LMFDB - Embedded newform 920.2.bo.a.373.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(37,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 22, 11, 42]))

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

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

chi := DirichletCharacter("920.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bo (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$2800$
Relative dimension:	$140$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			373.57
Character	$\chi$	$=$	920.373
Dual form			920.2.bo.a.37.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.391742 - 1.35887i) q^{2} +(0.166783 + 2.33193i) q^{3} +(-1.69308 + 1.06466i) q^{4} +(0.194105 + 2.22763i) q^{5} +(3.10347 - 1.14015i) q^{6} +(-1.37657 + 3.69073i) q^{7} +(2.10998 + 1.88361i) q^{8} +(-2.44063 + 0.350910i) q^{9} +O(q^{10})$	\(q+(-0.391742 - 1.35887i) q^{2} +(0.166783 + 2.33193i) q^{3} +(-1.69308 + 1.06466i) q^{4} +(0.194105 + 2.22763i) q^{5} +(3.10347 - 1.14015i) q^{6} +(-1.37657 + 3.69073i) q^{7} +(2.10998 + 1.88361i) q^{8} +(-2.44063 + 0.350910i) q^{9} +(2.95103 - 1.13642i) q^{10} +(5.24665 - 1.54056i) q^{11} +(-2.76508 - 3.77057i) q^{12} +(2.02042 + 5.41695i) q^{13} +(5.55450 + 0.424773i) q^{14} +(-5.16230 + 0.824171i) q^{15} +(1.73302 - 3.60509i) q^{16} +(1.29226 + 0.281114i) q^{17} +(1.43294 + 3.17904i) q^{18} +(0.790761 - 1.23045i) q^{19} +(-2.70029 - 3.56489i) q^{20} +(-8.83612 - 2.59452i) q^{21} +(-4.14875 - 6.52603i) q^{22} +(-4.15866 - 2.38863i) q^{23} +(-4.04054 + 5.23449i) q^{24} +(-4.92465 + 0.864788i) q^{25} +(6.56947 - 4.86754i) q^{26} +(0.265509 + 1.22052i) q^{27} +(-1.59872 - 7.71426i) q^{28} +(5.22979 - 3.36098i) q^{29} +(3.14224 + 6.69206i) q^{30} +(4.33286 + 5.00039i) q^{31} +(-5.57775 - 0.942685i) q^{32} +(4.46752 + 11.9779i) q^{33} +(-0.124234 - 1.86615i) q^{34} +(-8.48877 - 2.35010i) q^{35} +(3.75858 - 3.19255i) q^{36} +(1.32222 + 0.989802i) q^{37} +(-1.98180 - 0.592526i) q^{38} +(-12.2950 + 5.61493i) q^{39} +(-3.78642 + 5.06587i) q^{40} +(1.24547 - 8.66245i) q^{41} +(-0.0641446 + 13.0236i) q^{42} +(-7.42225 + 0.530850i) q^{43} +(-7.24282 + 8.19415i) q^{44} +(-1.25544 - 5.36870i) q^{45} +(-1.61672 + 6.58682i) q^{46} +(-4.40810 + 4.40810i) q^{47} +(8.69586 + 3.44001i) q^{48} +(-6.43629 - 5.57708i) q^{49} +(3.10433 + 6.35320i) q^{50} +(-0.440013 + 3.06035i) q^{51} +(-9.18791 - 7.02026i) q^{52} +(4.75649 - 12.7527i) q^{53} +(1.55453 - 0.838923i) q^{54} +(4.45018 + 11.3885i) q^{55} +(-9.85643 + 5.19446i) q^{56} +(3.00121 + 1.63878i) q^{57} +(-6.61588 - 5.78999i) q^{58} +(0.332903 - 0.728955i) q^{59} +(7.86272 - 6.89146i) q^{60} +(0.0557293 + 0.0643150i) q^{61} +(5.09753 - 7.84667i) q^{62} +(2.06459 - 9.49076i) q^{63} +(0.904051 + 7.94875i) q^{64} +(-11.6748 + 5.55220i) q^{65} +(14.5263 - 10.7630i) q^{66} +(-0.289707 + 0.158192i) q^{67} +(-2.48719 + 0.899867i) q^{68} +(4.87653 - 10.0961i) q^{69} +(0.131922 + 12.4558i) q^{70} +(-0.431678 - 0.126752i) q^{71} +(-5.81066 - 3.85678i) q^{72} +(-2.23979 - 10.2962i) q^{73} +(0.827046 - 2.18448i) q^{74} +(-2.83798 - 11.3397i) q^{75} +(-0.0288148 + 2.92513i) q^{76} +(-1.53661 + 21.4846i) q^{77} +(12.4465 + 14.5077i) q^{78} +(0.146226 - 0.320189i) q^{79} +(8.36718 + 3.16075i) q^{80} +(-9.89944 + 2.90674i) q^{81} +(-12.2591 + 1.70101i) q^{82} +(-0.911814 + 1.21804i) q^{83} +(17.7225 - 5.01471i) q^{84} +(-0.375383 + 2.93324i) q^{85} +(3.62896 + 9.87794i) q^{86} +(8.70983 + 11.6350i) q^{87} +(13.9721 + 6.63208i) q^{88} +(1.29494 - 1.49444i) q^{89} +(-6.80358 + 3.80912i) q^{90} -22.7737 q^{91} +(9.58400 - 0.383414i) q^{92} +(-10.9379 + 10.9379i) q^{93} +(7.71689 + 4.26321i) q^{94} +(2.89447 + 1.52268i) q^{95} +(1.26800 - 13.1642i) q^{96} +(8.74538 - 6.54671i) q^{97} +(-5.05718 + 10.9309i) q^{98} +(-12.2645 + 5.60103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{1}{22}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.391742	−	1.35887i	−0.277003	−	0.960869i
$2$	−0.391742	−	1.35887i	−0.277003	−	0.960869i
$3$	0.166783	+	2.33193i	0.0962923	+	1.34634i	0.784184	+	0.620529i	$0.213082\pi$
$3$	0.166783	+	2.33193i	0.0962923	+	1.34634i	−0.687892	+	0.725814i	$0.741464\pi$
$4$	−1.69308	+	1.06466i	−0.846538	+	0.532328i
$5$	0.194105	+	2.22763i	0.0868065	+	0.996225i
$5$	0.194105	+	2.22763i	0.0868065	+	0.996225i
$6$	3.10347	−	1.14015i	1.26699	−	0.465466i
$7$	−1.37657	+	3.69073i	−0.520295	+	1.39496i	0.365467	+	0.930824i	$0.380909\pi$
$7$	−1.37657	+	3.69073i	−0.520295	+	1.39496i	−0.885762	+	0.464140i	$0.846363\pi$
$8$	2.10998	+	1.88361i	0.745991	+	0.665956i
$9$	−2.44063	+	0.350910i	−0.813544	+	0.116970i
$10$	2.95103	−	1.13642i	0.933196	−	0.359367i
$11$	5.24665	−	1.54056i	1.58192	−	0.464495i	0.631481	−	0.775392i	$-0.282448\pi$
$11$	5.24665	−	1.54056i	1.58192	−	0.464495i	0.950444	+	0.310897i	$0.100629\pi$
$12$	−2.76508	−	3.77057i	−0.798211	−	1.08847i
$13$	2.02042	+	5.41695i	0.560363	+	1.50239i	0.840164	+	0.542333i	$0.182459\pi$
$13$	2.02042	+	5.41695i	0.560363	+	1.50239i	−0.279801	+	0.960058i	$0.590268\pi$
$14$	5.55450	+	0.424773i	1.48450	+	0.113525i
$15$	−5.16230	+	0.824171i	−1.33290	+	0.212800i
$16$	1.73302	−	3.60509i	0.433254	−	0.901272i
$17$	1.29226	+	0.281114i	0.313420	+	0.0681803i	0.366524	−	0.930409i	$-0.380548\pi$
$17$	1.29226	+	0.281114i	0.313420	+	0.0681803i	−0.0531041	+	0.998589i	$0.516911\pi$
$18$	1.43294	+	3.17904i	0.337747	+	0.749308i
$19$	0.790761	−	1.23045i	0.181413	−	0.282284i	−0.738622	−	0.674119i	$-0.764523\pi$
$19$	0.790761	−	1.23045i	0.181413	−	0.282284i	0.920035	+	0.391835i	$0.128160\pi$
$20$	−2.70029	−	3.56489i	−0.603804	−	0.797133i
$21$	−8.83612	−	2.59452i	−1.92820	−	0.566171i
$22$	−4.14875	−	6.52603i	−0.884517	−	1.39136i
$23$	−4.15866	−	2.38863i	−0.867141	−	0.498063i
$23$	−4.15866	−	2.38863i	−0.867141	−	0.498063i
$24$	−4.04054	+	5.23449i	−0.824771	+	1.06849i
$25$	−4.92465	+	0.864788i	−0.984929	+	0.172958i
$26$	6.56947	−	4.86754i	1.28838	−	0.954603i
$27$	0.265509	+	1.22052i	0.0510972	+	0.234890i
$28$	−1.59872	−	7.71426i	−0.302129	−	1.45786i
$29$	5.22979	−	3.36098i	0.971148	−	0.624119i	0.0440865	−	0.999028i	$-0.485962\pi$
$29$	5.22979	−	3.36098i	0.971148	−	0.624119i	0.927062	+	0.374909i	$0.122326\pi$
$30$	3.14224	+	6.69206i	0.573691	+	1.22180i
$31$	4.33286	+	5.00039i	0.778204	+	0.898096i	0.996978	−	0.0776799i	$-0.0247512\pi$
$31$	4.33286	+	5.00039i	0.778204	+	0.898096i	−0.218774	+	0.975776i	$0.570206\pi$
$32$	−5.57775	−	0.942685i	−0.986017	−	0.166645i
$33$	4.46752	+	11.9779i	0.777696	+	2.08508i
$34$	−0.124234	−	1.86615i	−0.0213060	−	0.320041i
$35$	−8.48877	−	2.35010i	−1.43486	−	0.397239i
$36$	3.75858	−	3.19255i	0.626429	−	0.532091i
$37$	1.32222	+	0.989802i	0.217372	+	0.162722i	0.702415	−	0.711768i	$-0.252105\pi$
$37$	1.32222	+	0.989802i	0.217372	+	0.162722i	−0.485043	+	0.874490i	$0.661196\pi$
$38$	−1.98180	−	0.592526i	−0.321490	−	0.0961204i
$39$	−12.2950	+	5.61493i	−1.96877	+	0.899109i
$40$	−3.78642	+	5.06587i	−0.598685	+	0.800985i
$41$	1.24547	−	8.66245i	0.194510	−	1.35285i	−0.625377	−	0.780323i	$-0.715055\pi$
$41$	1.24547	−	8.66245i	0.194510	−	1.35285i	0.819887	−	0.572525i	$-0.194036\pi$
$42$	−0.0641446	+	13.0236i	−0.00989773	+	2.00958i
$43$	−7.42225	+	0.530850i	−1.13188	+	0.0809538i	−0.624686	−	0.780876i	$-0.714773\pi$
$43$	−7.42225	+	0.530850i	−1.13188	+	0.0809538i	−0.507197	+	0.861830i	$0.669318\pi$
$44$	−7.24282	+	8.19415i	−1.09190	+	1.23532i
$45$	−1.25544	−	5.36870i	−0.187149	−	0.800319i
$46$	−1.61672	+	6.58682i	−0.238373	+	0.971174i
$47$	−4.40810	+	4.40810i	−0.642987	+	0.642987i	−0.951289	−	0.308302i	$-0.900239\pi$
$47$	−4.40810	+	4.40810i	−0.642987	+	0.642987i	0.308302	+	0.951289i	$0.400239\pi$
$48$	8.69586	+	3.44001i	1.25514	+	0.496522i
$49$	−6.43629	−	5.57708i	−0.919471	−	0.796726i
$50$	3.10433	+	6.35320i	0.439018	+	0.898478i
$51$	−0.440013	+	3.06035i	−0.0616141	+	0.428535i
$52$	−9.18791	−	7.02026i	−1.27413	−	0.973535i
$53$	4.75649	−	12.7527i	0.653355	−	1.75171i	−0.00611559	−	0.999981i	$-0.501947\pi$
$53$	4.75649	−	12.7527i	0.653355	−	1.75171i	0.659470	−	0.751731i	$-0.270781\pi$
$54$	1.55453	−	0.838923i	0.211544	−	0.114163i
$55$	4.45018	+	11.3885i	0.600063	+	1.53563i
$56$	−9.85643	+	5.19446i	−1.31712	+	0.694138i
$57$	3.00121	+	1.63878i	0.397520	+	0.217062i
$58$	−6.61588	−	5.78999i	−0.868708	−	0.760263i
$59$	0.332903	−	0.728955i	0.0433402	−	0.0949018i	−0.886723	−	0.462300i	$-0.847024\pi$
$59$	0.332903	−	0.728955i	0.0433402	−	0.0949018i	0.930064	+	0.367398i	$0.119751\pi$
$60$	7.86272	−	6.89146i	1.01507	−	0.889684i
$61$	0.0557293	+	0.0643150i	0.00713540	+	0.00823469i	0.759306	−	0.650734i	$-0.225539\pi$
$61$	0.0557293	+	0.0643150i	0.00713540	+	0.00823469i	−0.752171	+	0.658968i	$0.770993\pi$
$62$	5.09753	−	7.84667i	0.647387	−	0.996528i
$63$	2.06459	−	9.49076i	0.260114	−	1.19572i
$64$	0.904051	+	7.94875i	0.113006	+	0.993594i
$65$	−11.6748	+	5.55220i	−1.44808	+	0.688665i
