LMFDB - Embedded newform 88.2.c.a.45.9

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			45.9
Root			$-0.329042 - 1.37540i$ of defining polynomial
Character	$\chi$	$=$	88.45
Dual form			88.2.c.a.45.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23417 - 0.690521i) q^{2} +1.81026i q^{3} +(1.04636 - 1.70444i) q^{4} +0.282461i q^{5} +(1.25002 + 2.23417i) q^{6} -3.84939 q^{7} +(0.114433 - 2.82611i) q^{8} -0.277041 q^{9} +O(q^{10})$	\(q+(1.23417 - 0.690521i) q^{2} +1.81026i q^{3} +(1.04636 - 1.70444i) q^{4} +0.282461i q^{5} +(1.25002 + 2.23417i) q^{6} -3.84939 q^{7} +(0.114433 - 2.82611i) q^{8} -0.277041 q^{9} +(0.195045 + 0.348605i) q^{10} -1.00000i q^{11} +(3.08549 + 1.89418i) q^{12} -1.84939i q^{13} +(-4.75080 + 2.65808i) q^{14} -0.511328 q^{15} +(-1.81026 - 3.56693i) q^{16} -3.65222 q^{17} +(-0.341916 + 0.191303i) q^{18} +5.16555i q^{19} +(0.481439 + 0.295556i) q^{20} -6.96839i q^{21} +(-0.690521 - 1.23417i) q^{22} -2.05359 q^{23} +(5.11600 + 0.207154i) q^{24} +4.92022 q^{25} +(-1.27704 - 2.28246i) q^{26} +4.92926i q^{27} +(-4.02785 + 6.56106i) q^{28} +6.07825i q^{29} +(-0.631066 + 0.353083i) q^{30} +8.87137 q^{31} +(-4.69721 - 3.15218i) q^{32} +1.81026 q^{33} +(-4.50747 + 2.52194i) q^{34} -1.08730i q^{35} +(-0.289885 + 0.472201i) q^{36} -7.90298i q^{37} +(3.56693 + 6.37518i) q^{38} +3.34787 q^{39} +(0.798266 + 0.0323229i) q^{40} -0.426031 q^{41} +(-4.81182 - 8.60019i) q^{42} -11.3827i q^{43} +(-1.70444 - 1.04636i) q^{44} -0.0782532i q^{45} +(-2.53449 + 1.41805i) q^{46} -1.11900 q^{47} +(6.45706 - 3.27704i) q^{48} +7.81778 q^{49} +(6.07239 - 3.39751i) q^{50} -6.61147i q^{51} +(-3.15218 - 1.93512i) q^{52} +8.99238i q^{53} +(3.40376 + 6.08356i) q^{54} +0.282461 q^{55} +(-0.440498 + 10.8788i) q^{56} -9.35100 q^{57} +(4.19716 + 7.50161i) q^{58} -0.929264i q^{59} +(-0.535033 + 0.871529i) q^{60} +9.62052i q^{61} +(10.9488 - 6.12587i) q^{62} +1.06644 q^{63} +(-7.97381 - 0.646803i) q^{64} +0.522379 q^{65} +(2.23417 - 1.25002i) q^{66} -0.364342i q^{67} +(-3.82154 + 6.22501i) q^{68} -3.71754i q^{69} +(-0.750805 - 1.34192i) q^{70} -6.86053 q^{71} +(-0.0317027 + 0.782949i) q^{72} +9.84167 q^{73} +(-5.45718 - 9.75364i) q^{74} +8.90687i q^{75} +(8.80440 + 5.40503i) q^{76} +3.84939i q^{77} +(4.13185 - 2.31178i) q^{78} +2.06741 q^{79} +(1.00752 - 0.511328i) q^{80} -9.75437 q^{81} +(-0.525795 + 0.294183i) q^{82} -13.9516i q^{83} +(-11.8772 - 7.29145i) q^{84} -1.03161i q^{85} +(-7.86000 - 14.0482i) q^{86} -11.0032 q^{87} +(-2.82611 - 0.114433i) q^{88} -16.7818 q^{89} +(-0.0540355 - 0.0965779i) q^{90} +7.11900i q^{91} +(-2.14880 + 3.50024i) q^{92} +16.0595i q^{93} +(-1.38104 + 0.772696i) q^{94} -1.45907 q^{95} +(5.70626 - 8.50317i) q^{96} -11.6081 q^{97} +(9.64848 - 5.39834i) q^{98} +0.277041i 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 $

$2$	1.23417	−	0.690521i	0.872691	−	0.488272i
$2$	1.23417	−	0.690521i	0.872691	−	0.488272i
$3$			1.81026i			1.04515i	0.852592	+	0.522577i	$0.175029\pi$
$3$			1.81026i			1.04515i	−0.852592	+	0.522577i	$0.824971\pi$
$4$	1.04636	−	1.70444i	0.523180	−	0.852222i
$5$			0.282461i			0.126320i	0.998003	+	0.0631602i	$0.0201179\pi$
$5$			0.282461i			0.126320i	−0.998003	+	0.0631602i	$0.979882\pi$
$6$	1.25002	+	2.23417i	0.510320	+	0.912097i
$7$	−3.84939			−1.45493			−0.727466	−	0.686144i	$-0.759302\pi$
$7$	−3.84939			−1.45493			−0.727466	+	0.686144i	$0.759302\pi$
$8$	0.114433	−	2.82611i	0.0404583	−	0.999181i
$9$	−0.277041			−0.0923470
$10$	0.195045	+	0.348605i	0.0616787	+	0.110239i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	3.08549	+	1.89418i	0.890703	+	0.546804i
$13$		−	1.84939i		−	0.512928i	−0.966554	−	0.256464i	$-0.917443\pi$
$13$		−	1.84939i		−	0.512928i	0.966554	−	0.256464i	$-0.0825574\pi$
$14$	−4.75080	+	2.65808i	−1.26971	+	0.710403i
$15$	−0.511328			−0.132024
$16$	−1.81026	−	3.56693i	−0.452565	−	0.891731i
$17$	−3.65222			−0.885794			−0.442897	−	0.896572i	$-0.646049\pi$
$17$	−3.65222			−0.885794			−0.442897	+	0.896572i	$0.646049\pi$
$18$	−0.341916	+	0.191303i	−0.0805904	+	0.0450905i
$19$			5.16555i			1.18506i	0.805549	+	0.592530i	$0.201871\pi$
$19$			5.16555i			1.18506i	−0.805549	+	0.592530i	$0.798129\pi$
$20$	0.481439	+	0.295556i	0.107653	+	0.0660883i
$21$		−	6.96839i		−	1.52063i
$22$	−0.690521	−	1.23417i	−0.147220	−	0.263126i
$23$	−2.05359			−0.428204			−0.214102	−	0.976811i	$-0.568682\pi$
$23$	−2.05359			−0.428204			−0.214102	+	0.976811i	$0.568682\pi$
$24$	5.11600	+	0.207154i	1.04430	+	0.0422852i
$25$	4.92022			0.984043
$26$	−1.27704	−	2.28246i	−0.250448	−	0.447627i
$27$			4.92926i			0.948637i
$28$	−4.02785	+	6.56106i	−0.761191	+	1.23992i
$29$			6.07825i			1.12870i	0.825535	+	0.564352i	$0.190874\pi$
$29$			6.07825i			1.12870i	−0.825535	+	0.564352i	$0.809126\pi$
$30$	−0.631066	+	0.353083i	−0.115216	+	0.0644638i
$31$	8.87137			1.59335			0.796673	−	0.604411i	$-0.206592\pi$
$31$	8.87137			1.59335			0.796673	+	0.604411i	$0.206592\pi$
$32$	−4.69721	−	3.15218i	−0.830357	−	0.557231i
$33$	1.81026			0.315126
$34$	−4.50747	+	2.52194i	−0.773025	+	0.432509i
$35$		−	1.08730i		−	0.183787i
$36$	−0.289885	+	0.472201i	−0.0483141	+	0.0787002i
$37$		−	7.90298i		−	1.29924i	−0.760258	−	0.649621i	$-0.774928\pi$
$37$		−	7.90298i		−	1.29924i	0.760258	−	0.649621i	$-0.225072\pi$
$38$	3.56693	+	6.37518i	0.578632	+	1.03419i
$39$	3.34787			0.536088
$40$	0.798266	+	0.0323229i	0.126217	+	0.00511071i
$41$	−0.426031			−0.0665348			−0.0332674	−	0.999446i	$-0.510591\pi$
$41$	−0.426031			−0.0665348			−0.0332674	+	0.999446i	$0.510591\pi$
$42$	−4.81182	−	8.60019i	−0.742480	−	1.32704i
$43$		−	11.3827i		−	1.73585i	−0.496699	−	0.867923i	$-0.665455\pi$
$43$		−	11.3827i		−	1.73585i	0.496699	−	0.867923i	$-0.334545\pi$
$44$	−1.70444	−	1.04636i	−0.256955	−	0.157745i
$45$		−	0.0782532i		−	0.0116653i
$46$	−2.53449	+	1.41805i	−0.373690	+	0.209080i
$47$	−1.11900			−0.163223			−0.0816117	−	0.996664i	$-0.526007\pi$
$47$	−1.11900			−0.163223			−0.0816117	+	0.996664i	$0.526007\pi$
$48$	6.45706	−	3.27704i	0.931997	−	0.473000i
$49$	7.81778			1.11683
$50$	6.07239	−	3.39751i	0.858766	−	0.480481i
$51$		−	6.61147i		−	0.925791i
$52$	−3.15218	−	1.93512i	−0.437128	−	0.268354i
$53$			8.99238i			1.23520i	0.786493	+	0.617599i	$0.211895\pi$
$53$			8.99238i			1.23520i	−0.786493	+	0.617599i	$0.788105\pi$
$54$	3.40376	+	6.08356i	0.463193	+	0.827867i
$55$	0.282461			0.0380870
$56$	−0.440498	+	10.8788i	−0.0588640	+	1.45374i
$57$	−9.35100			−1.23857
$58$	4.19716	+	7.50161i	0.551115	+	0.985010i
$59$		−	0.929264i		−	0.120980i	−0.998169	−	0.0604899i	$-0.980734\pi$
$59$		−	0.929264i		−	0.120980i	0.998169	−	0.0604899i	$-0.0192663\pi$
$60$	−0.535033	+	0.871529i	−0.0690724	+	0.112514i
$61$			9.62052i			1.23178i	0.787832	+	0.615891i	$0.211204\pi$
$61$			9.62052i			1.23178i	−0.787832	+	0.615891i	$0.788796\pi$
$62$	10.9488	−	6.12587i	1.39050	−	0.777986i
$63$	1.06644			0.134359
$64$	−7.97381	−	0.646803i	−0.996726	−	0.0808503i
$65$	0.522379			0.0647932
$66$	2.23417	−	1.25002i	0.275008	−	0.153867i
$67$		−	0.364342i		−	0.0445114i	−0.999752	−	0.0222557i	$-0.992915\pi$
$67$		−	0.364342i		−	0.0445114i	0.999752	−	0.0222557i	$-0.00708480\pi$
$68$	−3.82154	+	6.22501i	−0.463430	+	0.754893i
$69$		−	3.71754i		−	0.447539i
$70$	−0.750805	−	1.34192i	−0.0897383	−	0.160390i
$71$	−6.86053			−0.814195			−0.407098	−	0.913385i	$-0.633459\pi$
$71$	−6.86053			−0.814195			−0.407098	+	0.913385i	$0.633459\pi$
$72$	−0.0317027	+	0.782949i	−0.00373620	+	0.0922714i
$73$	9.84167			1.15188			0.575940	−	0.817492i	$-0.304636\pi$
$73$	9.84167			1.15188			0.575940	+	0.817492i	$0.304636\pi$
$74$	−5.45718	−	9.75364i	−0.634384	−	1.13384i
$75$			8.90687i			1.02848i
$76$	8.80440	+	5.40503i	1.00993	+	0.620000i
$77$			3.84939i			0.438678i
$78$	4.13185	−	2.31178i	0.467840	−	0.261757i
$79$	2.06741			0.232602			0.116301	−	0.993214i	$-0.462896\pi$
$79$	2.06741			0.232602			0.116301	+	0.993214i	$0.462896\pi$
$80$	1.00752	−	0.511328i	0.112644	−	0.0571682i
