^{90} - 36 q^{92} + 24 q^{95} + 60 q^{96} - 20 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 10 * q^10 - 4 * q^12 - 12 * q^14 + 8 * q^15 - 4 * q^17 - 10 * q^18 + 12 * q^20 - 12 * q^23 - 6 * q^25 - 20 * q^26 - 12 * q^28 + 18 * q^30 - 4 * q^31 - 20 * q^32 + 32 * q^36 + 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 + 20 * q^42 + 4 * q^44 + 2 * q^46 - 4 * q^47 + 32 * q^48 - 6 * q^49 - 6 * q^50 - 20 * q^52 - 38 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^57 + 36 * q^58 - 4 * q^60 + 22 * q^62 - 40 * q^63 - 16 * q^64 + 16 * q^65 + 10 * q^66 - 28 * q^68 + 28 * q^70 - 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 + 44 * q^76 - 8 * q^78 + 16 * q^79 - 56 * q^80 - 6 * q^81 - 4 * q^82 - 52 * q^84 - 20 * q^86 + 32 * q^87 - 12 * q^88 - 4 * q^89 - 36 * q^90 - 36 * q^92 + 24 * q^95 + 60 * q^96 - 20 * q^97 + 24 * q^98

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