$66$	14.5263	−	10.7630i	1.78807	−	1.32484i
$67$	−0.289707	+	0.158192i	−0.0353933	+	0.0193262i	−0.496848	−	0.867837i	$-0.665509\pi$
$67$	−0.289707	+	0.158192i	−0.0353933	+	0.0193262i	0.461455	+	0.887164i	$0.347328\pi$
$68$	−2.48719	+	0.899867i	−0.301616	+	0.109125i
$69$	4.87653	−	10.0961i	0.587065	−	1.21543i
$70$	0.131922	+	12.4558i	0.0157677	+	1.48875i
$71$	−0.431678	−	0.126752i	−0.0512307	−	0.0150427i	0.256017	−	0.966672i	$-0.417590\pi$
$71$	−0.431678	−	0.126752i	−0.0512307	−	0.0150427i	−0.307248	+	0.951630i	$0.599408\pi$
$72$	−5.81066	−	3.85678i	−0.684793	−	0.454525i
$73$	−2.23979	−	10.2962i	−0.262148	−	1.20508i	−0.900336	−	0.435195i	$-0.856679\pi$
$73$	−2.23979	−	10.2962i	−0.262148	−	1.20508i	0.638188	−	0.769880i	$-0.279684\pi$
$74$	0.827046	−	2.18448i	0.0961422	−	0.253940i
$75$	−2.83798	−	11.3397i	−0.327701	−	1.30940i
$76$	−0.0288148	+	2.92513i	−0.00330529	+	0.335536i
$77$	−1.53661	+	21.4846i	−0.175113	+	2.44840i
$78$	12.4465	+	14.5077i	1.40928	+	1.64268i
$79$	0.146226	−	0.320189i	0.0164517	−	0.0360241i	−0.901228	−	0.433346i	$-0.857333\pi$
$79$	0.146226	−	0.320189i	0.0164517	−	0.0360241i	0.917679	+	0.397322i	$0.130060\pi$
$80$	8.36718	+	3.16075i	0.935479	+	0.353382i
$81$	−9.89944	+	2.90674i	−1.09994	+	0.322971i
$82$	−12.2591	+	1.70101i	−1.35379	+	0.187845i
$83$	−0.911814	+	1.21804i	−0.100085	+	0.133697i	−0.847788	−	0.530336i	$-0.822066\pi$
$83$	−0.911814	+	1.21804i	−0.100085	+	0.133697i	0.747703	+	0.664033i	$0.231157\pi$
$84$	17.7225	−	5.01471i	1.93368	−	0.547150i
$85$	−0.375383	+	2.93324i	−0.0407160	+	0.318155i
$86$	3.62896	+	9.87794i	0.391321	+	1.06517i
$87$	8.70983	+	11.6350i	0.933792	+	1.24740i
$88$	13.9721	+	6.63208i	1.48943	+	0.706982i
$89$	1.29494	−	1.49444i	0.137263	−	0.158410i	−0.682956	−	0.730460i	$-0.739306\pi$
$89$	1.29494	−	1.49444i	0.137263	−	0.158410i	0.820219	+	0.572049i	$0.193851\pi$
$90$	−6.80358	+	3.80912i	−0.717161	+	0.401517i
$91$	−22.7737			−2.38734
$92$	9.58400	−	0.383414i	0.999201	−	0.0399736i
$93$	−10.9379	+	10.9379i	−1.13421	+	1.13421i
$94$	7.71689	+	4.26321i	0.795936	+	0.439717i
$95$	2.89447	+	1.52268i	0.296966	+	0.156224i
$96$	1.26800	−	13.1642i	0.129415	−	1.34356i
$97$	8.74538	−	6.54671i	0.887959	−	0.664718i	−0.0546899	−	0.998503i	$-0.517417\pi$
$97$	8.74538	−	6.54671i	0.887959	−	0.664718i	0.942649	+	0.333785i	$0.108326\pi$
$98$	−5.05718	+	10.9309i	−0.510853	+	1.10419i
$99$	−12.2645	+	5.60103i	−1.23263	+	0.562924i
$100$	7.41710	−	6.70721i	0.741710	−	0.670721i
$101$	7.39920	−	1.06384i	0.736248	−	0.105856i	0.236017	−	0.971749i	$-0.424158\pi$
$101$	7.39920	−	1.06384i	0.736248	−	0.105856i	0.500230	+	0.865892i	$0.333249\pi$
$102$	4.33101	−	0.600948i	0.428834	−	0.0595027i
$103$	1.32964	−	2.43505i	0.131013	−	0.239933i	−0.803935	−	0.594717i	$-0.797264\pi$
$103$	1.32964	−	2.43505i	0.131013	−	0.239933i	0.934948	+	0.354785i	$0.115446\pi$
$104$	−5.94036	+	15.2353i	−0.582500	+	1.49395i
$105$	4.06449	−	20.1872i	0.396653	−	1.97007i
$106$	−19.1926	−	1.46773i	−1.86415	−	0.142558i
$107$	4.27116	+	0.305480i	0.412909	+	0.0295318i	0.276249	−	0.961086i	$-0.410909\pi$
$107$	4.27116	+	0.305480i	0.412909	+	0.0295318i	0.136660	+	0.990618i	$0.456363\pi$
$108$	−1.74896	−	1.78376i	−0.168294	−	0.171643i
$109$	4.27338	+	6.64952i	0.409316	+	0.636908i	0.983307	−	0.181953i	$-0.0582420\pi$
$109$	4.27338	+	6.64952i	0.409316	+	0.636908i	−0.573991	+	0.818861i	$0.694606\pi$
$110$	13.7323	−	10.5086i	1.30932	−	1.00196i
$111$	−2.08763	+	3.24841i	−0.198149	+	0.308326i
$112$	10.9198	+	11.3588i	1.03182	+	1.07330i
$113$	6.05394	−	3.30570i	0.569507	−	0.310974i	−0.168571	−	0.985689i	$-0.553915\pi$
$113$	6.05394	−	3.30570i	0.569507	−	0.310974i	0.738078	+	0.674715i	$0.235734\pi$
$114$	1.05120	−	4.72024i	0.0984540	−	0.442091i
$115$	4.51375	−	9.72759i	0.420910	−	0.907103i
$116$	−5.27615	+	11.2583i	−0.489878	+	1.04531i
$117$	−6.83195	−	12.5118i	−0.631614	−	1.15672i
$118$	−1.12097	−	0.166810i	−0.103194	−	0.0153561i
$119$	−2.81641	+	4.38242i	−0.258180	+	0.401736i
$120$	−12.4448	−	7.98476i	−1.13605	−	0.728906i
$121$	15.9002	−	10.2185i	1.44547	−	0.928950i
$122$	0.0655645	−	0.100924i	0.00593593	−	0.00913722i
$123$	20.4080	+	1.45961i	1.84013	+	0.131608i
$124$	−12.6596	−	3.85303i	−1.13686	−	0.346012i
$125$	−2.88233	−	10.8024i	−0.257803	−	0.966197i
$126$	−13.7055	+	0.912414i	−1.22099	+	0.0812843i
$127$	9.71623	−	17.7939i	0.862176	−	1.57896i	0.0476245	−	0.998865i	$-0.484835\pi$
$127$	9.71623	−	17.7939i	0.862176	−	1.57896i	0.814551	−	0.580092i	$-0.196983\pi$
$128$	10.4472	−	4.34235i	0.923411	−	0.383813i
$129$	−2.47581	−	17.2197i	−0.217983	−	1.51611i
$130$	12.1182	+	13.6895i	1.06284	+	1.20065i
$131$	−4.00150	+	1.82743i	−0.349613	+	0.159663i	−0.582479	−	0.812846i	$-0.697917\pi$
$131$	−4.00150	+	1.82743i	−0.349613	+	0.159663i	0.232866	+	0.972509i	$0.425190\pi$
$132$	−20.3162	−	15.5231i	−1.76830	−	1.35111i
$133$	3.45271	+	4.61228i	0.299388	+	0.399936i
$134$	0.328453	+	0.331705i	0.0283740	+	0.0286549i
$135$	−2.66733	+	0.828364i	−0.229568	+	0.0712942i
$136$	2.19714	+	3.02726i	0.188403	+	0.259585i
$137$	4.03003	+	4.03003i	0.344309	+	0.344309i	0.857984	−	0.513676i	$-0.171717\pi$
$137$	4.03003	+	4.03003i	0.344309	+	0.344309i	−0.513676	+	0.857984i	$0.671717\pi$
$138$	−15.6297	−	2.67152i	−1.33049	−	0.227415i
$139$	10.2859			0.872441			0.436220	−	0.899840i	$-0.356317\pi$
$139$	10.2859			0.872441			0.436220	+	0.899840i	$0.356317\pi$
$140$	16.8742	−	5.05873i	1.42613	−	0.427540i
$141$	−11.0146	−	9.54419i	−0.927595	−	0.803766i
$142$	−0.00313370	+	0.636250i	−0.000262975	+	0.0533929i
$143$	18.9455	+	25.3083i	1.58430	+	2.11638i
$144$	−2.96459	+	9.40682i	−0.247049	+	0.783902i
$145$	8.50215	+	10.9976i	0.706065	+	0.913305i
$146$	−13.1138	+	7.07704i	−1.08530	+	0.585700i
$147$	11.9319	−	15.9392i	0.984128	−	1.31464i
$148$	−3.29242	−	0.268100i	−0.270635	−	0.0220377i
$149$	−1.16466	−	3.96646i	−0.0954125	−	0.324945i	0.897931	−	0.440137i	$-0.145070\pi$
$149$	−1.16466	−	3.96646i	−0.0954125	−	0.324945i	−0.993343	+	0.115192i	$0.963252\pi$
$150$	−14.2975	+	8.29869i	−1.16738	+	0.677586i
$151$	−4.33761	+	9.49804i	−0.352990	+	0.772939i	0.646956	+	0.762527i	$0.276042\pi$
$151$	−4.33761	+	9.49804i	−0.352990	+	0.772939i	−0.999946	+	0.0104121i	$0.996686\pi$
$152$	3.98617	−	1.10674i	0.323321	−	0.0897685i
$153$	−3.25258	−	0.232629i	−0.262956	−	0.0188070i
$154$	29.7969	−	6.32838i	2.40110	−	0.509955i
$155$	−10.2980	+	10.6226i	−0.827152	+	0.853227i
$156$	14.8384	−	22.5964i	1.18802	−	1.80916i
$157$	−16.0453	+	3.49043i	−1.28055	+	0.278567i	−0.800850	−	0.598865i	$-0.795618\pi$
$157$	−16.0453	+	3.49043i	−1.28055	+	0.278567i	−0.479701	+	0.877432i	$0.659255\pi$
$158$	−0.492380	−	0.0732705i	−0.0391716	−	0.00582909i
$159$	30.5316	+	8.96490i	2.42132	+	0.710963i
$160$	1.01728	−	12.6081i	0.0804230	−	0.996761i
$161$	14.5405	−	12.0604i	1.14595	−	0.950491i
$162$	7.82792	+	12.3134i	0.615019	+	0.967432i
$163$	−14.2452	+	7.77844i	−1.11577	+	0.609255i	−0.927859	−	0.372932i	$-0.878353\pi$
$163$	−14.2452	+	7.77844i	−1.11577	+	0.609255i	−0.187908	+	0.982187i	$0.560171\pi$
$164$	7.11385	+	15.9922i	0.555499	+	1.24878i
$165$	−25.8151	+	12.2770i	−2.00970	+	0.955759i
$166$	2.01236	+	0.761883i	0.156189	+	0.0591336i
$167$	−0.109352	+	0.502681i	−0.00846188	+	0.0388986i	−0.981184	−	0.193074i	$-0.938154\pi$
$167$	−0.109352	+	0.502681i	−0.00846188	+	0.0388986i	0.972722	+	0.231972i	$0.0745179\pi$
$168$	−13.7570	−	22.1182i	−1.06138	−	1.70645i
$169$	−15.4365	+	13.3758i	−1.18742	+	1.02891i
$170$	4.13296	−	0.638977i	0.316984	−	0.0490073i
$171$	−1.49818	+	3.28056i	−0.114569	+	0.250870i
$172$	12.0013	−	8.80091i	0.915088	−	0.671063i
$173$	1.63313	−	2.99086i	0.124165	−	0.227391i	−0.808201	−	0.588906i	$-0.799559\pi$
$173$	1.63313	−	2.99086i	0.124165	−	0.227391i	0.932366	+	0.361516i	$0.117741\pi$
$174$	12.3985	−	16.3935i	0.939924	−	1.24279i
$175$	3.58743	−	19.3660i	0.271184	−	1.46393i
$176$	3.53869	−	21.5844i	0.266739	−	1.62699i
$177$	1.75540	+	0.654729i	0.131944	+	0.0492124i
$178$	−2.53804	−	1.17423i	−0.190234	−	0.0880119i
$179$	−0.122313	+	0.850705i	−0.00914210	+	0.0635847i	−0.993882	−	0.110449i	$-0.964771\pi$
$179$	−0.122313	+	0.850705i	−0.00914210	+	0.0635847i	0.984740	+	0.174034i	$0.0556802\pi$
$180$	7.84137	+	7.75302i	0.584461	+	0.577876i
$181$	10.9534	−	12.6409i	0.814157	−	0.939588i	−0.184910	−	0.982755i	$-0.559199\pi$
$181$	10.9534	−	12.6409i	0.814157	−	0.939588i	0.999068	+	0.0431676i	$0.0137450\pi$
$182$	8.92143	+	30.9466i	0.661301	+	2.29392i
$183$	−0.140684	+	0.140684i	−0.0103996	+	0.0103996i
$184$	−4.27547	−	12.8732i	−0.315191	−	0.949028i
$185$	−1.94826	+	3.13754i	−0.143239	+	0.230676i
$186$	19.1481	+	10.5784i	1.40401	+	0.775646i
$187$	7.21312	−	0.515892i	0.527476	−	0.0377258i
$188$	2.77014	−	12.1564i	0.202033	−	0.886593i
$189$	−4.87011	−	0.700217i	−0.354249	−	0.0509333i
$190$	0.935250	−	4.52972i	0.0678502	−	0.328620i
$191$	−18.0004	+	8.22050i	−1.30246	+	0.594814i	−0.941263	−	0.337675i	$-0.890360\pi$