$81$	−9.75437			−1.08382
$82$	−0.525795	+	0.294183i	−0.0580643	+	0.0324871i
$83$		−	13.9516i		−	1.53139i	−0.643204	−	0.765695i	$-0.722395\pi$
$83$		−	13.9516i		−	1.53139i	0.643204	−	0.765695i	$-0.277605\pi$
$84$	−11.8772	−	7.29145i	−1.29591	−	0.795562i
$85$		−	1.03161i		−	0.111894i
$86$	−7.86000	−	14.0482i	−0.847565	−	1.51486i
$87$	−11.0032			−1.17967
$88$	−2.82611	−	0.114433i	−0.301264	−	0.0121986i
$89$	−16.7818			−1.77886			−0.889432	−	0.457067i	$-0.848900\pi$
$89$	−16.7818			−1.77886			−0.889432	+	0.457067i	$0.848900\pi$
$90$	−0.0540355	−	0.0965779i	−0.00569584	−	0.0101802i
$91$			7.11900i			0.746274i
$92$	−2.14880	+	3.50024i	−0.224028	+	0.364925i
$93$			16.0595i			1.66529i
$94$	−1.38104	+	0.772696i	−0.142444	+	0.0796975i
$95$	−1.45907			−0.149697
$96$	5.70626	−	8.50317i	0.582393	−	0.867851i
$97$	−11.6081			−1.17863			−0.589314	−	0.807904i	$-0.700602\pi$
$97$	−11.6081			−1.17863			−0.589314	+	0.807904i	$0.700602\pi$
$98$	9.64848	−	5.39834i	0.974644	−	0.545315i
$99$			0.277041i			0.0278437i
$100$	5.14832	−	8.38623i	0.514832	−	0.838623i
$101$		−	3.17327i		−	0.315752i	−0.987459	−	0.157876i	$-0.949535\pi$
$101$		−	3.17327i		−	0.315752i	0.987459	−	0.157876i	$-0.0504646\pi$
$102$	−4.56536	−	8.15969i	−0.452038	−	0.807930i
$103$	5.69877			0.561517			0.280758	−	0.959778i	$-0.409414\pi$
$103$	5.69877			0.561517			0.280758	+	0.959778i	$0.409414\pi$
$104$	−5.22657	−	0.211631i	−0.512508	−	0.0207522i
$105$	1.96830			0.192086
$106$	6.20943	+	11.0981i	0.603113	+	1.07795i
$107$			2.21714i			0.214339i	0.994241	+	0.107170i	$0.0341788\pi$
$107$			2.21714i			0.214339i	−0.994241	+	0.107170i	$0.965821\pi$
$108$	8.40165	+	5.15779i	0.808450	+	0.496308i
$109$		−	0.360043i		−	0.0344859i	−0.999851	−	0.0172429i	$-0.994511\pi$
$109$		−	0.360043i		−	0.0344859i	0.999851	−	0.0172429i	$-0.00548887\pi$
$110$	0.348605	−	0.195045i	0.0332382	−	0.0185968i
$111$	14.3064			1.35791
$112$	6.96839	+	13.7305i	0.658451	+	1.29741i
$113$	−6.87947			−0.647166			−0.323583	−	0.946200i	$-0.604887\pi$
$113$	−6.87947			−0.647166			−0.323583	+	0.946200i	$0.604887\pi$
$114$	−11.5407	+	6.45706i	−1.08089	+	0.604759i
$115$		−	0.580060i		−	0.0540909i
$116$	10.3600	+	6.36004i	0.961906	+	0.590515i
$117$			0.512356i			0.0473673i
$118$	−0.641676	−	1.14687i	−0.0590711	−	0.105578i
$119$	14.0588			1.28877
$120$	−0.0585129	+	1.44507i	−0.00534147	+	0.131916i
$121$	−1.00000			−0.0909091
$122$	6.64317	+	11.8734i	0.601445	+	1.07496i
$123$		−	0.771226i		−	0.0695391i
$124$	9.28265	−	15.1208i	0.833607	−	1.35788i
$125$			2.80207i			0.250625i
$126$	1.31617	−	0.736398i	0.117254	−	0.0656036i
$127$	−14.5889			−1.29456			−0.647278	−	0.762254i	$-0.724093\pi$
$127$	−14.5889			−1.29456			−0.647278	+	0.762254i	$0.724093\pi$
$128$	−10.2877	+	4.70782i	−0.909311	+	0.416116i
$129$	20.6056			1.81423
$130$	0.644706	−	0.360714i	0.0565444	−	0.0316367i
$131$		−	1.48163i		−	0.129451i	−0.997903	−	0.0647253i	$-0.979383\pi$
$131$		−	1.48163i		−	0.129451i	0.997903	−	0.0647253i	$-0.0206171\pi$
$132$	1.89418	−	3.08549i	0.164868	−	0.268557i
$133$		−	19.8842i		−	1.72418i
$134$	−0.251586	−	0.449661i	−0.0217337	−	0.0388448i
$135$	−1.39232			−0.119832
$136$	−0.417936	+	10.3216i	−0.0358377	+	0.885069i
$137$	15.3359			1.31023			0.655115	−	0.755529i	$-0.272620\pi$
$137$	15.3359			1.31023			0.655115	+	0.755529i	$0.272620\pi$
$138$	−2.56704	−	4.58808i	−0.218521	−	0.390563i
$139$		−	8.43687i		−	0.715606i	−0.933797	−	0.357803i	$-0.883526\pi$
$139$		−	8.43687i		−	0.715606i	0.933797	−	0.357803i	$-0.116474\pi$
$140$	−1.85324	−	1.13771i	−0.156628	−	0.0961539i
$141$		−	2.02569i		−	0.170594i
$142$	−8.46707	+	4.73734i	−0.710541	+	0.397549i
$143$	−1.84939			−0.154653
$144$	0.501516	+	0.988185i	0.0417930	+	0.0823487i
$145$	−1.71687			−0.142578
$146$	12.1463	−	6.79589i	1.00524	−	0.562431i
$147$			14.1522i			1.16725i
$148$	−13.4702	−	8.26937i	−1.10724	−	0.679738i
$149$		−	19.8299i		−	1.62453i	−0.583287	−	0.812266i	$-0.698234\pi$
$149$		−	19.8299i		−	1.62453i	0.583287	−	0.812266i	$-0.301766\pi$
$150$	6.15038	+	10.9926i	0.502177	+	0.897543i
$151$	12.9141			1.05094			0.525468	−	0.850813i	$-0.323890\pi$
$151$	12.9141			1.05094			0.525468	+	0.850813i	$0.323890\pi$
$152$	14.5984	+	0.591112i	1.18409	+	0.0479455i
$153$	1.01182			0.0818004
$154$	2.65808	+	4.75080i	0.214194	+	0.382831i
$155$			2.50581i			0.201272i
$156$	3.50308	−	5.70626i	0.280471	−	0.456866i
$157$			4.66194i			0.372063i	0.982544	+	0.186032i	$0.0595627\pi$
$157$			4.66194i			0.372063i	−0.982544	+	0.186032i	$0.940437\pi$
$158$	2.55154	−	1.42759i	0.202990	−	0.113573i
$159$	−16.2785			−1.29097
$160$	0.890366	−	1.32678i	0.0703896	−	0.104891i
$161$	7.90508			0.623007
$162$	−12.0386	+	6.73560i	−0.945839	+	0.529199i
$163$			11.0267i			0.863675i	0.901951	+	0.431837i	$0.142135\pi$
$163$			11.0267i			0.863675i	−0.901951	+	0.431837i	$0.857865\pi$
$164$	−0.445782	+	0.726145i	−0.0348097	+	0.0567024i
$165$			0.511328i			0.0398068i
$166$	−9.63390	−	17.2187i	−0.747735	−	1.33643i
$167$	11.6553			0.901918			0.450959	−	0.892545i	$-0.351082\pi$
$167$	11.6553			0.901918			0.450959	+	0.892545i	$0.351082\pi$
$168$	−19.6934	−	0.797416i	−1.51938	−	0.0615220i
$169$	9.57977			0.736905
$170$	−0.712349	−	1.27318i	−0.0546346	−	0.0976487i
$171$		−	1.43107i		−	0.109437i
$172$	−19.4012	−	11.9104i	−1.47933	−	0.908160i
$173$			12.8178i			0.974518i	0.873258	+	0.487259i	$0.162003\pi$
$173$			12.8178i			0.974518i	−0.873258	+	0.487259i	$0.837997\pi$
$174$	−13.5799	+	7.59796i	−1.02949	+	0.576000i
$175$	−18.9398			−1.43172
$176$	−3.56693	+	1.81026i	−0.268867	+	0.136453i
$177$	1.68221			0.126443
$178$	−20.7116	+	11.5882i	−1.55240	+	0.868570i
$179$		−	2.21868i		−	0.165832i	−0.996557	−	0.0829158i	$-0.973577\pi$
$179$		−	2.21868i		−	0.165832i	0.996557	−	0.0829158i	$-0.0264232\pi$
$180$	−0.133378	−	0.0818811i	−0.00994143	−	0.00610306i
$181$		−	9.49781i		−	0.705967i	−0.935630	−	0.352983i	$-0.885167\pi$
$181$		−	9.49781i		−	0.705967i	0.935630	−	0.352983i	$-0.114833\pi$
$182$	4.91582	+	8.78607i	0.364385	+	0.651267i
$183$	−17.4156			−1.28740
$184$	−0.235000	+	5.80369i	−0.0173244	+	0.427853i
$185$	2.23228			0.164121
$186$	11.0894	+	19.8202i	0.813116	+	1.45329i
$187$			3.65222i			0.267077i
$188$	−1.17088	+	1.90728i	−0.0853953	+	0.139103i
$189$		−	18.9746i		−	1.38020i
$190$	−1.80074	+	1.00752i	−0.130639	+	0.0730930i
$191$	15.4748			1.11972			0.559858	−	0.828589i	$-0.310856\pi$
$191$	15.4748			1.11972			0.559858	+	0.828589i	$0.310856\pi$
$192$	1.17088	−	14.4347i	0.0845011	−	1.04173i
$193$	7.85853			0.565669			0.282835	−	0.959169i	$-0.408725\pi$
$193$	7.85853			0.565669			0.282835	+	0.959169i	$0.408725\pi$
$194$	−14.3265	+	8.01568i	−1.02858	+	0.575492i
$195$			0.945642i			0.0677188i
$196$	8.18021	−	13.3250i	0.584301	−	0.951783i
$197$			21.1887i			1.50963i	0.655938	+	0.754815i	$0.272273\pi$
$197$			21.1887i			1.50963i	−0.655938	+	0.754815i	$0.727727\pi$
$198$	0.191303	+	0.341916i	0.0135953	+	0.0242989i
$199$	−5.22753			−0.370570			−0.185285	−	0.982685i	$-0.559321\pi$
$199$	−5.22753			−0.370570			−0.185285	+	0.982685i	$0.559321\pi$
$200$	0.563037	−	13.9051i	0.0398127	−	0.983237i
$201$	0.659554			0.0465213
$202$	−2.19121	−	3.91636i	−0.154173	−	0.275554i
$203$		−	23.3975i		−	1.64219i
$204$	−11.2689	−	6.91798i	−0.788980	−	0.484356i
$205$		−	0.120337i		−	0.00840470i
$206$	7.03327	−	3.93512i	0.490031	−	0.274173i
$207$	0.568930			0.0395434
$208$	−6.59662	+	3.34787i	−0.457394	+	0.232133i
$209$	5.16555			0.357309
$210$	2.42922	−	1.35915i	0.167632	−	0.0937904i
$211$			6.19628i			0.426570i	0.976990	+	0.213285i	$0.0684162\pi$
$211$			6.19628i			0.426570i	−0.976990	+	0.213285i	$0.931584\pi$
$212$	15.3270	+	9.40927i	1.05266	+	0.646231i
$213$		−	12.4193i		−	0.850959i
$214$	1.53099	+	2.73634i	0.104656	+	0.187052i
$215$	3.21517			0.219273
$216$	13.9306	+	0.564072i	0.947860	+	0.0383802i
$217$	−34.1493			−2.31821
$218$	−0.248618	−	0.444355i	−0.0168385	−	0.0300955i