$191$	−18.0004	+	8.22050i	−1.30246	+	0.594814i	−0.361199	+	0.932489i	$0.617632\pi$
$192$	−18.3852	+	3.43390i	−1.32684	+	0.247821i
$193$	−6.61088	+	8.83111i	−0.475862	+	0.635677i	−0.972672	−	0.232182i	$-0.925413\pi$
$193$	−6.61088	+	8.83111i	−0.475862	+	0.635677i	0.496811	+	0.867859i	$0.334504\pi$
$194$	−12.3221	−	9.31925i	−0.884675	−	0.669083i
$195$	−14.8945	−	26.2988i	−1.06662	−	1.88329i
$196$	16.8348	+	2.58998i	1.20249	+	0.184999i
$197$	16.4378	−	6.13097i	1.17114	−	0.436814i	0.312765	−	0.949831i	$-0.398745\pi$
$197$	16.4378	−	6.13097i	1.17114	−	0.436814i	0.858379	+	0.513017i	$0.171472\pi$
$198$	12.4156	+	14.4718i	0.882340	+	1.02847i
$199$	−10.2145	−	11.7881i	−0.724084	−	0.835638i	0.267707	−	0.963500i	$-0.413734\pi$
$199$	−10.2145	−	11.7881i	−0.724084	−	0.835638i	−0.991792	+	0.127862i	$0.959188\pi$
$200$	−12.0198	−	7.45141i	−0.849931	−	0.526894i
$201$	−0.417211	−	0.649193i	−0.0294278	−	0.0457906i
$202$	−4.34421	−	9.63782i	−0.305657	−	0.678115i
$203$	5.20530	+	23.9284i	0.365341	+	1.67944i
$204$	−2.51325	−	5.64988i	−0.175963	−	0.395570i
$205$	19.5385	+	1.09302i	1.36463	+	0.0763399i
$206$	−3.82980	−	0.852899i	−0.266835	−	0.0594243i
$207$	10.9879	+	4.37044i	0.763715	+	0.303767i
$208$	23.0300	+	2.10387i	1.59684	+	0.145877i
$209$	2.25327	−	7.67394i	0.155862	−	0.530818i
$210$	−29.0241	+	2.38505i	−2.00285	+	0.164584i
$211$	11.4136	−	17.7599i	0.785745	−	1.22264i	−0.185049	−	0.982729i	$-0.559244\pi$
$211$	11.4136	−	17.7599i	0.785745	−	1.22264i	0.970794	−	0.239914i	$-0.0771192\pi$
$212$	5.52408	+	26.6552i	0.379395	+	1.83069i
$213$	0.223581	−	1.02778i	0.0153195	−	0.0704226i
$214$	−1.25809	−	5.92364i	−0.0860009	−	0.404932i
$215$	−2.62323	−	16.4310i	−0.178903	−	1.12058i
$216$	−1.73877	+	3.07540i	−0.118308	+	0.209254i
$217$	−24.4196	+	9.10803i	−1.65771	+	0.618293i
$218$	7.36179	−	8.41188i	0.498603	−	0.569725i
$219$	23.6364	−	6.94028i	1.59720	−	0.468980i
$220$	−19.6594	−	14.5438i	−1.32544	−	0.980541i
$221$	1.08813	+	7.56809i	0.0731953	+	0.509085i
$222$	5.23199	+	1.56428i	0.351148	+	0.104988i
$223$	1.02643	−	2.75197i	0.0687349	−	0.184285i	−0.898040	−	0.439913i	$-0.855009\pi$
$223$	1.02643	−	2.75197i	0.0687349	−	0.184285i	0.966775	+	0.255627i	$0.0822820\pi$
$224$	11.1574	−	19.2883i	0.745483	−	1.28875i
$225$	11.7158	−	3.83874i	0.781052	−	0.255916i
$226$	−6.86361	−	6.93156i	−0.456561	−	0.461081i
$227$	1.10736	+	15.4829i	0.0734982	+	1.02764i	0.891676	+	0.452674i	$0.149530\pi$
$227$	1.10736	+	15.4829i	0.0734982	+	1.02764i	−0.818178	+	0.574965i	$0.805016\pi$
$228$	−6.82602	+	0.420668i	−0.452064	+	0.0278594i
$229$			29.5066i			1.94985i	0.222535	+	0.974925i	$0.428567\pi$
$229$			29.5066i			1.94985i	−0.222535	+	0.974925i	$0.571433\pi$
$230$	−14.9868	−	2.32292i	−0.988200	−	0.153169i
$231$	−50.3570			−3.31325
$232$	17.3655	+	2.75926i	1.14010	+	0.181154i
$233$	4.20914	−	0.301044i	0.275750	−	0.0197220i	0.0672206	−	0.997738i	$-0.478587\pi$
$233$	4.20914	−	0.301044i	0.275750	−	0.0197220i	0.208529	+	0.978016i	$0.433132\pi$
$234$	−14.3256	+	14.1852i	−0.936492	+	0.927313i
$235$	−10.6752	−	8.96396i	−0.696376	−	0.584745i
$236$	0.212457	+	1.58860i	0.0138298	+	0.103409i
$237$	0.771048	+	0.287586i	0.0500850	+	0.0186807i
$238$	7.05846	+	2.11037i	0.457532	+	0.136795i
$239$	−29.4304	+	4.23146i	−1.90370	+	0.273710i	−0.990889	−	0.134680i	$-0.956999\pi$
$239$	−29.4304	+	4.23146i	−1.90370	+	0.273710i	−0.912807	+	0.408390i	$0.866090\pi$
$240$	−5.97514	+	20.0389i	−0.385694	+	1.29350i
$241$	0.0808054	+	0.275198i	0.00520513	+	0.0177271i	0.962055	−	0.272857i	$-0.0879686\pi$
$241$	0.0808054	+	0.275198i	0.00520513	+	0.0177271i	−0.956849	+	0.290584i	$0.906150\pi$
$242$	−20.1144	−	17.6034i	−1.29300	−	1.13159i
$243$	−7.11987	−	19.0891i	−0.456740	−	1.22457i
$244$	−0.162827	−	0.0495577i	−0.0104239	−	0.00317261i
$245$	11.1743	−	15.4202i	0.713902	−	0.985161i
$246$	−6.01124	−	28.3037i	−0.383263	−	1.80458i
$247$	8.26294	+	1.79749i	0.525758	+	0.114372i
$248$	−0.276505	+	18.7121i	−0.0175581	+	1.18822i
$249$	−2.99247	−	1.92314i	−0.189640	−	0.121874i
$250$	−13.5500	+	8.14848i	−0.856977	+	0.515355i
$251$	22.6725	+	6.65726i	1.43108	+	0.420202i	0.903238	−	0.429141i	$-0.141184\pi$
$251$	22.6725	+	6.65726i	1.43108	+	0.420202i	0.527841	+	0.849343i	$0.323002\pi$
$252$	6.60889	+	18.2667i	0.416321	+	1.15069i
$253$	−25.4988	−	6.12564i	−1.60310	−	0.385116i
$254$	−27.9860	−	6.23249i	−1.75600	−	0.391061i
$255$	−6.90274	−	0.386153i	−0.432266	−	0.0241818i
$256$	−9.99332	−	12.4953i	−0.624582	−	0.780959i
$257$	−16.4680	+	3.58240i	−1.02725	+	0.223464i	−0.694455	−	0.719536i	$-0.744354\pi$
$257$	−16.4680	+	3.58240i	−1.02725	+	0.223464i	−0.332792	+	0.943000i	$0.607991\pi$
$258$	−22.4295	+	10.1100i	−1.39640	+	0.629420i
$259$	−5.47322	+	3.51743i	−0.340089	+	0.218562i
$260$	13.8551	−	21.8299i	0.859257	−	1.35383i
$261$	−11.5846	+	10.0381i	−0.717068	+	0.621343i
$262$	4.05080	+	4.72166i	0.250259	+	0.291705i
$263$	4.73381	+	12.6918i	0.291899	+	0.782613i	0.997275	+	0.0737785i	$0.0235058\pi$
$263$	4.73381	+	12.6918i	0.291899	+	0.782613i	−0.705375	+	0.708834i	$0.749221\pi$
$264$	−13.1352	+	33.6882i	−0.808419	+	2.07337i
$265$	29.3314	+	8.12034i	1.80181	+	0.498828i
$266$	4.91494	−	6.49863i	0.301354	−	0.398456i
$267$	3.70091	+	2.77047i	0.226492	+	0.169550i
$268$	0.322076	−	0.576269i	0.0196739	−	0.0352012i
$269$	−0.844988	−	1.85027i	−0.0515199	−	0.112813i	0.882122	−	0.471022i	$-0.156115\pi$
$269$	−0.844988	−	1.85027i	−0.0515199	−	0.112813i	−0.933641	+	0.358209i	$0.883387\pi$
$270$	2.17055	+	3.30007i	0.132095	+	0.200836i
$271$	−0.525608	+	3.65568i	−0.0319284	+	0.222067i	−0.999538	−	0.0303831i	$-0.990327\pi$
$271$	−0.525608	+	3.65568i	−0.0319284	+	0.222067i	0.967610	+	0.252450i	$0.0812364\pi$
$272$	3.25295	−	4.17154i	0.197239	−	0.252937i
$273$	−3.79828	−	53.1068i	−0.229882	−	3.21417i
$274$	3.89757	−	7.05503i	0.235461	−	0.426210i
$275$	−24.5056	+	12.1239i	−1.47775	+	0.731100i
$276$	2.49254	+	22.2853i	0.150034	+	1.34142i
$277$	−20.2347	−	20.2347i	−1.21579	−	1.21579i	−0.969094	−	0.246694i	$-0.920656\pi$
$277$	−20.2347	−	20.2347i	−1.21579	−	1.21579i	−0.246694	−	0.969094i	$-0.579344\pi$
$278$	−4.02943	−	13.9773i	−0.241669	−	0.838301i
$279$	−12.3296	−	10.6837i	−0.738153	−	0.639613i
$280$	−13.4845	−	20.9482i	−0.805853	−	1.25189i
$281$	6.00555	+	0.863468i	0.358261	+	0.0515102i	0.319096	−	0.947723i	$-0.396621\pi$
$281$	6.00555	+	0.863468i	0.358261	+	0.0515102i	0.0391657	+	0.999233i	$0.487530\pi$
$282$	−8.65448	+	18.7063i	−0.515367	+	1.11394i
$283$	5.79455	−	15.5358i	0.344450	−	0.923507i	−0.643041	−	0.765832i	$-0.722328\pi$
$283$	5.79455	−	15.5358i	0.344450	−	0.923507i	0.987491	−	0.157675i	$-0.0503998\pi$
$284$	0.865811	−	0.244987i	0.0513764	−	0.0145373i
$285$	−3.06805	+	7.00367i	−0.181736	+	0.414862i
$286$	26.9690	−	35.6589i	1.59471	−	2.10855i
$287$	30.2563	+	16.5212i	1.78597	+	0.975215i
$288$	13.9440	+	0.343458i	0.821660	+	0.0202384i
$289$	−13.8728	−	6.33551i	−0.816049	−	0.372677i
$290$	11.6138	−	15.8616i	0.681984	−	0.931425i
$291$	16.7251	+	19.3018i	0.980441	+	1.13149i
$292$	14.7540	+	15.0476i	0.863414	+	0.880593i
$293$	11.2789	+	2.45357i	0.658920	+	0.143339i	0.529579	−	0.848261i	$-0.322350\pi$
$293$	11.2789	+	2.45357i	0.658920	+	0.143339i	0.129341	+	0.991600i	$0.458714\pi$
$294$	−26.3336	−	9.96992i	−1.53580	−	0.581458i
$295$	1.68846	+	0.600089i	0.0983058	+	0.0349385i
$296$	0.925464	+	4.57901i	0.0537915	+	0.266149i
$297$	3.27331	+	5.99463i	0.189937	+	0.347844i
$298$	−4.93367	+	3.13645i	−0.285800	+	0.181690i
$299$	4.53684	−	27.3533i	0.262372	−	1.58188i
$300$	16.8778	+	16.1775i	0.974440	+	0.934010i
$301$	8.25803	−	28.1243i	0.475985	−	1.62106i
$302$	14.6059	+	2.17348i	0.840473	+	0.125070i
$303$	3.71487	+	17.0770i	0.213414	+	0.981048i
$304$	−3.06547	−	4.98315i	−0.175817	−	0.285803i
$305$	−0.132453	+	0.136628i	−0.00758421	+	0.00782329i
$306$	0.958059	+	4.51098i	0.0547686	+	0.257875i
$307$	−0.426780	+	5.96717i	−0.0243576	+	0.340564i	0.970631	+	0.240574i	$0.0773357\pi$
$307$	−0.426780	+	5.96717i	−0.0243576	+	0.340564i	−0.994988	+	0.0999903i	$0.968119\pi$
$308$	−20.2722	−	38.0111i	−1.15511	−	2.16588i
$309$	5.90014	+	2.69450i	0.335647	+	0.153285i
$310$	18.4689	+	9.83232i	1.04896	+	0.558438i
$311$	−8.97238	+	2.63453i	−0.508777	+	0.149390i	−0.526039	−	0.850461i	$-0.676323\pi$
$311$	−8.97238	+	2.63453i	−0.508777	+	0.149390i	0.0172617	+	0.999851i	$0.494505\pi$
$312$	−36.5185	−	11.3115i	−2.06746	−	0.640389i
$313$	15.0228	+	11.2459i	0.849141	+	0.635659i	0.932624	−	0.360851i	$-0.117514\pi$
$313$	15.0228	+	11.2459i	0.849141	+	0.635659i	−0.0834831	+	0.996509i	$0.526604\pi$
$314$	11.0287	+	20.4361i	0.622383	+	1.15328i
$315$	21.5426	+	2.75693i	1.21379	+	0.155335i
$316$	0.0933204	+	0.697785i	0.00524969	+	0.0392535i
$317$	−14.3718	+	10.7586i	−0.807203	+	0.604265i	−0.921144	−	0.389223i	$-0.872744\pi$
$317$	−14.3718	+	10.7586i	−0.807203	+	0.604265i	0.113940	+	0.993488i	$0.463653\pi$
$318$	0.221640	−	45.0006i	0.0124290	−	2.52351i
$319$	22.2611	−	25.6907i	1.24638	−	1.43840i
$320$	−17.5314	+	3.55678i	−0.980034	+	0.198830i
$321$			10.0110i			0.558760i
$322$	−22.0846	−	15.0341i	−1.23073	−	0.837818i
$323$	1.36777	−	1.36777i	0.0761046	−	0.0761046i
$324$	13.6658	−	15.4608i	0.759213	−	0.858935i
$325$	−14.6344	−	24.9293i	−0.811768	−	1.38283i
$326$	16.1503	+	16.3102i	0.894485	+	0.903340i
$327$	−14.7935	+	11.0743i	−0.818082	+	0.612409i
$328$	18.9446	−	15.9316i	1.04604	−	0.879678i
$329$	−10.2010	−	22.3372i	−0.562402	−	1.23149i
$330$	26.7957	+	30.2701i	1.47505	+	1.66631i
$331$	2.23612	−	0.321506i	0.122908	−	0.0176716i	−0.0805861	−	0.996748i	$-0.525679\pi$
$331$	2.23612	−	0.321506i	0.122908	−	0.0176716i	0.203494	+	0.979076i	$0.434770\pi$
$332$	0.246976	−	3.03301i	0.0135546	−	0.166458i
$333$	−3.57438	−	1.95176i	−0.195875	−	0.106956i
$334$	0.725918	−	0.0483263i	0.0397205	−	0.00264430i
$335$	−0.408626	−	0.614653i	−0.0223256	−	0.0335821i
$336$	−24.6666	+	27.3587i	−1.34567	+	1.49254i
$337$	1.22684	−	17.1534i	0.0668301	−	0.934407i	−0.847852	−	0.530233i	$-0.822104\pi$
$337$	1.22684	−	17.1534i	0.0668301	−	0.934407i	0.914682	−	0.404174i	$-0.132441\pi$
$338$	24.2232	+	15.7364i	1.31757	+	0.855947i
$339$	8.71837	+	13.5660i	0.473517	+	0.736807i
$340$	−2.48734	−	5.36586i	−0.134895	−	0.291005i
$341$	30.4364	+	19.5603i	1.64822	+	1.05925i
$342$	5.04476	+	0.750705i	0.272789	+	0.0405935i
$343$	5.24272	−	2.86274i	0.283080	−	0.154573i
$344$	−16.6607	−	12.8605i	−0.898286	−	0.693393i
$345$	23.4369	+	8.90337i	1.26180	+	0.479342i
$346$	−4.70396	−	1.04758i	−0.252887	−	0.0563180i
$347$	11.9932	+	21.9640i	0.643831	+	1.17909i	0.972114	+	0.234508i	$0.0753481\pi$
$347$	11.9932	+	21.9640i	0.643831	+	1.17909i	−0.328283	+	0.944579i	$0.606470\pi$
$348$	−27.1337	−	10.4259i	−1.45452	−	0.558888i
$349$	−22.1108	−	14.2098i	−1.18357	−	0.760632i	−0.207527	−	0.978229i	$-0.566542\pi$
$349$	−22.1108	−	14.2098i	−1.18357	−	0.760632i	−0.976039	+	0.217598i	$0.930178\pi$
$350$	−27.7213	+	2.71161i	−1.48176	+	0.144942i
$351$	−6.07508	+	3.90421i	−0.324264	+	0.208392i
$352$	−30.7168	+	3.64690i	−1.63721	+	0.194380i
$353$	1.28397	−	17.9522i	0.0683388	−	0.955502i	−0.841425	−	0.540375i	$-0.818283\pi$
$353$	1.28397	−	17.9522i	0.0683388	−	0.955502i	0.909763	−	0.415127i	$-0.136263\pi$
$354$	0.202032	−	2.64185i	0.0107379	−	0.140413i
$355$	0.198565	−	0.986220i	0.0105388	−	0.0523431i
$356$	−0.601368	+	3.90887i	−0.0318724	+	0.207170i
$357$	−10.6892	−	5.83676i	−0.565734	−	0.308914i
$358$	1.20392	−	0.167049i	0.0636290	−	0.00882882i
$359$	3.09574	+	21.5313i	0.163387	+	1.13638i	0.892191	+	0.451658i	$0.149167\pi$
$359$	3.09574	+	21.5313i	0.163387	+	1.13638i	−0.728804	+	0.684722i	$0.759924\pi$
$360$	7.46358	−	13.6926i	0.393365	−	0.721664i
$361$	7.00419	+	15.3370i	0.368641	+	0.807212i
$362$	−21.4682	−	9.93229i	−1.12835	−	0.522030i
$363$	26.4806	+	35.3740i	1.38987	+	1.85665i
$364$	38.5577	−	24.2462i	2.02097	−	1.27085i
$365$	22.5013	−	6.98797i	1.17777	−	0.365767i
$366$	0.246283	+	0.136060i	0.0128734	+	0.00711195i
$367$	−2.05688	−	2.05688i	−0.107368	−	0.107368i	0.651382	−	0.758750i	$-0.274190\pi$
$367$	−2.05688	−	2.05688i	−0.107368	−	0.107368i	−0.758750	+	0.651382i	$0.774190\pi$
$368$	−15.8182	+	10.8528i	−0.824582	+	0.565742i
$369$			21.5789i			1.12335i
$370$	5.02674	+	1.41833i	0.261328	+	0.0737356i
$371$	40.5190	+	35.1099i	2.10364	+	1.82281i
$372$	6.87361	−	30.1638i	0.356380	−	1.56392i
$373$	−2.10967	+	1.57928i	−0.109235	+	0.0817722i	−0.652499	−	0.757790i	$-0.726279\pi$
$373$	−2.10967	+	1.57928i	−0.109235	+	0.0817722i	0.543264	+	0.839562i	$0.317188\pi$
$374$	−3.52671	−	9.59962i	−0.182362	−	0.496385i
$375$	24.7098	−	8.52305i	1.27601	−	0.440129i
$376$	−17.6041	+	0.997885i	−0.907864	+	0.0514620i
$377$	28.7726	+	21.5389i	1.48187	+	1.10931i
$378$	0.956322	+	6.89218i	0.0491879	+	0.354495i
$379$	−6.27862	−	21.3830i	−0.322511	−	1.09837i	−0.948035	−	0.318167i	$-0.896933\pi$
$379$	−6.27862	−	21.3830i	−0.322511	−	1.09837i	0.625523	−	0.780205i	$-0.284885\pi$
$380$	−6.52169	+	0.503595i	−0.334556	+	0.0258339i
$381$	43.1148	+	19.6899i	2.20884	+	1.00874i
$382$	18.2221	+	21.2399i	0.932325	+	1.08673i
$383$	10.5522	+	0.754706i	0.539191	+	0.0385637i	0.338279	−	0.941046i	$-0.390155\pi$
$383$	10.5522	+	0.754706i	0.539191	+	0.0385637i	0.200911	+	0.979609i	$0.435610\pi$
$384$	11.8685	+	23.6379i	0.605661	+	1.20627i
$385$	−48.1581	+	0.747284i	−2.45436	+	0.0380851i
$386$	14.5901	+	5.52384i	0.742618	+	0.281156i
$387$	17.9287	−	3.90015i	0.911366	−	0.198256i
$388$	−7.83661	+	20.3949i	−0.397843	+	1.03539i
$389$	−5.94576	+	20.2494i	−0.301462	+	1.02669i	0.659890	+	0.751362i	$0.270603\pi$
$389$	−5.94576	+	20.2494i	−0.301462	+	1.02669i	−0.961352	+	0.275323i	$0.911215\pi$
$390$	−29.9019	+	30.5421i	−1.51414	+	1.54656i
$391$	−4.70260	−	4.25579i	−0.237821	−	0.215225i
$392$	−3.07544	−	23.8910i	−0.155333	−	1.20668i
$393$	−4.92882	−	9.02646i	−0.248626	−	0.455324i
$394$	−14.7706	−	19.9351i	−0.744131	−	1.00432i
$395$	0.741646	+	0.263586i	0.0373163	+	0.0132624i
$396$	14.8016	−	22.5405i	0.743810	−	1.13270i
$397$	33.1736	+	7.21647i	1.66494	+	0.362184i	0.943776	−	0.330585i	$-0.107246\pi$
$397$	33.1736	+	7.21647i	1.66494	+	0.362184i	0.721159	+	0.692770i	$0.243610\pi$
$398$	−12.0171	+	18.4981i	−0.602365	+	0.927225i
$399$	−10.1797	+	8.82075i	−0.509622	+	0.441590i
$400$	−5.41685	+	19.2525i	−0.270842	+	0.962624i
$401$	−2.23676	−	1.02149i	−0.111698	−	0.0510110i	0.358782	−	0.933421i	$-0.383192\pi$
$401$	−2.23676	−	1.02149i	−0.111698	−	0.0510110i	−0.470481	+	0.882410i	$0.655919\pi$
$402$	−0.718733	+	0.821254i	−0.0358471	+	0.0409604i
$403$	−18.3326	+	33.5737i	−0.913214	+	1.67243i
$404$	−11.3948	+	9.67877i	−0.566911	+	0.481537i
$405$	−8.39666	−	21.4881i	−0.417234	−	1.06775i
$406$	30.4765	−	16.4471i	1.51252	−	0.816256i
$407$	8.46207	+	3.15619i	0.419449	+	0.156446i
$408$	−6.69292	+	5.62848i	−0.331349	+	0.278651i
$409$	25.4965	+	3.66585i	1.26072	+	0.181264i	0.740085	−	0.672514i	$-0.234785\pi$
$409$	25.4965	+	3.66585i	1.26072	+	0.181264i	0.520637	+	0.853778i	$0.325695\pi$
$410$	−6.16876	−	26.9785i	−0.304653	−	1.33237i
$411$	−8.72562	+	10.0699i	−0.430403	+	0.496711i
$412$	0.341312	+	5.53834i	0.0168152	+	0.272854i
$413$	2.23211	+	2.23211i	0.109835	+	0.109835i
$414$	1.63444	−	16.6433i	0.0803284	−	0.817975i
$415$	−2.89033	−	1.79475i	−0.141881	−	0.0881010i
$416$	−6.16292	−	32.1190i	−0.302162	−	1.57476i
$417$	1.71552	+	23.9861i	0.0840093	+	1.17460i
$418$	−11.3106	−	0.0557079i	−0.553220	−	0.00272476i
$419$	15.1340	+	2.17594i	0.739345	+	0.106302i	0.501689	−	0.865048i	$-0.332712\pi$
$419$	15.1340	+	2.17594i	0.739345	+	0.106302i	0.237655	+	0.971350i	$0.423621\pi$
$420$	14.6109	+	38.5058i	0.712941	+	1.87889i
$421$	−10.5719	−	23.1493i	−0.515245	−	1.12823i	−0.971209	−	0.238230i	$-0.923433\pi$
$421$	−10.5719	−	23.1493i	−0.515245	−	1.12823i	0.455964	−	0.889998i	$-0.349295\pi$
$422$	−28.6047	−	8.55234i	−1.39245	−	0.416322i
$423$	9.21169	−	12.3054i	0.447888	−	0.598308i
$424$	34.0571	−	17.9485i	1.65396	−	0.871657i
$425$	−6.60704	−	0.266856i	−0.320488	−	0.0129444i
$426$	−1.48421	+	0.0988081i	−0.0719104	+	0.00478727i
$427$	−0.314085	+	0.117148i	−0.0151996	+	0.00566917i
$428$	−7.55663	+	4.03012i	−0.365264	+	0.194803i
$429$	−55.8574	+	48.4007i	−2.69682	+	2.33681i
$430$	−21.3000	+	10.0013i	−1.02718	+	0.482308i
$431$	13.6604	+	21.2561i	0.658001	+	1.02387i	0.996556	+	0.0829225i	$0.0264254\pi$
$431$	13.6604	+	21.2561i	0.658001	+	1.02387i	−0.338555	+	0.940946i	$0.609938\pi$
$432$	4.86022	+	1.15800i	0.233838	+	0.0557145i
$433$	−0.0613070	+	0.0133365i	−0.00294623	+	0.000640912i	−0.214038	−	0.976825i	$-0.568662\pi$
$433$	−0.0613070	+	0.0133365i	−0.00294623	+	0.000640912i	0.211092	+	0.977466i	$0.432298\pi$
$434$	21.9428	+	29.6151i	1.05329	+	1.42157i
$435$	−24.2278	+	21.6607i	−1.16163	+	1.03855i
$436$	−14.3146	−	6.70845i	−0.685546	−	0.321277i
$437$	−6.22759	+	3.22818i	−0.297906	+	0.154425i
$438$	−18.6903	−	29.4001i	−0.893059	−	1.40479i
$439$	−11.6900	+	39.8125i	−0.557934	+	1.90015i	−0.144853	+	0.989453i	$0.546271\pi$
$439$	−11.6900	+	39.8125i	−0.557934	+	1.90015i	−0.413081	+	0.910694i	$0.635547\pi$
$440$	−12.0617	+	32.4120i	−0.575021	+	1.54518i
$441$	17.6657	+	11.3530i	0.841222	+	0.540621i
$442$	9.85781	−	4.44337i	0.468888	−	0.211349i
$443$	4.64807	−	21.3669i	0.220837	−	1.01517i	−0.724551	−	0.689221i	$-0.757953\pi$
$443$	4.64807	−	21.3669i	0.220837	−	1.01517i	0.945388	−	0.325948i	$-0.105684\pi$
$444$	0.0760718	−	7.72241i	0.00361021	−	0.366489i
$445$	3.58041	+	2.59457i	0.169728	+	0.122994i
$446$	−4.14167	−	0.316729i	−0.196114	−	0.0149975i
$447$	9.05527	−	3.37744i	0.428300	−	0.159748i
$448$	−30.5812	−	7.60542i	−1.44483	−	0.359322i
$449$	−6.47682	−	22.0580i	−0.305660	−	1.04098i	−0.958879	−	0.283814i	$-0.908400\pi$
$449$	−6.47682	−	22.0580i	−0.305660	−	1.04098i	0.653219	−	0.757169i	$-0.273418\pi$
$450$	−9.80592	−	14.4165i	−0.462256	−	0.679599i