$219$			17.8160i			1.20389i
$220$	0.295556	−	0.481439i	0.0199264	−	0.0324586i
$221$			6.75437i			0.454348i
$222$	17.6566	−	9.87891i	1.18503	−	0.663029i
$223$	−0.622524			−0.0416873			−0.0208436	−	0.999783i	$-0.506635\pi$
$223$	−0.622524			−0.0416873			−0.0208436	+	0.999783i	$0.506635\pi$
$224$	18.0814	+	12.1339i	1.20811	+	0.810733i
$225$	−1.36310			−0.0908734
$226$	−8.49044	+	4.75042i	−0.564776	+	0.315993i
$227$			7.26190i			0.481989i	0.970526	+	0.240995i	$0.0774736\pi$
$227$			7.26190i			0.481989i	−0.970526	+	0.240995i	$0.922526\pi$
$228$	−9.78451	+	15.9383i	−0.647995	+	1.05554i
$229$		−	22.1903i		−	1.46638i	−0.680026	−	0.733188i	$-0.738031\pi$
$229$		−	22.1903i		−	1.46638i	0.680026	−	0.733188i	$-0.261969\pi$
$230$	−0.400544	−	0.715894i	−0.0264111	−	0.0472046i
$231$	−6.96839			−0.458486
$232$	17.1778	+	0.695555i	1.12778	+	0.0456654i
$233$	−4.94841			−0.324181			−0.162091	−	0.986776i	$-0.551824\pi$
$233$	−4.94841			−0.324181			−0.162091	+	0.986776i	$0.551824\pi$
$234$	0.353793	+	0.632335i	0.0231282	+	0.0413370i
$235$		−	0.316075i		−	0.0206184i
$236$	−1.58388	−	0.972345i	−0.103102	−	0.0632942i
$237$			3.74256i			0.243105i
$238$	17.3510	−	9.70791i	1.12470	−	0.629271i
$239$	−10.6761			−0.690581			−0.345290	−	0.938496i	$-0.612220\pi$
$239$	−10.6761			−0.690581			−0.345290	+	0.938496i	$0.612220\pi$
$240$	0.925636	+	1.82387i	0.0597495	+	0.117730i
$241$	7.14469			0.460230			0.230115	−	0.973163i	$-0.426090\pi$
$241$	7.14469			0.460230			0.230115	+	0.973163i	$0.426090\pi$
$242$	−1.23417	+	0.690521i	−0.0793356	+	0.0443884i
$243$		−	2.87016i		−	0.184121i
$244$	16.3976	+	10.0665i	1.04975	+	0.644444i
$245$			2.20822i			0.141078i
$246$	−0.532548	−	0.951826i	−0.0339540	−	0.0606862i
$247$	9.55311			0.607850
$248$	1.01518	−	25.0715i	0.0644640	−	1.59204i
$249$	25.2561			1.60054
$250$	1.93489	+	3.45824i	0.122373	+	0.218718i
$251$			12.9509i			0.817456i	0.912656	+	0.408728i	$0.134028\pi$
$251$			12.9509i			0.817456i	−0.912656	+	0.408728i	$0.865972\pi$
$252$	1.11588	−	1.81768i	0.0702937	−	0.114503i
$253$			2.05359i			0.129108i
$254$	−18.0052	+	10.0740i	−1.12975	+	0.632096i
$255$	1.86748			0.116946
$256$	−9.44592	+	12.9141i	−0.590370	+	0.807133i
$257$	−27.5198			−1.71664			−0.858318	−	0.513118i	$-0.828490\pi$
$257$	−27.5198			−1.71664			−0.858318	+	0.513118i	$0.828490\pi$
$258$	25.4309	−	14.2286i	1.58326	−	0.885836i
$259$			30.4216i			1.89031i
$260$	0.546597	−	0.890366i	0.0338985	−	0.0552182i
$261$		−	1.68393i		−	0.104232i
$262$	−1.02310	−	1.82858i	−0.0632071	−	0.112970i
$263$	28.4402			1.75370			0.876848	−	0.480767i	$-0.159642\pi$
$263$	28.4402			1.75370			0.876848	+	0.480767i	$0.159642\pi$
$264$	0.207154	−	5.11600i	0.0127495	−	0.314868i
$265$	−2.53999			−0.156031
$266$	−13.7305	−	24.5405i	−0.841869	−	1.50468i
$267$		−	30.3794i		−	1.85919i
$268$	−0.621000	−	0.381233i	−0.0379336	−	0.0232875i
$269$		−	9.45011i		−	0.576183i	−0.957603	−	0.288092i	$-0.906979\pi$
$269$		−	9.45011i		−	0.576183i	0.957603	−	0.288092i	$-0.0930208\pi$
$270$	−1.71837	+	0.961429i	−0.104576	+	0.0585107i
$271$	−16.2245			−0.985566			−0.492783	−	0.870152i	$-0.664020\pi$
$271$	−16.2245			−0.985566			−0.492783	+	0.870152i	$0.664020\pi$
$272$	6.61147	+	13.0272i	0.400879	+	0.789890i
$273$	−12.8872			−0.779972
$274$	18.9271	−	10.5897i	1.14343	−	0.639749i
$275$		−	4.92022i		−	0.296700i
$276$	−6.33634	−	3.88989i	−0.381403	−	0.234144i
$277$			15.2068i			0.913685i	0.889548	+	0.456843i	$0.151020\pi$
$277$			15.2068i			0.913685i	−0.889548	+	0.456843i	$0.848980\pi$
$278$	−5.82584	−	10.4125i	−0.349411	−	0.624503i
$279$	−2.45773			−0.147141
$280$	−3.07283	−	0.124423i	−0.183637	−	0.00743573i
$281$	−3.30426			−0.197116			−0.0985578	−	0.995131i	$-0.531423\pi$
$281$	−3.30426			−0.197116			−0.0985578	+	0.995131i	$0.531423\pi$
$282$	−1.39878	−	2.50005i	−0.0832962	−	0.148876i
$283$			7.41297i			0.440656i	0.975426	+	0.220328i	$0.0707127\pi$
$283$			7.41297i			0.440656i	−0.975426	+	0.220328i	$0.929287\pi$
$284$	−7.17859	+	11.6934i	−0.425971	+	0.693875i
$285$		−	2.64129i		−	0.156457i
$286$	−2.28246	+	1.27704i	−0.134965	+	0.0755130i
$287$	1.63996			0.0968036
$288$	1.30132	+	0.873282i	0.0766810	+	0.0514586i
$289$	−3.66127			−0.215369
$290$	−2.11891	+	1.18553i	−0.124427	+	0.0696170i
$291$		−	21.0138i		−	1.23185i
$292$	10.2979	−	16.7746i	0.602641	−	0.981658i
$293$			30.0539i			1.75577i	0.478875	+	0.877883i	$0.341045\pi$
$293$			30.0539i			1.75577i	−0.478875	+	0.877883i	$0.658955\pi$
$294$	9.77240	+	17.4663i	0.569938	+	1.01865i
$295$	0.262481			0.0152822
$296$	−22.3347	−	0.904365i	−1.29818	−	0.0525651i
$297$	4.92926			0.286025
$298$	−13.6930	−	24.4736i	−0.793214	−	1.41772i
$299$			3.79789i			0.219638i
$300$	15.1813	+	9.31980i	0.876491	+	0.538079i
$301$			43.8164i			2.52554i
$302$	15.9383	−	8.91748i	0.917143	−	0.513143i
$303$	5.74444			0.330010
$304$	18.4251	−	9.35100i	1.05675	−	0.536316i
$305$	−2.71742			−0.155599
$306$	1.24875	−	0.698680i	0.0713865	−	0.0399409i
$307$		−	8.33694i		−	0.475814i	−0.971288	−	0.237907i	$-0.923539\pi$
$307$		−	8.33694i		−	0.475814i	0.971288	−	0.237907i	$-0.0764614\pi$
$308$	6.56106	+	4.02785i	0.373851	+	0.229508i
$309$			10.3163i			0.586872i
$310$	1.73032	+	3.09261i	0.0982755	+	0.175648i
$311$	1.27551			0.0723275			0.0361638	−	0.999346i	$-0.488486\pi$
$311$	1.27551			0.0723275			0.0361638	+	0.999346i	$0.488486\pi$
$312$	0.383108	−	9.46145i	0.0216892	−	0.535649i
$313$	−6.40688			−0.362139			−0.181069	−	0.983470i	$-0.557956\pi$
$313$	−6.40688			−0.362139			−0.181069	+	0.983470i	$0.557956\pi$
$314$	3.21917	+	5.75364i	0.181668	+	0.324696i
$315$			0.301227i			0.0169722i
$316$	2.16326	−	3.52379i	0.121693	−	0.198229i
$317$		−	19.1440i		−	1.07524i	−0.843189	−	0.537618i	$-0.819324\pi$
$317$		−	19.1440i		−	1.07524i	0.843189	−	0.537618i	$-0.180676\pi$
$318$	−20.0905	+	11.2407i	−1.12662	+	0.630346i
$319$	6.07825			0.340317
$320$	0.182696	−	2.25229i	0.0102130	−	0.125907i
$321$	−4.01361			−0.224018
$322$	9.75622	−	5.45863i	0.543693	−	0.304197i
$323$		−	18.8658i		−	1.04972i
$324$	−10.2066	+	16.6258i	−0.567033	+	0.923655i
$325$		−	9.09938i		−	0.504743i
$326$	7.61415	+	13.6088i	0.421709	+	0.753722i
$327$	0.651772			0.0360431
$328$	−0.0487521	+	1.20401i	−0.00269189	+	0.0664803i
$329$	4.30748			0.237479
$330$	0.353083	+	0.631066i	0.0194366	+	0.0347390i
$331$		−	5.71716i		−	0.314243i	−0.987579	−	0.157122i	$-0.949778\pi$
$331$		−	5.71716i		−	0.314243i	0.987579	−	0.157122i	$-0.0502215\pi$
$332$	−23.7798	−	14.5984i	−1.30508	−	0.801193i
$333$			2.18945i			0.119981i
$334$	14.3847	−	8.04827i	0.787096	−	0.440382i
$335$	0.102912			0.00562270
$336$	−24.8557	+	12.6146i	−1.35599	+	0.688183i
$337$	−3.00179			−0.163518			−0.0817590	−	0.996652i	$-0.526054\pi$
$337$	−3.00179			−0.163518			−0.0817590	+	0.996652i	$0.526054\pi$
$338$	11.8231	−	6.61504i	0.643091	−	0.359811i
$339$		−	12.4536i		−	0.676388i
$340$	−1.75832	−	1.07944i	−0.0953584	−	0.0585406i
$341$		−	8.87137i		−	0.480412i
$342$	−0.988185	−	1.76619i	−0.0534349	−	0.0955044i
$343$	−3.14794			−0.169973
$344$	−32.1688	−	1.30256i	−1.73442	−	0.0702293i
$345$	1.05006			0.0565333
$346$	8.85095	+	15.8193i	0.475830	+	0.850453i
$347$			2.00583i			0.107679i	0.998550	+	0.0538393i	$0.0171459\pi$
$347$			2.00583i			0.107679i	−0.998550	+	0.0538393i	$0.982854\pi$
$348$	−11.5133	+	18.7544i	−0.617179	+	1.00534i
$349$		−	6.57081i		−	0.351728i	−0.984415	−	0.175864i	$-0.943728\pi$
$349$		−	6.57081i		−	0.351728i	0.984415	−	0.175864i	$-0.0562718\pi$
$350$	−23.3750	+	13.0783i	−1.24945	+	0.699067i
$351$	9.11611			0.486582
$352$	−3.15218	+	4.69721i	−0.168012	+	0.250362i
$353$	18.9126			1.00662			0.503308	−	0.864107i	$-0.332116\pi$
$353$	18.9126			1.00662			0.503308	+	0.864107i	$0.332116\pi$
$354$	2.07613	−	1.16160i	0.110345	−	0.0617384i
$355$		−	1.93783i		−	0.102849i
$356$	−17.5598	+	28.6036i	−0.930667	+	1.51599i
$357$			25.4501i			1.34696i
$358$	−1.53204	−	2.73823i	−0.0809710	−	0.144720i
$359$	−17.3298			−0.914631			−0.457315	−	0.889305i	$-0.651189\pi$