$451$	−6.81043	−	47.3676i	−0.320691	−	2.23045i
$452$	−6.73035	+	12.0422i	−0.316569	+	0.566416i
$453$	−22.8722	−	8.53090i	−1.07463	−	0.400817i
$454$	20.6056	−	7.57008i	0.967067	−	0.355282i
$455$	−4.42050	−	50.7314i	−0.207236	−	2.37833i
$456$	3.24567	+	9.11090i	0.151993	+	0.426657i
$457$	−4.73865	+	0.338915i	−0.221665	+	0.0158538i	−0.181730	−	0.983349i	$-0.558170\pi$
$457$	−4.73865	+	0.338915i	−0.221665	+	0.0158538i	−0.0399349	+	0.999202i	$0.512715\pi$
$458$	40.0957	−	11.5590i	1.87355	−	0.540115i
$459$			1.65187i			0.0771029i
$460$	2.71441	+	21.2751i	0.126560	+	0.991959i
$461$			42.3935i			1.97446i	0.159293	+	0.987231i	$0.449078\pi$
$461$			42.3935i			1.97446i	−0.159293	+	0.987231i	$0.550922\pi$
$462$	19.7270	+	68.4289i	0.917782	+	3.18360i
$463$	3.50185	−	0.250457i	0.162745	−	0.0116397i	0.0102709	−	0.999947i	$-0.496731\pi$
$463$	3.50185	−	0.250457i	0.162745	−	0.0116397i	0.152474	+	0.988308i	$0.451276\pi$
$464$	−3.05333	−	24.6785i	−0.141747	−	1.14567i
$465$	−26.4887	−	22.2425i	−1.22838	−	1.03147i
$466$	−2.05798	−	5.60176i	−0.0953339	−	0.259496i
$467$	−2.35806	−	0.879511i	−0.109118	−	0.0406989i	0.294312	−	0.955709i	$-0.404909\pi$
$467$	−2.35806	−	0.879511i	−0.109118	−	0.0406989i	−0.403430	+	0.915010i	$0.632182\pi$
$468$	24.8878	+	13.9097i	1.15044	+	0.642978i
$469$	−0.185042	−	1.28699i	−0.00854443	−	0.0594278i
$470$	−7.99896	+	18.0179i	−0.368964	+	0.831102i
$471$	−10.8155	−	36.8343i	−0.498353	−	1.69724i
$472$	2.07548	−	0.911024i	0.0955318	−	0.0419333i
$473$	−38.1241	+	14.2196i	−1.75295	+	0.653816i
$474$	0.0887413	−	1.16042i	0.00407602	−	0.0532997i
$475$	−2.83014	+	6.74336i	−0.129856	+	0.309407i
$476$	0.102628	−	10.4183i	0.00470396	−	0.477521i
$477$	−7.13382	+	32.7936i	−0.326635	+	1.50152i
$478$	17.2792	+	38.3346i	0.790330	+	1.75338i
$479$	−23.2458	−	14.9392i	−1.06213	−	0.682587i	−0.111765	−	0.993735i	$-0.535650\pi$
$479$	−23.2458	−	14.9392i	−1.06213	−	0.682587i	−0.950362	+	0.311147i	$0.899287\pi$
$480$	29.5710	+	0.269402i	1.34973	+	0.0122965i
$481$	−2.69027	+	9.16221i	−0.122666	+	0.417761i
$482$	0.342304	−	0.217611i	0.0155915	−	0.00991190i
$483$	30.5491	+	31.8959i	1.39003	+	1.45132i
$484$	−16.0412	+	34.2289i	−0.729144	+	1.55586i
$485$	16.2812	+	18.2107i	0.739289	+	0.826905i
$486$	−23.1505	+	17.1530i	−1.05013	+	0.778076i
$487$	−11.1191	+	2.41881i	−0.503853	+	0.109607i	−0.457306	−	0.889310i	$-0.651186\pi$
$487$	−11.1191	+	2.41881i	−0.503853	+	0.109607i	−0.0465474	+	0.998916i	$0.514822\pi$
$488$	−0.00355641	+	0.240676i	−0.000160991	+	0.0108949i
$489$	−20.5147	−	31.9214i	−0.927705	−	1.44354i
$490$	−25.3316	−	9.14377i	−1.14436	−	0.413074i
$491$	−0.535583	+	0.464086i	−0.0241705	+	0.0209439i	−0.666862	−	0.745181i	$-0.732363\pi$
$491$	−0.535583	+	0.464086i	−0.0241705	+	0.0209439i	0.642692	+	0.766125i	$0.277818\pi$
$492$	−36.1063	+	19.2563i	−1.62780	+	0.868139i
$493$	7.70309	−	2.87310i	0.346930	−	0.129398i
$494$	−0.794375	−	11.9324i	−0.0357406	−	0.536866i
$495$	−14.8576	−	26.2336i	−0.667800	−	1.17911i
$496$	25.5357	−	6.95459i	1.14659	−	0.312270i
$497$	1.06204	−	1.41872i	0.0476391	−	0.0636384i
$498$	−1.44103	+	4.81976i	−0.0645742	+	0.215979i
$499$	14.1241	+	30.9274i	0.632281	+	1.38450i	0.906242	+	0.422760i	$0.138939\pi$
$499$	14.1241	+	30.9274i	0.632281	+	1.38450i	−0.273961	+	0.961741i	$0.588334\pi$
$500$	16.3809	+	15.2206i	0.732574	+	0.680687i
$501$	−1.19046	−	0.171162i	−0.0531857	−	0.00764695i
$502$	0.164588	−	33.4171i	0.00734593	−	1.49148i
$503$	−1.07371	−	15.0125i	−0.0478745	−	0.669372i	−0.963563	−	0.267483i	$-0.913808\pi$
$503$	−1.07371	−	15.0125i	−0.0478745	−	0.669372i	0.915688	−	0.401890i	$-0.131646\pi$
$504$	22.2331	−	16.1365i	0.990341	−	0.718775i
$505$	3.80607	+	16.2762i	0.169368	+	0.724279i
$506$	1.66499	+	37.0494i	0.0740178	+	1.64705i
$507$	−33.7660	−	33.7660i	−1.49960	−	1.49960i
$508$	2.49411	+	40.4709i	0.110658	+	1.79561i
$509$	−0.120788	+	0.139397i	−0.00535383	+	0.00617865i	−0.758420	−	0.651766i	$-0.774028\pi$
$509$	−0.120788	+	0.139397i	−0.00535383	+	0.00617865i	0.753066	+	0.657945i	$0.228574\pi$
$510$	2.17936	+	9.53122i	0.0965036	+	0.422050i
$511$	41.0836	+	5.90693i	1.81743	+	0.261307i
$512$	−13.0648	+	18.4746i	−0.577388	+	0.816470i
$513$	1.71174	+	0.638448i	0.0755754	+	0.0281882i
$514$	11.3192	+	20.9746i	0.499271	+	0.925150i
$515$	5.68248	+	2.48928i	0.250400	+	0.109691i
$516$	22.5247	+	26.5183i	0.991597	+	1.16740i
$517$	−16.3368	+	29.9187i	−0.718493	+	1.31582i
$518$	6.92383	+	6.05949i	0.304216	+	0.266239i
$519$	7.24686	+	3.30953i	0.318102	+	0.145272i
$520$	−35.0917	−	10.2756i	−1.53887	−	0.450617i
$521$	28.1928	−	24.4292i	1.23515	−	1.07026i	0.240112	−	0.970745i	$-0.422816\pi$
$521$	28.1928	−	24.4292i	1.23515	−	1.07026i	0.995036	−	0.0995166i	$-0.0317296\pi$
$522$	18.1787	+	11.8097i	0.795660	+	0.516894i
$523$	39.2095	+	8.52951i	1.71451	+	0.372969i	0.959273	−	0.282479i	$-0.0911568\pi$
$523$	39.2095	+	8.52951i	1.71451	+	0.372969i	0.755240	+	0.655449i	$0.227520\pi$
$524$	4.82927	−	7.35420i	0.210968	−	0.321270i
$525$	45.7585	+	5.13572i	1.99706	+	0.224141i
$526$	15.3922	−	11.4046i	0.671131	−	0.497263i
$527$	4.19351	+	7.67984i	0.182672	+	0.334539i
$528$	50.9236	+	4.65206i	2.21617	+	0.202455i
$529$	11.5889	+	19.8670i	0.503866	+	0.863782i
$530$	−0.455834	−	43.0388i	−0.0198002	−	1.86949i
$531$	−0.556695	+	1.89593i	−0.0241585	+	0.0822763i
$532$	−10.7562	−	4.13300i	−0.466341	−	0.179188i
$533$	49.4404	−	10.7551i	2.14150	−	0.465856i
$534$	2.31491	−	6.11438i	0.100176	−	0.264595i
$535$	0.148561	+	9.57385i	0.00642283	+	0.413914i
$536$	−0.909248	−	0.211912i	−0.0392735	−	0.00915319i
$537$	−2.00419	−	0.143342i	−0.0864871	−	0.00618568i
$538$	−2.18326	+	1.87306i	−0.0941271	+	0.0807533i
$539$	−42.3608	−	19.3455i	−1.82461	−	0.833270i
$540$	3.63408	−	4.24228i	0.156386	−	0.182559i
$541$	8.40259	+	28.6166i	0.361256	+	1.23032i	0.916972	+	0.398952i	$0.130626\pi$
$541$	8.40259	+	28.6166i	0.361256	+	1.23032i	−0.555716	+	0.831372i	$0.687556\pi$
$542$	5.17352	−	0.717850i	0.222222	−	0.0308343i
$543$	31.3045	+	23.4342i	1.34340	+	1.00566i
$544$	−6.94292	−	2.78618i	−0.297675	−	0.119457i
$545$	−13.9832	+	10.8102i	−0.598973	+	0.463059i
$546$	−70.6776	+	25.9656i	−3.02472	+	1.11122i
$547$	17.9074	−	13.4053i	0.765665	−	0.573169i	−0.143478	−	0.989653i	$-0.545829\pi$
$547$	17.9074	−	13.4053i	0.765665	−	0.573169i	0.909143	+	0.416484i	$0.136738\pi$
$548$	−11.1137	−	2.53255i	−0.474755	−	0.108185i
$549$	−0.158583	−	0.137413i	−0.00676817	−	0.00586465i
$550$	26.0748	+	28.5506i	1.11183	+	1.21740i
$551$		−	9.09273i		−	0.387363i
$552$	29.3065	−	12.1171i	1.24737	−	0.515740i
$553$	0.980443	+	0.980443i	0.0416927	+	0.0416927i
$554$	−19.5697	+	35.4232i	−0.831435	+	1.50499i
$555$	−7.64147	−	4.01992i	−0.324362	−	0.170636i
$556$	−17.4149	+	10.9510i	−0.738554	+	0.464425i
$557$	18.4013	+	24.5812i	0.779687	+	1.04154i	0.997844	+	0.0656267i	$0.0209047\pi$
$557$	18.4013	+	24.5812i	0.779687	+	1.04154i	−0.218157	+	0.975914i	$0.570004\pi$
$558$	−9.68772	+	20.9396i	−0.410114	+	0.886444i
$559$	−17.8716	−	39.1334i	−0.755889	−	1.65517i
$560$	−23.1835	+	26.5300i	−0.979681	+	1.12110i
$561$	2.40605	+	16.7345i	0.101584	+	0.706530i
$562$	−1.17928	−	8.49905i	−0.0497451	−	0.358511i
$563$	−35.4408	−	19.3521i	−1.49365	−	0.815595i	−0.495070	−	0.868853i	$-0.664858\pi$
$563$	−35.4408	−	19.3521i	−1.49365	−	0.815595i	−0.998581	+	0.0532583i	$0.983039\pi$
$564$	28.8098	+	4.43230i	1.21311	+	0.186634i
$565$	8.53897	+	12.8443i	0.359237	+	0.540362i
$566$	−23.3811	−	1.78804i	−0.982783	−	0.0751570i
$567$	2.89930	−	40.5375i	0.121759	−	1.70242i
$568$	−0.672081	−	1.08056i	−0.0281999	−	0.0453391i
$569$	−19.5788	+	12.5825i	−0.820786	+	0.527487i	−0.882338	−	0.470617i	$-0.844031\pi$
$569$	−19.5788	+	12.5825i	−0.820786	+	0.527487i	0.0615519	+	0.998104i	$0.480395\pi$
$570$	10.7190	+	1.42546i	0.448969	+	0.0597059i
$571$	−22.2667	−	14.3099i	−0.931832	−	0.598852i	−0.0157645	−	0.999876i	$-0.505018\pi$
$571$	−22.2667	−	14.3099i	−0.931832	−	0.598852i	−0.916068	+	0.401023i	$0.868655\pi$
$572$	−59.0208	−	22.6784i	−2.46778	−	0.948230i
$573$	−22.1718	−	40.6046i	−0.926240	−	1.69628i
$574$	10.5975	−	47.5865i	0.442333	−	1.98622i
$575$	22.5456	+	8.16678i	0.940216	+	0.340578i
$576$	−4.99575	−	19.0827i	−0.208156	−	0.795114i
$577$	−24.2398	+	13.2359i	−1.00912	+	0.551019i	−0.896698	−	0.442642i	$-0.854041\pi$
$577$	−24.2398	+	13.2359i	−1.00912	+	0.551019i	−0.112417	+	0.993661i	$0.535859\pi$
$578$	−3.17459	+	21.3333i	−0.132045	+	0.887349i
$579$	−21.6961	−	13.9433i	−0.901660	−	0.579462i
$580$	−26.1035	−	9.56799i	−1.08389	−	0.397289i
$581$	−3.24028	−	5.04198i	−0.134430	−	0.209177i
$582$	19.6768	−	30.2886i	0.815628	−	1.25550i
$583$	5.30949	−	74.2363i	0.219897	−	3.07456i
$584$	14.6680	−	25.9436i	0.606966	−	1.07355i
$585$	26.5455	−	17.6476i	1.09752	−	0.729640i
$586$	−1.08432	−	16.2878i	−0.0447929	−	0.672841i
$587$	−32.0398	−	17.4950i	−1.32242	−	0.722098i	−0.346056	−	0.938214i	$-0.612479\pi$
$587$	−32.0398	−	17.4950i	−1.32242	−	0.722098i	−0.976368	+	0.216116i	$0.930661\pi$
$588$	−3.23191	+	39.6896i	−0.133282	+	1.63677i
$589$	9.57897	−	1.37725i	0.394695	−	0.0567485i
$590$	0.154005	−	2.52948i	0.00634029	−	0.104137i
$591$	17.0386	+	37.3093i	0.700873	+	1.53470i
$592$	5.85975	−	3.05138i	0.240834	−	0.125411i
$593$	10.2113	−	7.64409i	0.419328	−	0.313905i	−0.368695	−	0.929550i	$-0.620195\pi$
$593$	10.2113	−	7.64409i	0.419328	−	0.313905i	0.788024	+	0.615645i	$0.211105\pi$
$594$	6.86365	−	6.79637i	0.281619	−	0.278858i
$595$	−10.3091	−	5.42326i	−0.422631	−	0.222332i
$596$	6.19477	+	5.47556i	0.253748	+	0.224288i
$597$	25.7855	−	25.7855i	1.05533	−	1.05533i
$598$	−38.9469	+	4.55043i	−1.59266	+	0.186081i
$599$		−	1.23221i		−	0.0503466i	−0.999683	−	0.0251733i	$-0.991986\pi$
$599$		−	1.23221i		−	0.0503466i	0.999683	−	0.0251733i	$-0.00801376\pi$
$600$	15.3715	−	29.2722i	0.627538	−	1.19503i
$601$	−10.8752	+	12.5507i	−0.443610	+	0.511953i	−0.932884	−	0.360177i	$-0.882716\pi$
$601$	−10.8752	+	12.5507i	−0.443610	+	0.511953i	0.489274	+	0.872130i	$0.337262\pi$
$602$	−41.4524	−	0.204164i	−1.68947	−	0.00832111i
$603$	0.651556	−	0.487749i	0.0265334	−	0.0198627i
$604$	−2.76824	−	20.6990i	−0.112638	−	0.842229i
$605$	25.8492	+	33.4363i	1.05092	+	1.35938i
$606$	21.7502	−	11.7378i	0.883542	−	0.476817i
$607$	−22.5049	−	16.8470i	−0.913447	−	0.683798i	0.0354538	−	0.999371i	$-0.488712\pi$
$607$	−22.5049	−	16.8470i	−0.913447	−	0.683798i	−0.948901	+	0.315573i	$0.897803\pi$
$608$	−5.57060	+	6.11770i	−0.225917	+	0.248105i
$609$	−54.9313	+	16.1293i	−2.22593	+	0.653591i
$610$	0.237547	+	0.126463i	0.00961801	+	0.00512035i
$611$	−32.7846	−	14.9722i	−1.32632	−	0.605712i
$612$	5.75454	−	3.06902i	0.232613	−	0.124058i
$613$	2.99467	−	41.8709i	0.120953	−	1.69115i	−0.468592	−	0.883415i	$-0.655238\pi$
$613$	2.99467	−	41.8709i	0.120953	−	1.69115i	0.589545	−	0.807735i	$-0.299307\pi$
$614$	8.27582	−	1.75765i	0.333985	−	0.0709330i
$615$	0.709835	+	45.7447i	0.0286233	+	1.84460i
$616$	−43.7109	+	42.4379i	−1.76116	+	1.70987i
$617$	0.158966	+	0.730755i	0.00639973	+	0.0294191i	0.980236	−	0.197832i	$-0.0633899\pi$
$617$	0.158966	+	0.730755i	0.00639973	+	0.0294191i	−0.973836	+	0.227251i	$0.927026\pi$
$618$	1.35016	−	9.07309i	0.0543113	−	0.364973i
$619$	−0.740120	+	2.52062i	−0.0297479	+	0.101312i	−0.973029	−	0.230684i	$-0.925904\pi$
$619$	−0.740120	+	2.52062i	−0.0297479	+	0.101312i	0.943281	+	0.331996i	$0.107722\pi$
$620$	6.12583	−	28.9487i	0.246019	−	1.16261i
$621$	1.81122	−	5.70994i	0.0726816	−	0.229132i
$622$	7.09485	+	11.1603i	0.284478	+	0.447486i
$623$	3.73300	+	6.83648i	0.149559	+	0.273898i
$624$	−1.06508	+	54.0553i	−0.0426372	+	2.16394i
$625$	23.5043	−	8.51755i	0.940171	−	0.340702i
$626$	9.39675	−	24.8196i	0.375570	−	0.991992i
$627$	18.2709	+	3.97460i	0.729670	+	0.158730i
$628$	23.4497	−	22.9922i	0.935746	−	0.917490i
$629$	1.43041	+	1.65078i	0.0570341	+	0.0658209i
$630$	−4.69284	−	30.3537i	−0.186967	−	1.20932i
$631$	−2.86959	−	1.31050i	−0.114236	−	0.0521700i	0.357477	−	0.933922i	$-0.383637\pi$
$631$	−2.86959	−	1.31050i	−0.114236	−	0.0521700i	−0.471713	+	0.881752i	$0.656364\pi$
$632$	0.911644	−	0.400162i	0.0362633	−	0.0159176i
$633$	43.3185	+	23.6537i	1.72176	+	0.940151i
$634$	20.2497	+	15.3149i	0.804217	+	0.608233i
$635$	41.5242	+	18.1902i	1.64784	+	0.721857i
$636$	−61.2369	+	17.3274i	−2.42820	+	0.687077i
$637$	17.2068	−	46.1331i	0.681757	−	1.82786i
$638$	−43.6310	−	20.1859i	−1.72737	−	0.799168i
$639$	1.09804	+	0.157875i	0.0434380	+	0.00624544i
$640$	11.7010	+	22.4296i	0.462523	+	0.886608i
$641$	21.6677	+	18.7752i	0.855824	+	0.741576i	0.967689	−	0.252148i	$-0.0811369\pi$
$641$	21.6677	+	18.7752i	0.855824	+	0.741576i	−0.111865	+	0.993723i	$0.535682\pi$
$642$	13.6037	−	3.92173i	0.536895	−	0.154778i
$643$	7.38283	+	7.38283i	0.291150	+	0.291150i	0.837535	−	0.546384i	$-0.183996\pi$
$643$	7.38283	+	7.38283i	0.291150	+	0.291150i	−0.546384	+	0.837535i	$0.683996\pi$
$644$	−11.7780	+	35.8997i	−0.464117	+	1.41465i
$645$	37.8784	−	8.85761i	1.49146	−	0.348768i
$646$	−2.39444	−	1.32281i	−0.0942078	−	0.0520453i
$647$	−1.04243	−	14.5751i	−0.0409821	−	0.573005i	−0.975911	−	0.218170i	$-0.929991\pi$
$647$	−1.04243	−	14.5751i	−0.0409821	−	0.573005i	0.934929	−	0.354836i	$-0.115463\pi$
$648$	−26.3628	−	12.5135i	−1.03563	−	0.491576i
$649$	0.623628	−	4.33742i	0.0244795	−	0.170259i
$650$	−28.1429	+	29.6521i	−1.10386	+	1.16305i
$651$	−25.3121	−	55.4257i	−0.992058	−	2.17231i
$652$	15.8368	−	28.3357i	0.620216	−	1.10971i
$653$	−2.03006	−	1.51968i	−0.0794424	−	0.0594698i	0.558818	−	0.829290i	$-0.311255\pi$
$653$	−2.03006	−	1.51968i	−0.0794424	−	0.0594698i	−0.638261	+	0.769820i	$0.720346\pi$
$654$	20.8438	+	15.7642i	0.815056	+	0.616430i
$655$	−4.84754	−	8.55915i	−0.189409	−	0.334434i
$656$	−29.0705	−	19.5022i	−1.13501	−	0.761433i
$657$	9.07953	+	24.3432i	0.354226	+	0.949718i
$658$	−26.3572	+	22.6123i	−1.02751	+	0.881520i
$659$	3.37800	−	2.92705i	0.131588	−	0.114022i	−0.586580	−	0.809891i	$-0.699526\pi$
$659$	3.37800	−	2.92705i	0.131588	−	0.114022i	0.718168	+	0.695869i	$0.244981\pi$
$660$	30.6362	−	48.2700i	1.19251	−	1.87891i
$661$	24.7782	−	15.9240i	0.963762	−	0.619372i	0.0387254	−	0.999250i	$-0.487670\pi$
$661$	24.7782	−	15.9240i	0.963762	−	0.619372i	0.925037	+	0.379878i	$0.124034\pi$
$662$	−1.31287	−	2.91266i	−0.0510261	−	0.113204i
$663$	−17.4668	+	3.79967i	−0.678354	+	0.147567i
$664$	−4.21822	+	0.852546i	−0.163699	+	0.0330852i
$665$	−9.60426	+	8.58663i	−0.372437	+	0.332975i
$666$	−1.25196	+	5.62172i	−0.0485125	+	0.217837i
$667$	−29.7771	+	1.48516i	−1.15297	+	0.0575058i
$668$	−0.350042	−	0.967499i	−0.0135435	−	0.0374337i
$669$	6.58860	+	1.93459i	0.254730	+	0.0747954i
$670$	−0.675160	+	0.796057i	−0.0260837	+	0.0307544i
$671$	0.391473	+	0.251584i	0.0151126	+	0.00971230i
$672$	46.8399	+	22.8013i	1.80689	+	0.879578i
$673$	−34.7632	−	7.56226i	−1.34002	−	0.291504i	−0.515284	−	0.857020i	$-0.672313\pi$
$673$	−34.7632	−	7.56226i	−1.34002	−	0.291504i	−0.824737	+	0.565516i	$0.808677\pi$
$674$	−23.7900	+	5.05260i	−0.916355	+	0.194619i
$675$	−2.36303	−	5.78104i	−0.0909531	−	0.222512i
$676$	11.8945	−	39.0808i	0.457483	−	1.50311i
$677$	0.749224	+	2.00875i	0.0287950	+	0.0772025i	0.950552	−	0.310566i	$-0.100519\pi$
$677$	0.749224	+	2.00875i	0.0287950	+	0.0772025i	−0.921757	+	0.387769i	$0.873246\pi$
$678$	15.0192	−	17.1616i	0.576809	−	0.659086i
$679$	12.1235	+	41.2889i	0.465257	+	1.58452i
$680$	−6.31713	+	5.48202i	−0.242251	+	0.210226i
$681$	−35.9205	+	5.16459i	−1.37648	+	0.197907i
$682$	14.6567	−	49.0217i	0.561235	−	1.87714i
$683$	−16.0839	−	5.99900i	−0.615435	−	0.229545i	0.0223622	−	0.999750i	$-0.492881\pi$
$683$	−16.0839	−	5.99900i	−0.615435	−	0.229545i	−0.637797	+	0.770205i	$0.720154\pi$
$684$	−0.956131	−	7.14928i	−0.0365586	−	0.273359i
$685$	−8.19515	+	9.75965i	−0.313121	+	0.372897i
$686$	−5.94389	−	6.00273i	−0.226939	−	0.229185i
$687$	−68.8074	+	4.92120i	−2.62516	+	0.187755i
$688$	−10.9491	+	27.6778i	−0.417431	+	1.05521i
$689$	78.6906			2.99787
$690$	2.91734	−	35.3356i	0.111061	−	1.34520i
$691$			5.16182i			0.196365i	0.995168	+	0.0981825i	$0.0313029\pi$
$691$			5.16182i			0.196365i	−0.995168	+	0.0981825i	$0.968697\pi$
$692$	0.419217	+	6.80247i	0.0159363	+	0.258591i
$693$	−3.78887	−	52.9753i	−0.143927	−	2.01237i
$694$	25.1480	−	24.9015i	0.954605	−	0.945248i
$695$	1.99655	+	22.9132i	0.0757335	+	0.869147i
$696$	−3.53812	+	40.9555i	−0.134112	+	1.55241i
$697$	4.04462	−	10.8440i	0.153201	−	0.410747i
$698$	−10.6475	+	35.6124i	−0.403016	+	1.34795i
$699$	1.40403	+	9.76522i	0.0531052	+	0.369355i
$700$	14.5443	+	36.6075i	0.549724	+	1.38363i
$701$	23.6064	−	6.93146i	0.891601	−	0.261798i	0.196324	−	0.980539i	$-0.437100\pi$
$701$	23.6064	−	6.93146i	0.891601	−	0.261798i	0.695277	+	0.718742i	$0.255282\pi$
$702$	7.68520	+	6.72582i	0.290059	+	0.253850i
$703$	2.26346	−	0.844227i	0.0853680	−	0.0318406i
$704$	16.9887	+	40.3116i	0.640287	+	1.51930i
$705$	19.1229	−	26.3890i	0.720211	−	0.993866i
$706$	−24.8978	+	5.28790i	−0.937042	+	0.199013i
$707$	−6.25916	+	28.7729i	−0.235400	+	1.08212i
$708$	−3.66908	+	0.760387i	−0.137893	+	0.0285771i
$709$	−8.33339	+	12.9670i	−0.312967	+	0.486986i	−0.961728	−	0.274006i	$-0.911651\pi$
$709$	−8.33339	+	12.9670i	−0.312967	+	0.486986i	0.648761	+	0.760992i	$0.275288\pi$
$710$	−1.41794	+	0.116519i	−0.0532142	+	0.00437287i
$711$	−0.244525	+	0.832776i	−0.00917041	+	0.0312315i
$712$	5.54724	−	0.714085i	0.207892	−	0.0267615i
$713$	−6.07483	−	31.1445i	−0.227504	−	1.16637i
$714$	−3.74400	+	16.8118i	−0.140116	+	0.629167i
$715$	−52.7000	+	47.1160i	−1.97087	+	1.76204i
$716$	−0.698623	−	1.57053i	−0.0261088	−	0.0586935i
$717$	−14.7760	−	67.9241i	−0.551819	−	2.53667i
$718$	28.0456	−	12.6414i	1.04665	−	0.471774i
$719$	−9.92671	−	15.4463i	−0.370204	−	0.576048i	0.605309	−	0.795990i	$-0.293049\pi$
$719$	−9.92671	−	15.4463i	−0.370204	−	0.576048i	−0.975513	+	0.219942i	$0.929413\pi$