$359$	−17.3298			−0.914631			−0.457315	+	0.889305i	$0.651189\pi$
$360$	−0.221152	−	0.00895478i	−0.0116558	−	0.000471958i
$361$	−7.68295			−0.404366
$362$	−6.55844	−	11.7219i	−0.344704	−	0.616091i
$363$		−	1.81026i		−	0.0950140i
$364$	12.1339	+	7.44904i	0.635991	+	0.390436i
$365$			2.77989i			0.145506i
$366$	−21.4939	+	12.0259i	−1.12350	+	0.628602i
$367$	−5.55284			−0.289856			−0.144928	−	0.989442i	$-0.546295\pi$
$367$	−5.55284			−0.289856			−0.144928	+	0.989442i	$0.546295\pi$
$368$	3.71754	+	7.32502i	0.193790	+	0.381843i
$369$	0.118028			0.00614429
$370$	2.75502	−	1.54144i	0.143227	−	0.0801356i
$371$		−	34.6151i		−	1.79713i
$372$	27.3725	+	16.8040i	1.41920	+	0.871247i
$373$			13.2690i			0.687045i	0.939145	+	0.343522i	$0.111620\pi$
$373$			13.2690i			0.687045i	−0.939145	+	0.343522i	$0.888380\pi$
$374$	2.52194	+	4.50747i	0.130406	+	0.233076i
$375$	−5.07248			−0.261942
$376$	−0.128051	+	3.16243i	−0.00660374	+	0.163090i
$377$	11.2410			0.578943
$378$	−13.1024	−	23.4180i	−0.673915	−	1.20449i
$379$			7.75769i			0.398486i	0.979950	+	0.199243i	$0.0638483\pi$
$379$			7.75769i			0.398486i	−0.979950	+	0.199243i	$0.936152\pi$
$380$	−1.52671	+	2.48690i	−0.0783185	+	0.127575i
$381$		−	26.4097i		−	1.35301i
$382$	19.0985	−	10.6857i	0.977166	−	0.546726i
$383$	−10.4589			−0.534427			−0.267214	−	0.963637i	$-0.586103\pi$
$383$	−10.4589			−0.534427			−0.267214	+	0.963637i	$0.586103\pi$
$384$	−8.52238	−	18.6234i	−0.434906	−	0.950370i
$385$	−1.08730			−0.0554140
$386$	9.69877	−	5.42648i	0.493655	−	0.276201i
$387$			3.15347i			0.160300i
$388$	−12.1463	+	19.7854i	−0.616635	+	1.00445i
$389$		−	29.0722i		−	1.47402i	−0.675882	−	0.737010i	$-0.736237\pi$
$389$		−	29.0722i		−	1.47402i	0.675882	−	0.737010i	$-0.263763\pi$
$390$	0.652986	+	1.16709i	0.0330652	+	0.0590976i
$391$	7.50018			0.379301
$392$	0.894614	−	22.0939i	0.0451848	−	1.11591i
$393$	2.68213			0.135296
$394$	14.6312	+	26.1504i	0.737110	+	1.31744i
$395$			0.583963i			0.0293824i
$396$	0.472201	+	0.289885i	0.0237290	+	0.0145673i
$397$			4.83587i			0.242705i	0.992609	+	0.121353i	$0.0387232\pi$
$397$			4.83587i			0.242705i	−0.992609	+	0.121353i	$0.961277\pi$
$398$	−6.45167	+	3.60972i	−0.323393	+	0.180939i
$399$	35.9956			1.80203
$400$	−8.90687	−	17.5500i	−0.445343	−	0.877502i
$401$	0.510299			0.0254831			0.0127416	−	0.999919i	$-0.495944\pi$
$401$	0.510299			0.0254831			0.0127416	+	0.999919i	$0.495944\pi$
$402$	0.814002	−	0.455436i	0.0405988	−	0.0227151i
$403$		−	16.4066i		−	0.817271i
$404$	−5.40866	−	3.32038i	−0.269091	−	0.165195i
$405$		−	2.75523i		−	0.136908i
$406$	−16.1565	−	28.8766i	−0.801834	−	1.43312i
$407$	−7.90298			−0.391736
$408$	−18.6848	−	0.756573i	−0.925033	−	0.0374559i
$409$	2.75896			0.136422			0.0682109	−	0.997671i	$-0.478271\pi$
$409$	2.75896			0.136422			0.0682109	+	0.997671i	$0.478271\pi$
$410$	−0.0830953	−	0.148517i	−0.00410378	−	0.00733471i
$411$			27.7619i			1.36939i
$412$	5.96297	−	9.71324i	0.293774	−	0.478537i
$413$			3.57709i			0.176017i
$414$	0.702157	−	0.392858i	0.0345091	−	0.0193079i
$415$	3.94079			0.193446
$416$	−5.82959	+	8.68696i	−0.285819	+	0.425913i
$417$	15.2729			0.747919
$418$	6.37518	−	3.56693i	0.311820	−	0.174464i
$419$			28.9400i			1.41381i	0.707308	+	0.706906i	$0.249910\pi$
$419$			28.9400i			1.41381i	−0.707308	+	0.706906i	$0.750090\pi$
$420$	2.05955	−	3.35485i	0.100496	−	0.163700i
$421$			18.1439i			0.884280i	0.896946	+	0.442140i	$0.145780\pi$
$421$			18.1439i			0.884280i	−0.896946	+	0.442140i	$0.854220\pi$
$422$	4.27866	+	7.64728i	0.208282	+	0.372264i
$423$	0.310010			0.0150732
$424$	25.4135	+	1.02903i	1.23419	+	0.0499740i
$425$	−17.9697			−0.871660
$426$	−8.57582	−	15.3276i	−0.415500	−	0.742625i
$427$		−	37.0331i		−	1.79216i
$428$	3.77900	+	2.31993i	0.182665	+	0.112138i
$429$		−	3.34787i		−	0.161637i
$430$	3.96807	−	2.22014i	0.191357	−	0.107065i
$431$	13.3501			0.643052			0.321526	−	0.946901i	$-0.395804\pi$
$431$	13.3501			0.643052			0.321526	+	0.946901i	$0.395804\pi$
$432$	17.5823	−	8.92325i	0.845930	−	0.429320i
$433$	12.4023			0.596016			0.298008	−	0.954563i	$-0.403678\pi$
$433$	12.4023			0.596016			0.298008	+	0.954563i	$0.403678\pi$
$434$	−42.1461	+	23.5808i	−2.02308	+	1.13192i
$435$		−	3.10798i		−	0.149016i
$436$	−0.613674	−	0.376735i	−0.0293896	−	0.0180423i
$437$		−	10.6080i		−	0.507447i
$438$	12.3023	+	21.9880i	0.587828	+	1.05063i
$439$	6.69021			0.319306			0.159653	−	0.987173i	$-0.448962\pi$
$439$	6.69021			0.319306			0.159653	+	0.987173i	$0.448962\pi$
$440$	0.0323229	−	0.798266i	0.00154094	−	0.0380558i
$441$	−2.16584			−0.103135
$442$	4.66404	+	8.33605i	0.221846	+	0.396506i
$443$			17.0858i			0.811769i	0.913924	+	0.405885i	$0.133037\pi$
$443$			17.0858i			0.811769i	−0.913924	+	0.405885i	$0.866963\pi$
$444$	14.9697	−	24.3845i	0.710431	−	1.15724i
$445$		−	4.74019i		−	0.224707i
$446$	−0.768301	+	0.429866i	−0.0363801	+	0.0203547i
$447$	35.8974			1.69789
$448$	30.6943	+	2.48979i	1.45017	+	0.117632i
$449$	1.66411			0.0785344			0.0392672	−	0.999229i	$-0.487498\pi$
$449$	1.66411			0.0785344			0.0392672	+	0.999229i	$0.487498\pi$
$450$	−1.68230	+	0.941251i	−0.0793045	+	0.0443710i
$451$			0.426031i			0.0200610i
$452$	−7.19840	+	11.7257i	−0.338584	+	0.551529i
$453$			23.3779i			1.09839i
$454$	5.01450	+	8.96244i	0.235342	+	0.420628i
$455$	−2.01084			−0.0942696
$456$	−1.07007	+	26.4270i	−0.0501104	+	1.23756i
$457$	22.4491			1.05013			0.525063	−	0.851063i	$-0.324042\pi$
$457$	22.4491			1.05013			0.525063	+	0.851063i	$0.324042\pi$
$458$	−15.3229	−	27.3867i	−0.715991	−	1.27969i
$459$		−	18.0028i		−	0.840297i
$460$	−0.988680	−	0.606952i	−0.0460974	−	0.0282993i
$461$		−	12.0546i		−	0.561440i	−0.959790	−	0.280720i	$-0.909427\pi$
$461$		−	12.0546i		−	0.561440i	0.959790	−	0.280720i	$-0.0905732\pi$
$462$	−8.60019	+	4.81182i	−0.400117	+	0.223866i
$463$	41.5732			1.93207			0.966035	−	0.258412i	$-0.0831994\pi$
$463$	41.5732			1.93207			0.966035	+	0.258412i	$0.0831994\pi$
$464$	21.6807	−	11.0032i	1.00650	−	0.510812i
$465$	−4.53618			−0.210360
$466$	−6.10719	+	3.41698i	−0.282910	+	0.158289i
$467$			38.8089i			1.79586i	0.440137	+	0.897931i	$0.354930\pi$
$467$			38.8089i			1.79586i	−0.440137	+	0.897931i	$0.645070\pi$
$468$	0.873282	+	0.536109i	0.0403675	+	0.0247816i
$469$			1.40249i			0.0647611i
$470$	−0.218256	−	0.390090i	−0.0100674	−	0.0179935i
$471$	−8.43932			−0.388864
$472$	−2.62620	−	0.106339i	−0.120881	−	0.00489464i
$473$	−11.3827			−0.523377
$474$	2.58431	+	4.61896i	0.118702	+	0.212156i
$475$			25.4156i			1.16615i
$476$	14.7106	−	23.9625i	0.674259	−	1.09832i
$477$		−	2.49126i		−	0.114067i
$478$	−13.1762	+	7.37209i	−0.602664	+	0.337191i
$479$	−31.4627			−1.43757			−0.718783	−	0.695235i	$-0.755300\pi$
$479$	−31.4627			−1.43757			−0.718783	+	0.695235i	$0.755300\pi$
$480$	2.40181	+	1.61179i	0.109627	+	0.0735680i
$481$	−14.6157			−0.666417
$482$	8.81778	−	4.93356i	0.401639	−	0.224718i
$483$			14.3102i			0.651139i
$484$	−1.04636	+	1.70444i	−0.0475618	+	0.0774747i
$485$		−	3.27885i		−	0.148885i
$486$	−1.98190	−	3.54227i	−0.0899010	−	0.160680i
$487$	−35.0718			−1.58926			−0.794629	−	0.607096i	$-0.792334\pi$
$487$	−35.0718			−1.58926			−0.794629	+	0.607096i	$0.792334\pi$
$488$	27.1887	+	1.10091i	1.23077	+	0.0498358i
$489$	−19.9611			−0.902673
$490$	1.52482	+	2.72532i	0.0688844	+	0.123117i
$491$			16.5274i			0.745871i	0.927857	+	0.372935i	$0.121649\pi$
$491$			16.5274i			0.745871i	−0.927857	+	0.372935i	$0.878351\pi$
$492$	−1.31451	−	0.806981i	−0.0592628	−	0.0363815i
$493$		−	22.1991i		−	0.999799i
$494$	11.7902	−	6.59662i	0.530465	−	0.296796i
$495$	−0.0782532			−0.00351722
$496$	−16.0595	−	31.6435i	−0.721092	−	1.42084i
$497$	26.4088			1.18460
$498$	31.1703	−	17.4399i	1.39678	−	0.781499i
$499$		−	16.9371i		−	0.758211i	−0.925353	−	0.379105i	$-0.876232\pi$
$499$		−	16.9371i		−	0.758211i	0.925353	−	0.379105i	$-0.123768\pi$
$500$	4.77598	+	2.93198i	0.213588	+	0.131122i
$501$			21.0992i			0.942643i