$720$	−21.5303	−	4.77809i	−0.802388	−	0.178069i
$721$	7.15678	+	8.25936i	0.266532	+	0.307595i
$722$	18.0973	−	15.5260i	0.673510	−	0.577816i
$723$	−0.628266	+	0.234331i	−0.0233655	+	0.00871487i
$724$	−5.08672	+	33.0635i	−0.189047	+	1.22880i
$725$	−22.8483	+	21.0743i	−0.848566	+	0.782681i
$726$	37.6952	−	49.8413i	1.39900	−	1.84979i
$727$	−11.6704	+	15.5898i	−0.432831	+	0.578194i	−0.962933	−	0.269739i	$-0.913062\pi$
$727$	−11.6704	+	15.5898i	−0.432831	+	0.578194i	0.530103	+	0.847933i	$0.322153\pi$
$728$	−48.0522	−	42.8968i	−1.78093	−	1.58986i
$729$	15.1720	−	6.92882i	0.561926	−	0.256623i
$730$	−18.3105	−	27.8389i	−0.677700	−	1.03036i
$731$	−9.74072	−	1.40050i	−0.360274	−	0.0517995i
$732$	0.0884084	−	0.387968i	0.00326767	−	0.0143397i
$733$	−22.1461	+	1.58392i	−0.817984	+	0.0585034i	−0.474058	−	0.880494i	$-0.657211\pi$
$733$	−22.1461	+	1.58392i	−0.817984	+	0.0585034i	−0.343926	+	0.938997i	$0.611757\pi$
$734$	−1.98928	+	3.60081i	−0.0734255	+	0.132908i
$735$	37.8226	+	23.4860i	1.39511	+	0.866293i
$736$	20.9443	+	17.2435i	0.772016	+	0.635603i
$737$	−1.27629	+	1.27629i	−0.0470126	+	0.0470126i
$738$	29.3230	−	8.45336i	1.07939	−	0.311173i
$739$	0.845107	−	0.975306i	0.0310878	−	0.0358772i	−0.739993	−	0.672615i	$-0.765171\pi$
$739$	0.845107	−	0.975306i	0.0310878	−	0.0358772i	0.771081	+	0.636738i	$0.219717\pi$
$740$	−0.0418484	−	7.38632i	−0.00153838	−	0.271526i
$741$	−2.81351	+	19.5684i	−0.103357	+	0.718864i
$742$	31.8369	−	68.8142i	1.16877	−	2.52625i
$743$	−41.0350	−	15.3053i	−1.50543	−	0.561495i	−0.544613	−	0.838687i	$-0.683323\pi$
$743$	−41.0350	−	15.3053i	−1.50543	−	0.561495i	−0.960815	+	0.277192i	$0.910596\pi$
$744$	−43.6815	+	2.47608i	−1.60144	+	0.0907774i
$745$	8.60973	−	3.36433i	0.315436	−	0.123260i
$746$	2.97249	+	2.24811i	0.108831	+	0.0823092i
$747$	1.79798	−	3.29275i	0.0657846	−	0.120476i
$748$	−11.6631	+	8.55294i	−0.426446	+	0.312726i
$749$	−7.00700	+	15.3432i	−0.256030	+	0.560628i
$750$	−21.2616	−	30.2386i	−0.776364	−	1.10416i
$751$	5.09920	−	4.41848i	0.186072	−	0.161233i	−0.556843	−	0.830617i	$-0.687988\pi$
$751$	5.09920	−	4.41848i	0.186072	−	0.161233i	0.742916	+	0.669385i	$0.233442\pi$
$752$	8.25228	+	23.5309i	0.300930	+	0.858083i
$753$	−11.7429	+	53.9812i	−0.427934	+	1.96718i
$754$	17.9972	−	47.5361i	0.655421	−	1.73116i
$755$	−22.0000	−	7.81895i	−0.800663	−	0.284561i
$756$	8.99097	−	3.99948i	0.326998	−	0.145460i
$757$	25.6832	−	14.0241i	0.933473	−	0.509715i	0.0608702	−	0.998146i	$-0.480612\pi$
$757$	25.6832	−	14.0241i	0.933473	−	0.509715i	0.872603	+	0.488431i	$0.162431\pi$
$758$	−26.5972	+	16.9085i	−0.966055	+	0.614144i
$759$	10.0318	−	60.4833i	0.364132	−	2.19540i
$760$	3.23914	+	8.66488i	0.117496	+	0.314308i
$761$	−46.7303	−	13.7212i	−1.69397	−	0.497395i	−0.714611	−	0.699522i	$-0.753396\pi$
$761$	−46.7303	−	13.7212i	−1.69397	−	0.497395i	−0.979359	+	0.202127i	$0.935214\pi$
$762$	9.86617	−	66.3009i	0.357413	−	2.40183i
$763$	−30.4242	+	6.61838i	−1.10143	+	0.239601i
$764$	21.7240	−	33.0821i	0.785947	−	1.19687i
$765$	−0.113132	−	7.29069i	−0.00409030	−	0.263596i
$766$	−3.10818	−	14.6347i	−0.112303	−	0.528774i
$767$	4.62131	+	0.330523i	0.166866	+	0.0119345i
$768$	27.4716	−	25.3878i	0.991296	−	0.916102i
$769$	−15.2974	+	33.4966i	−0.551637	+	1.20792i	0.404376	+	0.914593i	$0.367489\pi$
$769$	−15.2974	+	33.4966i	−0.551637	+	1.20792i	−0.956013	+	0.293324i	$0.905238\pi$
$770$	19.8810	+	65.1480i	0.716461	+	2.34777i
$771$	−11.1005	−	37.8049i	−0.399775	−	1.36151i
$772$	1.79064	−	21.9901i	0.0644466	−	0.791439i
$773$	30.6161	−	40.8983i	1.10118	−	1.47101i	0.234525	−	0.972110i	$-0.424647\pi$
$773$	30.6161	−	40.8983i	1.10118	−	1.47101i	0.866660	−	0.498900i	$-0.166262\pi$
$774$	−12.3232	−	22.8350i	−0.442949	−	0.820786i
$775$	−25.6621	−	20.8781i	−0.921809	−	0.749964i
$776$	30.7840	+	2.65942i	1.10508	+	0.0954675i
$777$	−9.11524	−	12.1765i	−0.327007	−	0.436831i
$778$	29.8456	+	0.146998i	1.07002	+	0.00527012i
$779$	−9.67383	−	8.38242i	−0.346601	−	0.300331i
$780$	53.2167	+	28.6683i	1.90546	+	1.02649i
$781$	−2.46013			−0.0880304
$782$	−3.94088	+	8.05742i	−0.140926	+	0.288133i
$783$	5.49072	+	5.49072i	0.196222	+	0.196222i
$784$	−31.2601	+	13.5382i	−1.11643	+	0.483509i
$785$	−10.8898	−	35.0653i	−0.388675	−	1.25154i
$786$	−10.3350	+	10.2337i	−0.368637	+	0.365023i
$787$	−11.2199	−	14.9880i	−0.399946	−	0.534266i	0.554683	−	0.832062i	$-0.312839\pi$
$787$	−11.2199	−	14.9880i	−0.399946	−	0.534266i	−0.954630	+	0.297796i	$0.903749\pi$
$788$	−21.3030	+	27.8808i	−0.758889	+	0.993212i
$789$	−28.8070	+	13.1557i	−1.02556	+	0.468356i
$790$	0.0676459	−	1.11106i	0.00240673	−	0.0395298i
$791$	3.86677	+	26.8940i	0.137487	+	0.956240i
$792$	−36.4281	−	11.2835i	−1.29442	−	0.400942i
$793$	−0.235795	+	0.431826i	−0.00837332	+	0.0153346i
$794$	−3.18921	−	47.9057i	−0.113181	−	1.70011i
$795$	−14.0441	+	69.7532i	−0.498093	+	2.47389i
$796$	29.8442	+	9.08330i	1.05780	+	0.321949i
$797$	−29.3874	−	2.10183i	−1.04096	−	0.0744507i	−0.459621	−	0.888115i	$-0.652015\pi$
$797$	−29.3874	−	2.10183i	−1.04096	−	0.0744507i	−0.581335	+	0.813664i	$0.697469\pi$
$798$	15.9741	+	10.3775i	0.565477	+	0.367358i
$799$	−6.93560	+	4.45724i	−0.245364	+	0.157686i
$800$	28.2837	−	0.181187i	0.999979	−	0.00640594i
$801$	−2.63606	+	4.10178i	−0.0931405	+	0.144929i
$802$	−0.511849	+	3.43964i	−0.0180740	+	0.121458i
$803$	−27.6132	−	50.5698i	−0.974450	−	1.78457i
$804$	1.39754	+	0.654947i	0.0492874	+	0.0230982i
$805$	29.6884	+	30.0498i	1.04638	+	1.05912i
$806$	52.8041	+	11.7595i	1.85995	+	0.414211i
$807$	4.17377	−	2.27905i	0.146924	−	0.0802263i
$808$	17.6160	+	11.6925i	0.619730	+	0.411340i
$809$	−4.64450	+	7.22699i	−0.163292	+	0.254087i	−0.913251	−	0.407397i	$-0.866437\pi$
$809$	−4.64450	+	7.22699i	−0.163292	+	0.254087i	0.749959	+	0.661484i	$0.230073\pi$
$810$	−25.9102	+	19.8278i	−0.910393	+	0.696677i
$811$	25.5360	+	39.7348i	0.896690	+	1.39528i	0.918460	+	0.395514i	$0.129434\pi$
$811$	25.5360	+	39.7348i	0.896690	+	1.39528i	−0.0217697	+	0.999763i	$0.506930\pi$
$812$	−34.2885	−	34.9707i	−1.20329	−	1.22723i
$813$	−8.61247	−	0.615976i	−0.302053	−	0.0216032i
$814$	0.973914	−	12.7353i	0.0341357	−	0.446372i
$815$	−20.0925	−	30.2231i	−0.703811	−	1.05867i
$816$	10.2703	+	6.88993i	0.359532	+	0.241196i
$817$	−5.21604	+	9.55247i	−0.182486	+	0.334199i
$818$	−5.00663	−	36.0826i	−0.175053	−	1.26160i
$819$	55.5823	−	7.99153i	1.94220	−	0.279247i
$820$	−34.2438	+	18.9512i	−1.19585	+	0.661804i
$821$	−25.9617	+	11.8563i	−0.906069	+	0.413788i	−0.813263	−	0.581896i	$-0.802311\pi$
$821$	−25.9617	+	11.8563i	−0.906069	+	0.413788i	−0.0928063	+	0.995684i	$0.529584\pi$
$822$	17.1019	+	7.91221i	0.596498	+	0.275970i
$823$	17.8175	−	13.3380i	0.621078	−	0.464933i	−0.241813	−	0.970323i	$-0.577742\pi$
$823$	17.8175	−	13.3380i	0.621078	−	0.464933i	0.862891	+	0.505390i	$0.168651\pi$
$824$	7.39219	−	2.63340i	0.257519	−	0.0917388i
$825$	−32.3593	−	55.1234i	−1.12661	−	1.91915i
$826$	2.15875	−	3.90757i	0.0751124	−	0.135962i
$827$	17.4229	−	17.4229i	0.605855	−	0.605855i	−0.336005	−	0.941860i	$-0.609076\pi$
$827$	17.4229	−	17.4229i	0.605855	−	0.605855i	0.941860	+	0.336005i	$0.109076\pi$
$828$	−23.2565	+	4.29889i	−0.808218	+	0.149397i
$829$	5.59865			0.194449			0.0972246	−	0.995262i	$-0.469003\pi$
$829$	5.59865			0.194449			0.0972246	+	0.995262i	$0.469003\pi$
$830$	−1.30658	+	4.63067i	−0.0453521	+	0.160733i
$831$	43.8112	−	50.5608i	1.51979	−	1.75394i
$832$	−41.2314	+	20.9570i	−1.42944	+	0.726553i
$833$	−6.74958	−	9.01639i	−0.233859	−	0.312399i
$834$	31.9220	−	11.7275i	1.10537	−	0.406091i
$835$	−1.14101	−	0.146022i	−0.0394863	−	0.00505328i
$836$	4.35514	+	15.3915i	0.150626	+	0.532327i
$837$	−4.95268	+	6.61600i	−0.171190	+	0.228682i
$838$	−2.97180	−	21.4176i	−0.102659	−	0.739859i
$839$	19.5367	−	5.73649i	0.674482	−	0.198046i	0.0734839	−	0.997296i	$-0.476588\pi$
$839$	19.5367	−	5.73649i	0.674482	−	0.198046i	0.600998	+	0.799251i	$0.294770\pi$
$840$	46.6007	−	34.9387i	1.60788	−	1.20550i
$841$	4.00749	−	8.77518i	0.138189	−	0.302593i
$842$	−27.3155	+	23.4345i	−0.941355	+	0.807606i
$843$	−1.01193	+	14.1486i	−0.0348526	+	0.487302i
$844$	−0.415905	+	42.2205i	−0.0143160	+	1.45329i
$845$	−32.7926	−	31.7905i	−1.12810	−	1.09363i
$846$	−20.3301	−	7.69700i	−0.698962	−	0.264628i
$847$	15.8258	+	72.7499i	0.543780	+	2.49972i
$848$	−37.7314	−	39.2481i	−1.29570	−	1.34779i
$849$	37.1948	+	10.9214i	1.27652	+	0.374821i
$850$	2.22563	+	9.08267i	0.0763385	+	0.311533i
$851$	−3.13440	−	7.27454i	−0.107446	−	0.249368i
$852$	0.715697	+	1.97815i	0.0245194	+	0.0677704i
$853$	−11.9454	+	6.52268i	−0.409003	+	0.223332i	−0.670560	−	0.741856i	$-0.733946\pi$
$853$	−11.9454	+	6.52268i	−0.409003	+	0.223332i	0.261557	+	0.965188i	$0.415764\pi$
$854$	0.282229	+	0.380910i	0.00965767	+	0.0130345i
$855$	−7.59866	−	2.70061i	−0.259869	−	0.0923590i
$856$	8.43667	+	8.68975i	0.288360	+	0.297009i