$502$	8.94290	+	15.9837i	0.399141	+	0.713387i
$503$	−16.3751			−0.730129			−0.365064	−	0.930982i	$-0.618953\pi$
$503$	−16.3751			−0.730129			−0.365064	+	0.930982i	$0.618953\pi$
$504$	0.122036	−	3.01387i	0.00543592	−	0.134249i
$505$	0.896324			0.0398859
$506$	1.41805	+	2.53449i	0.0630400	+	0.112672i
$507$			17.3419i			0.770180i
$508$	−15.2653	+	24.8660i	−0.677286	+	1.10325i
$509$		−	29.3045i		−	1.29890i	−0.760404	−	0.649450i	$-0.774999\pi$
$509$		−	29.3045i		−	1.29890i	0.760404	−	0.649450i	$-0.225001\pi$
$510$	2.30479	−	1.28954i	0.102058	−	0.0571016i
$511$	−37.8844			−1.67591
$512$	−2.74041	+	22.4609i	−0.121110	+	0.992639i
$513$	−25.4624			−1.12419
$514$	−33.9641	+	19.0030i	−1.49809	+	0.838186i
$515$			1.60968i			0.0709310i
$516$	21.5609	−	35.1212i	0.949167	−	1.54612i
$517$			1.11900i			0.0492137i
$518$	21.0068	+	37.5455i	0.922985	+	1.64966i
$519$	−23.2035			−1.01852
$520$	0.0597776	−	1.47630i	0.00262142	−	0.0647401i
$521$	−4.95237			−0.216967			−0.108484	−	0.994098i	$-0.534600\pi$
$521$	−4.95237			−0.216967			−0.108484	+	0.994098i	$0.534600\pi$
$522$	−1.16279	−	2.07825i	−0.0508938	−	0.0909627i
$523$			0.0756714i			0.00330888i	0.999999	+	0.00165444i	$0.000526625\pi$
$523$			0.0756714i			0.00330888i	−0.999999	+	0.00165444i	$0.999473\pi$
$524$	−2.52535	−	1.55032i	−0.110321	−	0.0677259i
$525$		−	34.2860i		−	1.49636i
$526$	35.1001	−	19.6386i	1.53044	−	0.856282i
$527$	−32.4002			−1.41138
$528$	−3.27704	−	6.45706i	−0.142615	−	0.281008i
$529$	−18.7828			−0.816641
$530$	−3.13479	+	1.75392i	−0.136167	+	0.0761854i
$531$			0.257444i			0.0111721i
$532$	−33.8915	−	20.8061i	−1.46938	−	0.902057i
$533$			0.787895i			0.0341275i
$534$	−20.9776	−	37.4934i	−0.907790	−	1.62250i
$535$	−0.626256			−0.0270754
$536$	−1.02967	−	0.0416929i	−0.0444750	−	0.00180086i
$537$	4.01638			0.173320
$538$	−6.52550	−	11.6631i	−0.281334	−	0.502830i
$539$		−	7.81778i		−	0.336735i
$540$	−1.45687	+	2.37314i	−0.0626938	+	0.102124i
$541$		−	16.4880i		−	0.708873i	−0.935080	−	0.354437i	$-0.884673\pi$
$541$		−	16.4880i		−	0.708873i	0.935080	−	0.354437i	$-0.115327\pi$
$542$	−20.0238	+	11.2033i	−0.860095	+	0.481225i
$543$	17.1935			0.737844
$544$	17.1553	+	11.5124i	0.735526	+	0.493592i
$545$	0.101698			0.00435627
$546$	−15.9051	+	8.89892i	−0.680674	+	0.380839i
$547$			14.3707i			0.614447i	0.951637	+	0.307223i	$0.0993999\pi$
$547$			14.3707i			0.614447i	−0.951637	+	0.307223i	$0.900600\pi$
$548$	16.0468	−	26.1391i	0.685487	−	1.11661i
$549$		−	2.66528i		−	0.113751i
$550$	−3.39751	−	6.07239i	−0.144871	−	0.258928i
$551$	−31.3975			−1.33758
$552$	−10.5062	−	0.425410i	−0.447173	−	0.0181067i
$553$	−7.95827			−0.338420
$554$	10.5006	+	18.7677i	0.446127	+	0.797365i
$555$			4.04101i			0.171531i
$556$	−14.3802	−	8.82801i	−0.609855	−	0.374391i
$557$		−	34.5074i		−	1.46213i	−0.682310	−	0.731063i	$-0.739025\pi$
$557$		−	34.5074i		−	1.46213i	0.682310	−	0.731063i	$-0.260975\pi$
$558$	−3.03327	+	1.69712i	−0.128408	+	0.0718447i
$559$	−21.0510			−0.890363
$560$	−3.87832	+	1.96830i	−0.163889	+	0.0831757i
$561$	−6.61147			−0.279137
$562$	−4.07802	+	2.28166i	−0.172021	+	0.0962461i
$563$			14.5301i			0.612369i	0.951972	+	0.306184i	$0.0990524\pi$
$563$			14.5301i			0.612369i	−0.951972	+	0.306184i	$0.900948\pi$
$564$	−3.45267	−	2.11960i	−0.145384	−	0.0892512i
$565$		−	1.94318i		−	0.0817502i
$566$	5.11882	+	9.14889i	0.215160	+	0.384556i
$567$	37.5483			1.57688
$568$	−0.785074	+	19.3886i	−0.0329410	+	0.813529i
$569$	40.1778			1.68434			0.842170	−	0.539212i	$-0.181278\pi$
$569$	40.1778			1.68434			0.842170	+	0.539212i	$0.181278\pi$
$570$	−1.82387	−	3.25981i	−0.0763934	−	0.136538i
$571$		−	12.7835i		−	0.534972i	−0.963562	−	0.267486i	$-0.913807\pi$
$571$		−	12.7835i		−	0.534972i	0.963562	−	0.267486i	$-0.0861930\pi$
$572$	−1.93512	+	3.15218i	−0.0809116	+	0.131799i
$573$			28.0134i			1.17027i
$574$	2.02399	−	1.13243i	0.0844796	−	0.0472665i
$575$	−10.1041			−0.421371
$576$	2.20907	+	0.179191i	0.0920447	+	0.00746629i
$577$	8.55938			0.356332			0.178166	−	0.984000i	$-0.442984\pi$
$577$	8.55938			0.356332			0.178166	+	0.984000i	$0.442984\pi$
$578$	−4.51864	+	2.52819i	−0.187951	+	0.105159i
$579$			14.2260i			0.591211i
$580$	−1.79646	+	2.92631i	−0.0745941	+	0.121508i
$581$			53.7052i			2.22807i
$582$	−14.5105	−	25.9346i	−0.601478	−	1.07502i
$583$	8.99238			0.372426
$584$	1.12622	−	27.8137i	0.0466031	−	1.15094i
$585$	−0.144720			−0.00598345
$586$	20.7528	+	37.0916i	0.857292	+	1.53224i
$587$		−	33.7279i		−	1.39210i	−0.717994	−	0.696050i	$-0.754939\pi$
$587$		−	33.7279i		−	1.39210i	0.717994	−	0.696050i	$-0.245061\pi$
$588$	24.1216	+	14.8083i	0.994760	+	0.610684i
$589$			45.8255i			1.88821i
$590$	0.323946	−	0.181248i	0.0133367	−	0.00746188i
$591$	−38.3570			−1.57780
$592$	−28.1893	+	14.3064i	−1.15857	+	0.587991i
$593$	−14.1680			−0.581808			−0.290904	−	0.956752i	$-0.593956\pi$
$593$	−14.1680			−0.581808			−0.290904	+	0.956752i	$0.593956\pi$
$594$	6.08356	−	3.40376i	0.249611	−	0.139658i
$595$			3.97106i			0.162798i
$596$	−33.7990	−	20.7493i	−1.38446	−	0.849923i
$597$		−	9.46319i		−	0.387303i
$598$	2.62252	+	4.68725i	0.107243	+	0.191676i
$599$	24.8258			1.01435			0.507177	−	0.861842i	$-0.330689\pi$
$599$	24.8258			1.01435			0.507177	+	0.861842i	$0.330689\pi$
$600$	25.1718	+	1.01924i	1.02763	+	0.0416104i
$601$	−1.76342			−0.0719314			−0.0359657	−	0.999353i	$-0.511451\pi$
$601$	−1.76342			−0.0719314			−0.0359657	+	0.999353i	$0.511451\pi$
$602$	30.2562	+	54.0770i	1.23315	+	2.20401i
$603$			0.100938i			0.00411050i
$604$	13.5128	−	22.0114i	0.549829	−	0.895631i
$605$		−	0.282461i		−	0.0114837i
$606$	7.08963	−	3.96666i	0.287996	−	0.161135i
$607$	11.6767			0.473941			0.236971	−	0.971517i	$-0.423845\pi$
$607$	11.6767			0.473941			0.236971	+	0.971517i	$0.423845\pi$
$608$	16.2827	−	24.2637i	0.660352	−	0.984023i
$609$	42.3556			1.71634
$610$	−3.35376	+	1.87644i	−0.135790	+	0.0759747i
$611$			2.06947i			0.0837218i
$612$	1.05872	−	1.72458i	0.0427964	−	0.0697121i
$613$		−	3.46760i		−	0.140055i	−0.997545	−	0.0700275i	$-0.977691\pi$
$613$		−	3.46760i		−	0.140055i	0.997545	−	0.0700275i	$-0.0223087\pi$
$614$	−5.75683	−	10.2892i	−0.232327	−	0.415239i
$615$	0.217841			0.00878420
$616$	10.8788	+	0.440498i	0.438319	+	0.0177482i
$617$	24.0009			0.966242			0.483121	−	0.875554i	$-0.339503\pi$
$617$	24.0009			0.966242			0.483121	+	0.875554i	$0.339503\pi$
$618$	7.12360	+	12.7320i	0.286553	+	0.512158i
$619$			40.1370i			1.61324i	0.591070	+	0.806620i	$0.298706\pi$
$619$			40.1370i			1.61324i	−0.591070	+	0.806620i	$0.701294\pi$
$620$	4.27102	+	2.62199i	0.171528	+	0.105301i
$621$		−	10.1227i		−	0.406210i
$622$	1.57420	−	0.880767i	0.0631196	−	0.0353155i
$623$	64.5995			2.58813
$624$	−6.06052	−	11.9416i	−0.242615	−	0.478047i
$625$	23.8096			0.952384
$626$	−7.90720	+	4.42409i	−0.316035	+	0.176822i
$627$			9.35100i			0.373443i
$628$	7.94602	+	4.87807i	0.317081	+	0.194656i
$629$			28.8634i			1.15086i
$630$	0.208004	+	0.371766i	0.00828706	+	0.0148115i
$631$	−21.0938			−0.839729			−0.419865	−	0.907587i	$-0.637922\pi$
$631$	−21.0938			−0.839729			−0.419865	+	0.907587i	$0.637922\pi$
$632$	0.236581	−	5.84274i	0.00941069	−	0.232412i
$633$	−11.2169			−0.445831
$634$	−13.2194	−	23.6270i	−0.525008	−	0.938348i
$635$		−	4.12080i		−	0.163529i
$636$	−17.0332	+	27.7459i	−0.675411	+	1.10020i
$637$		−	14.4581i		−	0.572850i
$638$	7.50161	−	4.19716i	0.296992	−	0.166167i
$639$	1.90065			0.0751885
$640$	−1.32977	−	2.90587i	−0.0525640	−	0.114864i
$641$	−3.13213			−0.123712			−0.0618559	−	0.998085i	$-0.519702\pi$
$641$	−3.13213			−0.123712			−0.0618559	+	0.998085i	$0.519702\pi$
$642$	−4.95348	+	2.77148i	−0.195498	+	0.109382i
$643$		−	24.9835i		−	0.985253i	−0.870241	−	0.492626i	$-0.836037\pi$
$643$		−	24.9835i		−	0.985253i	0.870241	−	0.492626i	$-0.163963\pi$
$644$	8.27156	−	13.4738i	0.325945	−	0.530941i
$645$			5.82029i			0.229174i
$646$	−13.0272	−	23.2836i	−0.512549	−	0.916080i
$647$	−1.71241			−0.0673217			−0.0336608	−	0.999433i	$-0.510717\pi$
$647$	−1.71241			−0.0673217			−0.0336608	+	0.999433i	$0.510717\pi$
$648$	−1.11623	+	27.5669i	−0.0438495	+	1.08293i
$649$	−0.929264			−0.0364768
$650$	−6.28332	−	11.2302i	−0.246452	−	0.440485i
$651$		−	61.8192i		−	2.42288i
$652$	18.7943	+	11.5379i	0.736043	+	0.451858i
$653$		−	35.6115i		−	1.39359i	−0.717273	−	0.696793i	$-0.754610\pi$
$653$		−	35.6115i		−	1.39359i	0.717273	−	0.696793i	$-0.245390\pi$
$654$	0.804399	−	0.450063i	0.0314545	−	0.0175988i
$655$	0.418502			0.0163522
$656$	0.771226	+	1.51962i	0.0301113	+	0.0593312i
$657$	−2.72655			−0.106373
$658$	5.31617	−	2.97441i	0.207246	−	0.115954i
$659$			13.2498i			0.516140i	0.966126	+	0.258070i	$0.0830865\pi$
$659$			13.2498i			0.516140i	−0.966126	+	0.258070i	$0.916914\pi$
$660$	0.871529	+	0.535033i	0.0339242	+	0.0208261i
$661$		−	9.36299i		−	0.364178i	−0.983282	−	0.182089i	$-0.941714\pi$
$661$		−	9.36299i		−	0.364178i	0.983282	−	0.182089i	$-0.0582859\pi$
$662$	−3.94782	−	7.05596i	−0.153436	−	0.274238i
$663$	−12.2272			−0.474864
$664$	−39.4289	−	1.59653i	−1.53014	−	0.0619574i
$665$	5.61651			0.217799
$666$	1.51186	+	2.70216i	0.0585835	+	0.104706i
$667$		−	12.4823i		−	0.483315i
$668$	12.1957	−	19.8659i	0.471866	−	0.768634i
$669$		−	1.12693i		−	0.0435696i
$670$	0.127011	−	0.0710632i	0.00490688	−	0.00274541i
$671$	9.62052			0.371396
$672$	−21.9656	+	32.7320i	−0.847341	+	1.26266i
$673$	−9.04281			−0.348575			−0.174287	−	0.984695i	$-0.555762\pi$
$673$	−9.04281			−0.348575			−0.174287	+	0.984695i	$0.555762\pi$
$674$	−3.70473	+	2.07280i	−0.142701	+	0.0798413i
$675$			24.2530i			0.933500i
$676$	10.0239	−	16.3282i	0.385534	−	0.628007i
$677$		−	14.8966i		−	0.572522i	−0.958152	−	0.286261i	$-0.907588\pi$
$677$		−	14.8966i		−	0.572522i	0.958152	−	0.286261i	$-0.0924124\pi$
$678$	−8.59949	−	15.3699i	−0.330261	−	0.590278i
$679$	44.6843			1.71482
$680$	−2.91544	−	0.118051i	−0.111802	−	0.00452703i
$681$	−13.1459			−0.503753
$682$	−6.12587	−	10.9488i	−0.234572	−	0.419251i
$683$		−	25.5360i		−	0.977106i	−0.872534	−	0.488553i	$-0.837525\pi$
$683$		−	25.5360i		−	0.977106i	0.872534	−	0.488553i	$-0.162475\pi$
$684$	−2.43918	−	1.49742i	−0.0932644	−	0.0572551i
$685$			4.33178i			0.165509i
$686$	−3.88510	+	2.17372i	−0.148334	+	0.0829930i
$687$	40.1702			1.53259
$688$	−40.6012	+	20.6056i	−1.54791	+	0.785583i
$689$	16.6304			0.633567
$690$	1.29595	−	0.725088i	0.0493361	−	0.0276036i
$691$		−	30.7844i		−	1.17109i	−0.810639	−	0.585546i	$-0.800880\pi$
$691$		−	30.7844i		−	1.17109i	0.810639	−	0.585546i	$-0.199120\pi$
$692$	21.8472	+	13.4120i	0.830505	+	0.509848i
$693$		−	1.06644i		−	0.0405106i
$694$	1.38507	+	2.47554i	0.0525765	+	0.0939701i
$695$	2.38309			0.0903956
$696$	−1.25914	+	31.0963i	−0.0477274	+	1.17870i
$697$	1.55596			0.0589361
$698$	−4.53729	−	8.10951i	−0.171739	−	0.306950i
$699$		−	8.95791i		−	0.338819i
$700$	−19.8179	+	32.2819i	−0.749045	+	1.22014i
$701$			1.53407i			0.0579411i	0.999580	+	0.0289706i	$0.00922290\pi$
$701$			1.53407i			0.0579411i	−0.999580	+	0.0289706i	$0.990777\pi$
$702$	11.2509	−	6.29487i	0.424636	−	0.237585i
$703$	40.8233			1.53968
$704$	−0.646803	+	7.97381i	−0.0243773	+	0.300524i
$705$	0.572177			0.0215494
$706$	23.3414	−	13.0596i	0.878465	−	0.491503i
$707$			12.2151i			0.459398i
$708$	1.76020	−	2.86723i	0.0661522	−	0.107757i
$709$		−	47.7207i		−	1.79219i	−0.443863	−	0.896095i	$-0.646392\pi$
$709$		−	47.7207i		−	1.79219i	0.443863	−	0.896095i	$-0.353608\pi$
$710$	−1.33811	−	2.39162i	−0.0502185	−	0.0897558i
$711$	−0.572758			−0.0214801
$712$	−1.92039	+	47.4272i	−0.0719698	+	1.77741i
$713$	−18.2182			−0.682277
$714$	17.5738	+	31.4098i	0.657685	+	1.17548i
$715$		−	0.522379i		−	0.0195359i
$716$	−3.78161	−	2.32153i	−0.141325	−	0.0867598i
$717$		−	19.3265i		−	0.721763i
$718$	−21.3879	+	11.9666i	−0.798190	+	0.446589i
$719$	−48.7950			−1.81975			−0.909873	−	0.414888i	$-0.863821\pi$
$719$	−48.7950			−1.81975			−0.909873	+	0.414888i	$0.863821\pi$
$720$	−0.279123	+	0.141659i	−0.0104023	+	0.00527931i
$721$	−21.9368			−0.816968
$722$	−9.48208	+	5.30524i	−0.352886	+	0.197441i
$723$			12.9337i			0.481011i
$724$	−16.1885	−	9.93814i	−0.601641	−	0.369348i
$725$			29.9063i			1.11069i
$726$	−1.25002	−	2.23417i	−0.0463927	−	0.0829179i
$727$	−23.3775			−0.867023			−0.433511	−	0.901148i	$-0.642726\pi$
$727$	−23.3775			−0.867023			−0.433511	+	0.901148i	$0.642726\pi$
$728$	20.1191	+	0.814651i	0.745663	+	0.0301930i
$729$	−24.0674			−0.891385
$730$	1.91957	+	3.43086i	0.0710465	+	0.126982i
$731$			41.5721i			1.53760i
$732$	−18.2230	+	29.6840i	−0.673543	+	1.09715i
$733$			19.8665i			0.733788i	0.930263	+	0.366894i	$0.119579\pi$
$733$			19.8665i			0.733788i	−0.930263	+	0.366894i	$0.880421\pi$
$734$	−6.85316	+	3.83435i	−0.252955	+	0.141529i
$735$	−3.99744			−0.147448
$736$	9.64616	+	6.47329i	0.355562	+	0.238609i
$737$	−0.364342			−0.0134207
$738$	0.145667	−	0.0815008i	0.00536207	−	0.00300009i
$739$		−	32.9394i		−	1.21170i	−0.795580	−	0.605848i	$-0.792834\pi$
$739$		−	32.9394i		−	1.21170i	0.795580	−	0.605848i	$-0.207166\pi$
$740$	2.33577	−	3.80480i	0.0858647	−	0.139867i
$741$			17.2936i			0.635296i
$742$	−23.9025	−	42.7210i	−0.877488	−	1.56834i
$743$	22.3465			0.819815			0.409907	−	0.912127i	$-0.365561\pi$
$743$	22.3465			0.819815			0.409907	+	0.912127i	$0.365561\pi$
$744$	45.3859	+	1.83774i	1.66393	+	0.0673748i
$745$	5.60118			0.205212
$746$	9.16255	+	16.3763i	0.335465	+	0.599578i
$747$			3.86517i			0.141419i
$748$	6.22501	+	3.82154i	0.227609	+	0.139729i
$749$		−	8.53465i		−	0.311849i
$750$	−6.26031	+	3.50266i	−0.228594	+	0.127899i
$751$	−2.75883			−0.100671			−0.0503356	−	0.998732i	$-0.516029\pi$
$751$	−2.75883			−0.100671			−0.0503356	+	0.998732i	$0.516029\pi$
$752$	2.02569	+	3.99140i	0.0738692	+	0.145551i
$753$	−23.4446			−0.854368
$754$	13.8734	−	7.76218i	0.505239	−	0.282682i
$755$			3.64773i			0.132755i
$756$	−32.3412	−	19.8543i	−1.17624	−	0.722094i
$757$			46.0072i			1.67216i	0.548608	+	0.836080i	$0.315158\pi$
$757$			46.0072i			1.67216i	−0.548608	+	0.836080i	$0.684842\pi$
$758$	5.35685	+	9.57433i	0.194570	+	0.347755i
$759$	−3.71754			−0.134938
$760$	−0.166966	+	4.12348i	−0.00605649	+	0.149575i
$761$	46.1971			1.67464			0.837322	−	0.546710i	$-0.184120\pi$
$761$	46.1971			1.67464			0.837322	+	0.546710i	$0.184120\pi$
$762$	−18.2365	−	32.5941i	−0.660638	−	1.18076i
$763$			1.38595i			0.0501746i
$764$	16.1922	−	26.3759i	0.585813	−	0.954246i
$765$			0.285798i			0.0103331i
$766$	−12.9081	+	7.22213i	−0.466390	+	0.260946i
$767$	−1.71857			−0.0620539
$768$	−23.3779	−	17.0996i	−0.843578	−	0.617027i
$769$	−38.6685			−1.39442			−0.697211	−	0.716866i	$-0.745576\pi$
$769$	−38.6685			−1.39442			−0.697211	+	0.716866i	$0.745576\pi$
$770$	−1.34192	+	0.750805i	−0.0483593	+	0.0270571i
$771$		−	49.8179i		−	1.79415i
$772$	8.22285	−	13.3944i	0.295947	−	0.482076i
$773$			9.50073i			0.341717i	0.985296	+	0.170859i	$0.0546542\pi$
$773$			9.50073i			0.341717i	−0.985296	+	0.170859i	$0.945346\pi$
$774$	2.17754	+	3.89193i	0.0782701	+	0.139892i
$775$	43.6491			1.56792
$776$	−1.32836	+	32.8059i	−0.0476853	+	1.17766i
$777$	−55.0711			−1.97566
$778$	−20.0750	−	35.8801i	−0.719723	−	1.28636i
$779$		−	2.20068i		−	0.0788477i
$780$	1.61179	+	0.989483i	0.0577115	+	0.0354292i
$781$			6.86053i			0.245489i
$782$	9.25651	−	5.17904i	0.331012	−	0.185202i
$783$	−29.9613			−1.07073
$784$	−14.1522	−	27.8854i	−0.505436	−	0.995908i
$785$	−1.31682			−0.0469992
$786$	3.31021	−	1.85207i	0.118071	−	0.0660612i
$787$		−	33.9196i		−	1.20910i	−0.796566	−	0.604551i	$-0.793352\pi$
$787$		−	33.9196i		−	1.20910i	0.796566	−	0.604551i	$-0.206648\pi$
$788$	36.1149	+	22.1710i	1.28654	+	0.789808i
$789$			51.4841i			1.83288i
$790$	0.403239	+	0.720711i	0.0143466	+	0.0256418i
$791$	26.4817			0.941582
$792$	0.782949	+	0.0317027i	0.0278209	+	0.00112651i
$793$	17.7921			0.631815
$794$	3.33927	+	5.96830i	0.118506	+	0.211807i
$795$		−	4.59805i		−	0.163076i
$796$	−5.46988	+	8.91004i	−0.193875	+	0.315808i
$797$		−	18.9106i		−	0.669848i	−0.942245	−	0.334924i	$-0.891289\pi$
$797$		−	18.9106i		−	0.669848i	0.942245	−	0.334924i	$-0.108711\pi$
$798$	44.4248	−	24.8557i	1.57262	−	0.879883i
$799$	4.08685			0.144582
$800$	−23.1113	−	15.5094i	−0.817107	−	0.548340i
$801$	4.64924			0.164273
$802$	0.629797	−	0.352372i	0.0222389	−	0.0124427i
$803$		−	9.84167i		−	0.347305i
$804$	0.690131	−	1.12417i	0.0243390	−	0.0396465i
$805$			2.23287i			0.0786985i
$806$	−11.3291	−	20.2486i	−0.399051	−	0.713225i
$807$	17.1072			0.602201
$808$	−8.96801	−	0.363128i	−0.315493	−	0.0127748i
$809$	−39.2457			−1.37980			−0.689902	−	0.723903i	$-0.742346\pi$
$809$	−39.2457			−1.37980			−0.689902	+	0.723903i	$0.742346\pi$
$810$	−1.90254	−	3.40042i	−0.0668486	−	0.119479i
$811$			17.2378i			0.605301i	0.953102	+	0.302650i	$0.0978714\pi$
$811$			17.2378i			0.605301i	−0.953102	+	0.302650i	$0.902129\pi$
$812$	−39.8798	−	24.4823i	−1.39951	−	0.859159i
$813$		−	29.3705i		−	1.03007i
$814$	−9.75364	+	5.45718i	−0.341865	+	0.191274i
$815$	−3.11460			−0.109100
$816$	−23.5826	+	11.9685i	−0.825557	+	0.418981i
$817$	58.7979			2.05708
$818$	3.40503	−	1.90512i	0.119054	−	0.0666110i
$819$		−	1.97226i		−	0.0689162i
$820$	−0.205108	−	0.125916i	−0.00716267	−	0.00439717i
$821$			3.69820i			0.129068i	0.997916	+	0.0645340i	$0.0205561\pi$
$821$			3.69820i			0.129068i	−0.997916	+	0.0645340i	$0.979444\pi$
$822$	19.1702	+	34.2629i	0.668637	+	1.19506i
$823$	−34.1316			−1.18975			−0.594877	−	0.803817i	$-0.702799\pi$
$823$	−34.1316			−1.18975			−0.594877	+	0.803817i	$0.702799\pi$
$824$	0.652130	−	16.1054i	0.0227180	−	0.561057i
$825$	8.90687			0.310097
$826$	2.47006	+	4.41475i	0.0859444	+	0.153609i
$827$			24.1871i			0.841066i	0.907277	+	0.420533i	$0.138157\pi$
$827$			24.1871i			0.841066i	−0.907277	+	0.420533i	$0.861843\pi$
$828$	0.595306	−	0.969709i	0.0206883	−	0.0336997i
$829$			54.9138i			1.90723i	0.301021	+	0.953617i	$0.402672\pi$
$829$			54.9138i			1.90723i	−0.301021	+	0.953617i	$0.597328\pi$
$830$	4.86361	−	2.72120i	0.168818	−	0.0944542i
$831$	−27.5282			−0.954942
$832$	−1.19619	+	14.7467i	−0.0414704	+	0.511248i
$833$	−28.5523			−0.989277
$834$	18.8494	−	10.5463i	0.652702	−	0.365188i
$835$			3.29218i			0.113931i
$836$	5.40503	−	8.80440i	0.186937	−	0.304506i
$837$			43.7293i			1.51151i
$838$	19.9837	+	35.7169i	0.690325	+	1.23382i
$839$	16.1821			0.558667			0.279333	−	0.960194i	$-0.409887\pi$
$839$	16.1821			0.558667			0.279333	+	0.960194i	$0.409887\pi$
$840$	0.225239	−	5.56263i	0.00777148	−	0.191929i
$841$	−7.94516			−0.273971
$842$	12.5288	+	22.3927i	0.431769	+	0.771703i
$843$		−	5.98157i		−	0.206016i
$844$	10.5612	+	6.48354i	0.363532	+	0.223173i
$845$			2.70591i			0.0930861i
$846$	0.382605	−	0.214068i	0.0131542	−	0.00735983i
$847$	3.84939			0.132266
$848$	32.0751	−	16.2785i	1.10147	−	0.559007i
$849$	−13.4194			−0.460553
$850$	−22.1777	+	12.4085i	−0.760690	+	0.425607i
$851$			16.2295i			0.556341i
$852$	−21.1681	−	12.9951i	−0.725206	−	0.445205i
$853$		−	25.6247i		−	0.877373i	−0.898640	−	0.438687i	$-0.855444\pi$
$853$		−	25.6247i		−	0.877373i	0.898640	−	0.438687i	$-0.144556\pi$
$854$	−25.5721	−	45.7052i	−0.875061	−	1.56400i
$855$	0.404221			0.0138241
$856$	6.26590	+	0.253715i	0.214164	+	0.00867181i
$857$	15.4515			0.527812			0.263906	−	0.964548i	$-0.414989\pi$
$857$	15.4515			0.527812			0.263906	+	0.964548i	$0.414989\pi$
$858$	−2.31178	−	4.13185i	−0.0789227	−	0.141059i
$859$			12.1299i			0.413867i	0.978355	+	0.206934i	$0.0663485\pi$
$859$			12.1299i			0.413867i	−0.978355	+	0.206934i	$0.933652\pi$
$860$	3.36422	−	5.48007i	0.114719	−	0.186869i
$861$			2.96875i			0.101175i
$862$	16.4763	−	9.21854i	0.561186	−	0.313985i
$863$	−29.7629			−1.01314			−0.506571	−	0.862198i	$-0.669087\pi$
$863$	−29.7629			−1.01314			−0.506571	+	0.862198i	$0.669087\pi$
$864$	15.5379	−	23.1538i	0.528610	−	0.787708i
$865$	−3.62052			−0.123101
$866$	15.3066	−	8.56405i	0.520138	−	0.291018i
$867$		−	6.62785i		−	0.225094i
$868$	−35.7325	+	58.2056i	−1.21284	+	1.97563i
$869$		−	2.06741i		−	0.0701322i
$870$	−2.14613	−	3.83578i	−0.0727605	−	0.130045i
$871$	−0.673809			−0.0228311
$872$	−1.01752	−	0.0412010i	−0.0344577	−	0.00139524i
$873$	3.21593			0.108843
$874$	−7.32502	−	13.0920i	−0.247772	−	0.442845i
$875$		−	10.7863i		−	0.364642i
$876$	30.3664	+	18.6419i	1.02598	+	0.629853i
$877$			17.0156i			0.574576i	0.957844	+	0.287288i	$0.0927537\pi$
$877$			17.0156i			0.574576i	−0.957844	+	0.287288i	$0.907246\pi$
$878$	8.25686	−	4.61973i	0.278656	−	0.155908i
$879$	−54.4053			−1.83505
$880$	−0.511328	−	1.00752i	−0.0172368	−	0.0339634i
$881$	10.3132			0.347461			0.173730	−	0.984793i	$-0.444418\pi$
$881$	10.3132			0.347461			0.173730	+	0.984793i	$0.444418\pi$
$882$	−2.67302	+	1.49556i	−0.0900054	+	0.0503582i
$883$		−	44.6494i		−	1.50257i	−0.659976	−	0.751286i	$-0.729434\pi$
$883$		−	44.6494i		−	1.50257i	0.659976	−	0.751286i	$-0.270566\pi$
$884$	11.5124	+	7.06751i	0.387206	+	0.237706i
$885$			0.475158i			0.0159723i
$886$	11.7981	+	21.0868i	0.396365	+	0.708424i
$887$	−13.0381			−0.437776			−0.218888	−	0.975750i	$-0.570243\pi$
$887$	−13.0381			−0.437776			−0.218888	+	0.975750i	$0.570243\pi$
$888$	1.63713	−	40.4316i	0.0549386	−	1.35680i
$889$	56.1584			1.88349
$890$	−3.27321	−	5.85021i	−0.109718	−	0.196100i
$891$			9.75437i			0.326784i
$892$	−0.651384	+	1.06106i	−0.0218100	+	0.0355268i
$893$		−	5.78027i		−	0.193429i
$894$	44.3035	−	24.7879i	1.48173	−	0.829031i
$895$	0.626689			0.0209479
$896$	39.6013	−	18.1222i	1.32299	−	0.605421i
$897$	−6.87517			−0.229555
$898$	2.05380	−	1.14911i	0.0685363	−	0.0383462i
$899$			53.9224i			1.79841i
$900$	−1.42630	+	2.32333i	−0.0475432	+	0.0774443i
$901$		−	32.8422i		−	1.09413i
$902$	0.294183	+	0.525795i	0.00979523	+	0.0175071i
$903$	−79.3191			−2.63957
$904$	−0.787240	+	19.4421i	−0.0261832	+	0.646636i
$905$	2.68276			0.0891780
$906$	16.1430	+	28.8524i	0.536314	+	0.958556i
$907$			9.57768i			0.318022i	0.987277	+	0.159011i	$0.0508305\pi$
$907$			9.57768i			0.318022i	−0.987277	+	0.159011i	$0.949170\pi$
$908$	12.3775	+	7.59857i	0.410762	+	0.252167i
$909$			0.879125i			0.0291588i
$910$	−2.48172	+	1.38853i	−0.0822683	+	0.0460292i
$911$	30.9906			1.02676			0.513382	−	0.858160i	$-0.328392\pi$
$911$	30.9906			1.02676			0.513382	+	0.858160i	$0.328392\pi$
$912$	16.9277	+	33.3543i	0.560533	+	1.10447i
$913$	−13.9516			−0.461731
$914$	27.7061	−	15.5016i	0.916436	−	0.512748i
$915$		−	4.91924i		−	0.162625i
$916$	−37.8221	−	23.2191i	−1.24968	−	0.767179i
$917$			5.70336i			0.188342i
$918$	−12.4313	−	22.2185i	−0.410294	−	0.733320i
$919$	47.3545			1.56208			0.781040	−	0.624481i	$-0.214689\pi$
$919$	47.3545			1.56208			0.781040	+	0.624481i	$0.214689\pi$
$920$	−1.63931	−	0.0663782i	−0.0540466	−	0.00218842i
$921$	15.0920			0.497299
$922$	−8.32397	−	14.8775i	−0.274136	−	0.489964i
$923$			12.6878i			0.417623i
$924$	−7.29145	+	11.8772i	−0.239871	+	0.390732i
$925$		−	38.8844i		−	1.27851i
$926$	51.3084	−	28.7072i	1.68610	−	0.943376i
$927$	−1.57879			−0.0518544
$928$	19.1597	−	28.5508i	0.628949	−	0.937227i
$929$	−49.2212			−1.61490			−0.807448	−	0.589939i	$-0.799152\pi$
$929$	−49.2212			−1.61490			−0.807448	+	0.589939i	$0.799152\pi$
$930$	−5.59842	+	3.13233i	−0.183579	+	0.102713i
$931$			40.3831i			1.32350i
$932$	−5.17782	+	8.43429i	−0.169605	+	0.276274i
$933$			2.30900i			0.0755934i
$934$	26.7984	+	47.8968i	0.876869	+	1.56723i
$935$	−1.03161			−0.0337372
$936$	1.44797	+	0.0586306i	0.0473285	+	0.00191640i
$937$	−27.4927			−0.898146			−0.449073	−	0.893495i	$-0.648246\pi$
$937$	−27.4927			−0.898146			−0.449073	+	0.893495i	$0.648246\pi$
$938$	0.968451	+	1.73092i	0.0316211	+	0.0565164i
$939$		−	11.5981i		−	0.378491i
$940$	−0.538732	−	0.330728i	−0.0175715	−	0.0107872i
$941$		−	47.6946i		−	1.55480i	−0.629008	−	0.777399i	$-0.716539\pi$
$941$		−	47.6946i		−	1.55480i	0.629008	−	0.777399i	$-0.283461\pi$
$942$	−10.4156	+	5.82753i	−0.339358	+	0.189871i
$943$	0.874894			0.0284905
$944$	−3.31461	+	1.68221i	−0.107882	+	0.0547512i
$945$	5.35959			0.174348
$946$	−14.0482	+	7.86000i	−0.456747	+	0.255551i
$947$		−	48.8887i		−	1.58867i	−0.607481	−	0.794334i	$-0.707820\pi$
$947$		−	48.8887i		−	1.58867i	0.607481	−	0.794334i	$-0.292180\pi$
$948$	6.37898	+	3.91606i	0.207180	+	0.127188i
$949$		−	18.2011i		−	0.590831i
$950$	17.5500	+	31.3673i	0.569399	+	1.01769i
$951$	34.6557			1.12379
$952$	1.60880	−	39.7318i	0.0521414	−	1.28771i
$953$	−34.1065			−1.10482			−0.552409	−	0.833573i	$-0.686291\pi$
$953$	−34.1065			−1.10482			−0.552409	+	0.833573i	$0.686291\pi$
$954$	−1.72027	−	3.07464i	−0.0556957	−	0.0995451i
$955$			4.37102i			0.141443i
$956$	−11.1711	+	18.1968i	−0.361298	+	0.588528i
$957$			11.0032i			0.355684i
$958$	−38.8303	+	21.7256i	−1.25455	+	0.701923i
$959$	−59.0336			−1.90630
$960$	4.07723	+	0.330728i	0.131592	+	0.0106742i
$961$	47.7012			1.53875
$962$	−18.0382	+	10.0924i	−0.581576	+	0.325393i
$963$		−	0.614240i		−	0.0197936i
$964$	7.47592	−	12.1777i	0.240783	−	0.392218i
$965$			2.21973i			0.0714555i
$966$	9.88153	+	17.6613i	0.317933	+	0.568243i
$967$	37.5143			1.20638			0.603189	−	0.797598i	$-0.293896\pi$
$967$	37.5143			1.20638			0.603189	+	0.797598i	$0.293896\pi$
$968$	−0.114433	+	2.82611i	−0.00367803	+	0.0908347i
$969$	34.1519			1.09712
$970$	−2.26411	−	4.04666i	−0.0726963	−	0.129930i
$971$		−	14.8188i		−	0.475559i	−0.971319	−	0.237779i	$-0.923580\pi$
$971$		−	14.8188i		−	0.475559i	0.971319	−	0.237779i	$-0.0764195\pi$
$972$	−4.89202	−	3.00322i	−0.156912	−	0.0963283i
$973$			32.4768i			1.04116i
$974$	−43.2847	+	24.2179i	−1.38693	+	0.775990i
$975$	16.4722			0.527534
$976$	34.3157	−	17.4156i	1.09842	−	0.557461i
$977$	60.7398			1.94324			0.971620	−	0.236548i	$-0.0760160\pi$
$977$	60.7398			1.94324			0.971620	+	0.236548i	$0.0760160\pi$
$978$	−24.6355	+	13.7836i	−0.787755	+	0.440750i
$979$			16.7818i			0.536348i
$980$	3.76378	+	2.31059i	0.120230	+	0.0738091i
$981$			0.0997468i			0.00318467i
$982$	11.4125	+	20.3976i	0.364188	+	0.650915i
$983$	−20.5063			−0.654050			−0.327025	−	0.945016i	$-0.606046\pi$
$983$	−20.5063			−0.654050			−0.327025	+	0.945016i	$0.606046\pi$
$984$	−2.17957	−	0.0882540i	−0.0694822	−	0.00281343i
$985$	−5.98497			−0.190697
$986$	−15.3290	−	27.3975i	−0.488174	−	0.872516i
$987$			7.79765i			0.248202i
$988$	9.99599	−	16.2827i	0.318015	−	0.518023i
$989$			23.3754i			0.743296i
$990$	−0.0965779	+	0.0540355i	−0.00306945	+	0.00171736i
$991$	47.2702			1.50159			0.750793	−	0.660537i	$-0.229672\pi$
$991$	47.2702			1.50159			0.750793	+	0.660537i	$0.229672\pi$
$992$	−41.6707	−	27.9641i	−1.32305	−	0.887862i
$993$	10.3495			0.328433
$994$	32.5930	−	18.2359i	1.03379	−	0.578407i
$995$		−	1.47657i		−	0.0468105i
$996$	26.4270	−	43.0476i	0.837370	−	1.36401i
$997$		−	56.5321i		−	1.79039i	−0.445674	−	0.895195i	$-0.647036\pi$
$997$		−	56.5321i		−	1.79039i	0.445674	−	0.895195i	$-0.352964\pi$
$998$	−11.6955	−	20.9033i	−0.370213	−	0.661684i
$999$	38.9559			1.23251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.c.a.45.9	✓	10
3.2	odd	2		792.2.f.g.397.2		10
4.3	odd	2		352.2.c.a.177.3		10
8.3	odd	2		352.2.c.a.177.8		10
8.5	even	2	inner	88.2.c.a.45.10	yes	10
11.2	odd	10		968.2.o.h.565.10		40
11.3	even	5		968.2.o.g.493.5		40
11.4	even	5		968.2.o.g.269.7		40
11.5	even	5		968.2.o.g.245.4		40
11.6	odd	10		968.2.o.h.245.7		40
11.7	odd	10		968.2.o.h.269.4		40
11.8	odd	10		968.2.o.h.493.6		40
11.9	even	5		968.2.o.g.565.1		40
11.10	odd	2		968.2.c.d.485.2		10
12.11	even	2		3168.2.f.g.1585.5		10
16.3	odd	4		2816.2.a.p.1.4		5
16.5	even	4		2816.2.a.r.1.4		5
16.11	odd	4		2816.2.a.q.1.2		5
16.13	even	4		2816.2.a.o.1.2		5
24.5	odd	2		792.2.f.g.397.1		10
24.11	even	2		3168.2.f.g.1585.6		10
44.43	even	2		3872.2.c.f.1937.3		10
88.5	even	10		968.2.o.g.245.1		40
88.13	odd	10		968.2.o.h.565.7		40
88.21	odd	2		968.2.c.d.485.1		10
88.29	odd	10		968.2.o.h.269.6		40
88.37	even	10		968.2.o.g.269.5		40
88.43	even	2		3872.2.c.f.1937.8		10
88.53	even	10		968.2.o.g.565.4		40
88.61	odd	10		968.2.o.h.245.10		40
88.69	even	10		968.2.o.g.493.7		40
88.85	odd	10		968.2.o.h.493.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.9	✓	10	1.1	even	1	trivial
88.2.c.a.45.10	yes	10	8.5	even	2	inner
352.2.c.a.177.3		10	4.3	odd	2
352.2.c.a.177.8		10	8.3	odd	2
792.2.f.g.397.1		10	24.5	odd	2
792.2.f.g.397.2		10	3.2	odd	2
968.2.c.d.485.1		10	88.21	odd	2
968.2.c.d.485.2		10	11.10	odd	2
968.2.o.g.245.1		40	88.5	even	10
968.2.o.g.245.4		40	11.5	even	5
968.2.o.g.269.5		40	88.37	even	10
968.2.o.g.269.7		40	11.4	even	5
968.2.o.g.493.5		40	11.3	even	5
968.2.o.g.493.7		40	88.69	even	10
968.2.o.g.565.1		40	11.9	even	5
968.2.o.g.565.4		40	88.53	even	10
968.2.o.h.245.7		40	11.6	odd	10
968.2.o.h.245.10		40	88.61	odd	10
968.2.o.h.269.4		40	11.7	odd	10
968.2.o.h.269.6		40	88.29	odd	10
968.2.o.h.493.4		40	88.85	odd	10
968.2.o.h.493.6		40	11.8	odd	10
968.2.o.h.565.7		40	88.13	odd	10
968.2.o.h.565.10		40	11.2	odd	10
2816.2.a.o.1.2		5	16.13	even	4
2816.2.a.p.1.4		5	16.3	odd	4
2816.2.a.q.1.2		5	16.11	odd	4
2816.2.a.r.1.4		5	16.5	even	4
3168.2.f.g.1585.5		10	12.11	even	2
3168.2.f.g.1585.6		10	24.11	even	2
3872.2.c.f.1937.3		10	44.43	even	2
3872.2.c.f.1937.8		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)

\(f(q)\)	\(=\)	\(q+(1.23417 - 0.690521i) q^{2} +1.81026i q^{3} +(1.04636 - 1.70444i) q^{4} +0.282461i q^{5} +(1.25002 + 2.23417i) q^{6} -3.84939 q^{7} +(0.114433 - 2.82611i) q^{8} -0.277041 q^{9} +O(q^{10})\)	\(q+(1.23417 - 0.690521i) q^{2} +1.81026i q^{3} +(1.04636 - 1.70444i) q^{4} +0.282461i q^{5} +(1.25002 + 2.23417i) q^{6} -3.84939 q^{7} +(0.114433 - 2.82611i) q^{8} -0.277041 q^{9} +(0.195045 + 0.348605i) q^{10} -1.00000i q^{11} +(3.08549 + 1.89418i) q^{12} -1.84939i q^{13} +(-4.75080 + 2.65808i) q^{14} -0.511328 q^{15} +(-1.81026 - 3.56693i) q^{16} -3.65222 q^{17} +(-0.341916 + 0.191303i) q^{18} +5.16555i q^{19} +(0.481439 + 0.295556i) q^{20} -6.96839i q^{21} +(-0.690521 - 1.23417i) q^{22} -2.05359 q^{23} +(5.11600 + 0.207154i) q^{24} +4.92022 q^{25} +(-1.27704 - 2.28246i) q^{26} +4.92926i q^{27} +(-4.02785 + 6.56106i) q^{28} +6.07825i q^{29} +(-0.631066 + 0.353083i) q^{30} +8.87137 q^{31} +(-4.69721 - 3.15218i) q^{32} +1.81026 q^{33} +(-4.50747 + 2.52194i) q^{34} -1.08730i q^{35} +(-0.289885 + 0.472201i) q^{36} -7.90298i q^{37} +(3.56693 + 6.37518i) q^{38} +3.34787 q^{39} +(0.798266 + 0.0323229i) q^{40} -0.426031 q^{41} +(-4.81182 - 8.60019i) q^{42} -11.3827i q^{43} +(-1.70444 - 1.04636i) q^{44} -0.0782532i q^{45} +(-2.53449 + 1.41805i) q^{46} -1.11900 q^{47} +(6.45706 - 3.27704i) q^{48} +7.81778 q^{49} +(6.07239 - 3.39751i) q^{50} -6.61147i q^{51} +(-3.15218 - 1.93512i) q^{52} +8.99238i q^{53} +(3.40376 + 6.08356i) q^{54} +0.282461 q^{55} +(-0.440498 + 10.8788i) q^{56} -9.35100 q^{57} +(4.19716 + 7.50161i) q^{58} -0.929264i q^{59} +(-0.535033 + 0.871529i) q^{60} +9.62052i q^{61} +(10.9488 - 6.12587i) q^{62} +1.06644 q^{63} +(-7.97381 - 0.646803i) q^{64} +0.522379 q^{65} +(2.23417 - 1.25002i) q^{66} -0.364342i q^{67} +(-3.82154 + 6.22501i) q^{68} -3.71754i q^{69} +(-0.750805 - 1.34192i) q^{70} -6.86053 q^{71} +(-0.0317027 + 0.782949i) q^{72} +9.84167 q^{73} +(-5.45718 - 9.75364i) q^{74} +8.90687i q^{75} +(8.80440 + 5.40503i) q^{76} +3.84939i q^{77} +(4.13185 - 2.31178i) q^{78} +2.06741 q^{79} +(1.00752 - 0.511328i) q^{80} -9.75437 q^{81} +(-0.525795 + 0.294183i) q^{82} -13.9516i q^{83} +(-11.8772 - 7.29145i) q^{84} -1.03161i q^{85} +(-7.86000 - 14.0482i) q^{86} -11.0032 q^{87} +(-2.82611 - 0.114433i) q^{88} -16.7818 q^{89} +(-0.0540355 - 0.0965779i) q^{90} +7.11900i q^{91} +(-2.14880 + 3.50024i) q^{92} +16.0595i q^{93} +(-1.38104 + 0.772696i) q^{94} -1.45907 q^{95} +(5.70626 - 8.50317i) q^{96} -11.6081 q^{97} +(9.64848 - 5.39834i) q^{98} +0.277041i 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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