$857$	−3.97545	+	18.2749i	−0.135799	+	0.624258i	0.858055	+	0.513558i	$0.171673\pi$
$857$	−3.97545	+	18.2749i	−0.135799	+	0.624258i	−0.993854	+	0.110700i	$0.964691\pi$
$858$	87.6521	+	56.9426i	2.99239	+	1.94399i
$859$	−27.0996	−	31.2746i	−0.924625	−	1.06707i	−0.997565	−	0.0697380i	$-0.977784\pi$
$859$	−27.0996	−	31.2746i	−0.924625	−	1.06707i	0.0729402	−	0.997336i	$-0.476762\pi$
$860$	21.9347	+	25.0260i	0.747966	+	0.853381i
$861$	−33.4801	+	73.3111i	−1.14100	+	2.49844i
$862$	23.5329	−	26.8897i	0.801535	−	0.915868i
$863$	−45.3127	−	24.7426i	−1.54246	−	0.842248i	−0.999998	−	0.00217013i	$-0.999309\pi$
$863$	−45.3127	−	24.7426i	−1.54246	−	0.842248i	−0.542465	−	0.840078i	$-0.682509\pi$
$864$	−0.330373	−	7.05807i	−0.0112395	−	0.240120i
$865$	6.97951	+	3.05747i	0.237311	+	0.103957i
$866$	0.0421392	+	0.0780840i	0.00143195	+	0.00265340i
$867$	12.4602	−	33.4072i	0.423171	−	1.13457i
$868$	31.6473	−	41.4190i	1.07418	−	1.40585i
$869$	0.273925	−	1.90519i	0.00929227	−	0.0646291i
$870$	38.9251	+	24.4371i	1.31969	+	0.828494i
$871$	−1.44225	−	1.24971i	−0.0488687	−	0.0423449i
$872$	−3.50831	+	22.0797i	−0.118806	+	0.747714i
$873$	−19.0469	+	19.0469i	−0.644641	+	0.644641i
$874$	6.82630	+	7.19789i	0.230903	+	0.243472i
$875$	43.8365	+	4.23241i	1.48195	+	0.143081i
$876$	−32.6292	+	36.9151i	−1.10244	+	1.24724i
$877$	−44.6455	+	3.19311i	−1.50757	+	0.107824i	−0.800507	−	0.599324i	$-0.795436\pi$
$877$	−44.6455	+	3.19311i	−1.50757	+	0.107824i	−0.707066	+	0.707147i	$0.749982\pi$
$878$	58.6797	+	0.289013i	1.98034	+	0.00975373i
$879$	−3.84044	+	26.7108i	−0.129535	+	0.900934i
$880$	48.7690	+	3.69322i	1.64400	+	0.124498i
$881$	26.3967	−	12.0550i	0.889329	−	0.406143i	0.0822672	−	0.996610i	$-0.473784\pi$
$881$	26.3967	−	12.0550i	0.889329	−	0.406143i	0.807061	+	0.590468i	$0.201057\pi$
$882$	8.50696	−	28.4529i	0.286444	−	0.958058i
$883$	−1.93475	−	1.44833i	−0.0651094	−	0.0487403i	0.566227	−	0.824249i	$-0.308402\pi$
$883$	−1.93475	−	1.44833i	−0.0651094	−	0.0487403i	−0.631337	+	0.775509i	$0.717493\pi$
$884$	−9.89969	−	11.6549i	−0.332963	−	0.391996i
$885$	−1.11776	+	4.03746i	−0.0375731	+	0.135718i
$886$	−30.8557	+	2.05415i	−1.03662	+	0.0690104i
$887$	−12.4554	−	33.3942i	−0.418211	−	1.12127i	−0.959815	−	0.280633i	$-0.909456\pi$
$887$	−12.4554	−	33.3942i	−0.418211	−	1.12127i	0.541604	−	0.840634i	$-0.317817\pi$
$888$	−10.5236	+	2.92182i	−0.353148	+	0.0980499i
$889$	52.2976	+	60.3546i	1.75400	+	2.02423i
$890$	2.12309	−	5.88173i	0.0711661	−	0.197156i
$891$	−47.4609	+	30.5013i	−1.59000	+	1.02183i
$892$	1.19207	+	5.75209i	0.0399136	+	0.192594i
$893$	1.93818	+	8.90969i	0.0648589	+	0.298151i
$894$	−8.13685	−	10.9819i	−0.272137	−	0.367289i
$895$	−1.91880	−	0.107341i	−0.0641383	−	0.00358802i
$896$	1.64514	+	44.5354i	0.0549601	+	1.48782i
$897$	64.5427	+	6.01755i	2.15502	+	0.200920i
$898$	−27.4368	+	17.4422i	−0.915579	+	0.582055i
$899$	39.4662	+	11.5883i	1.31627	+	0.386492i
$900$	−15.7488	+	18.9725i	−0.524959	+	0.632418i
$901$	9.73159	−	15.1427i	0.324206	−	0.504475i
$902$	−61.6986	+	27.8104i	−2.05434	+	0.925984i
$903$	66.9612	+	14.5665i	2.22833	+	0.484743i
$904$	19.0004	+	4.42827i	0.631942	+	0.147282i
$905$	30.2852	+	21.9464i	1.00672	+	0.729522i
$906$	−2.63240	+	34.4224i	−0.0874558	+	1.14361i
$907$	6.05538	+	16.2351i	0.201066	+	0.539078i	0.997875	−	0.0651527i	$-0.0207535\pi$
$907$	6.05538	+	16.2351i	0.201066	+	0.539078i	−0.796810	+	0.604230i	$0.793481\pi$
$908$	−18.3588	−	25.0348i	−0.609260	−	0.830810i
$909$	−17.6854	+	5.19290i	−0.586587	+	0.172238i
$910$	−67.2059	+	25.8805i	−2.22785	+	0.857931i
$911$	35.2274	−	5.06494i	1.16714	−	0.167809i	0.468619	−	0.883401i	$-0.344752\pi$
$911$	35.2274	−	5.06494i	1.16714	−	0.167809i	0.698519	+	0.715592i	$0.253843\pi$
$912$	11.1091	−	7.97958i	0.367859	−	0.264230i
$913$	−2.90751	+	7.79534i	−0.0962245	+	0.257988i
$914$	2.31687	+	6.30646i	0.0766353	+	0.208599i
$915$	−0.340698	−	0.286083i	−0.0112631	−	0.00945762i
$916$	−31.4144	−	49.9569i	−1.03796	−	1.65062i
$917$	−1.23618	−	17.2841i	−0.0408223	−	0.570770i
$918$	2.24469	−	0.647109i	0.0740858	−	0.0213578i
$919$	−26.3650			−0.869702			−0.434851	−	0.900502i	$-0.643199\pi$
$919$	−26.3650			−0.869702			−0.434851	+	0.900502i	$0.643199\pi$
$920$	27.8469	−	12.0229i	0.918085	−	0.396384i
$921$	−13.9862			−0.460862
$922$	57.6074	−	16.6073i	1.89720	−	0.546933i
$923$	−0.185560	−	2.59447i	−0.00610778	−	0.0853980i
$924$	85.2583	−	53.6129i	2.80479	−	1.76374i
$925$	−7.36744	−	3.73098i	−0.242240	−	0.122674i
$926$	−1.71216	−	4.66045i	−0.0562651	−	0.153152i
$927$	−2.39067	+	6.40965i	−0.0785200	+	0.210520i
$928$	−32.3389	+	13.8167i	−1.06157	+	0.453555i
$929$	23.8153	−	3.42413i	0.781356	−	0.112342i	0.259917	−	0.965631i	$-0.416305\pi$
$929$	23.8153	−	3.42413i	0.781356	−	0.112342i	0.521439	+	0.853289i	$0.325396\pi$
$930$	−19.8480	+	44.7081i	−0.650842	+	1.46604i
$931$	−11.9519	+	3.50939i	−0.391707	+	0.115016i
$932$	−6.80589	+	4.99097i	−0.222934	+	0.163485i
$933$	−7.63999	−	20.4836i	−0.250122	−	0.670603i
$934$	−0.271393	+	3.54885i	−0.00888026	+	0.116122i
$935$	2.54932	+	15.9680i	0.0833717	+	0.522210i
$936$	9.15199	−	39.2684i	0.299142	−	1.28353i
$937$	46.9569	+	10.2149i	1.53402	+	0.333705i	0.898706	−	0.438552i	$-0.144508\pi$
$937$	46.9569	+	10.2149i	1.53402	+	0.333705i	0.635311	+	0.772257i	$0.280872\pi$
$938$	−1.67637	+	0.755617i	−0.0547355	+	0.0246718i
$939$	−23.7192	+	36.9079i	−0.774048	+	1.20444i
$940$	27.6175	+	3.81122i	0.900784	+	0.124308i
$941$	−0.0339893	−	0.00998014i	−0.00110802	−	0.000325343i	0.281179	−	0.959655i	$-0.409275\pi$
$941$	−0.0339893	−	0.00998014i	−0.00110802	−	0.000325343i	−0.282287	+	0.959330i	$0.591093\pi$
$942$	−45.8163	+	29.1265i	−1.49278	+	0.948992i
$943$	−25.8709	+	33.0492i	−0.842472	+	1.07623i
$944$	−2.05102	−	2.46343i	−0.0667551	−	0.0801779i
$945$	0.614507	−	10.9847i	0.0199899	−	0.357333i
$946$	34.2574	+	46.2355i	1.11380	+	1.50325i
$947$	6.67007	+	30.6618i	0.216748	+	0.996375i	0.948984	+	0.315324i	$0.102113\pi$
$947$	6.67007	+	30.6618i	0.216748	+	0.996375i	−0.732236	+	0.681051i	$0.761523\pi$
$948$	−1.61162	+	0.333996i	−0.0523431	+	0.0108477i
$949$	51.2485	−	32.9354i	1.66360	−	1.06913i
$950$	10.2721	+	1.20415i	0.333270	+	0.0390677i
$951$	−27.4854	−	31.7198i	−0.891275	−	1.02859i
$952$	−14.1973	+	3.94182i	−0.460138	+	0.127755i
$953$	−3.89402	−	10.4403i	−0.126140	−	0.338194i	0.858495	−	0.512823i	$-0.171400\pi$
$953$	−3.89402	−	10.4403i	−0.126140	−	0.338194i	−0.984634	+	0.174629i	$0.944127\pi$
$954$	47.3570	−	3.15268i	1.53324	−	0.102072i
$955$	−21.8062	−	38.5025i	−0.705631	−	1.24591i
$956$	45.3229	−	38.4975i	1.46585	−	1.24510i
$957$	63.6217	+	47.6266i	2.05660	+	1.53955i
$958$	−11.1941	+	37.4404i	−0.361664	+	1.20964i
$959$	−20.4214	+	9.32613i	−0.659440	+	0.301156i
$960$	−11.2181	−	40.2888i	−0.362063	−	1.30032i
$961$	−1.81843	+	12.6475i	−0.0586590	+	0.407983i
$962$	13.5042	+	0.0665118i	0.435392	+	0.00214443i
$963$	−10.5315	+	0.753229i	−0.339374	+	0.0242725i
$964$	−0.429801	−	0.379901i	−0.0138429	−	0.0122358i
$965$	−20.9556	−	13.0124i	−0.674585	−	0.418885i
$966$	31.3752	−	54.0074i	1.00948	−	1.73766i
$967$	19.6327	−	19.6327i	0.631345	−	0.631345i	−0.317060	−	0.948405i	$-0.602696\pi$
$967$	19.6327	−	19.6327i	0.631345	−	0.631345i	0.948405	+	0.317060i	$0.102696\pi$
$968$	52.7967	+	8.38901i	1.69695	+	0.269633i
$969$	3.41766	+	2.96142i	0.109791	+	0.0951346i
$970$	18.3680	−	29.2579i	0.589762	−	0.939416i
$971$	3.30166	−	22.9636i	0.105955	−	0.736936i	−0.865705	−	0.500555i	$-0.833129\pi$
$971$	3.30166	−	22.9636i	0.105955	−	0.736936i	0.971660	−	0.236381i	$-0.0759614\pi$
$972$	32.3778	+	24.7391i	1.03852	+	0.793507i
$973$	−14.1593	+	37.9626i	−0.453927	+	1.21702i
$974$	7.64266	+	14.1619i	0.244887	+	0.453776i
$975$	55.6928	−	38.2841i	1.78360	−	1.22607i
$976$	0.328441	−	0.0894500i	0.0105131	−	0.00286323i
$977$	22.3410	+	12.1991i	0.714751	+	0.390284i	0.795096	−	0.606483i	$-0.207420\pi$
$977$	22.3410	+	12.1991i	0.714751	+	0.390284i	−0.0803449	+	0.996767i	$0.525602\pi$
$978$	−35.3408	+	40.3818i	−1.13007	+	1.29127i
$979$	4.49183	−	9.83573i	0.143559	−	0.314351i
$980$	−2.50179	+	38.0044i	−0.0799169	+	1.21401i
$981$	−12.7631	−	14.7294i	−0.407495	−	0.470275i
$982$	0.840444	+	0.545988i	0.0268197	+	0.0174232i
$983$	5.49104	−	25.2419i	0.175137	−	0.805091i	−0.802810	−	0.596235i	$-0.796662\pi$
$983$	5.49104	−	25.2419i	0.175137	−	0.805091i	0.977946	−	0.208856i	$-0.0669739\pi$
$984$	40.3112	+	41.5204i	1.28507	+	1.32362i
$985$	16.8482	+	35.4272i	0.536828	+	1.12880i
$986$	−6.92181	−	9.34201i	−0.220435	−	0.297510i
$987$	50.3874	−	27.5136i	1.60385	−	0.875768i
$988$	−15.9035	+	5.75390i	−0.505958	+	0.183056i
$989$	32.1346	+	15.5214i	1.02182	+	0.493551i
$990$	−29.8278	+	30.4664i	−0.947991	+	0.968287i
$991$	0.551197	+	0.161846i	0.0175094	+	0.00514121i	0.290476	−	0.956882i	$-0.406187\pi$
$991$	0.551197	+	0.161846i	0.0175094	+	0.00514121i	−0.272966	+	0.962024i	$0.588005\pi$
$992$	−19.4538	−	31.9754i	−0.617660	−	1.01522i
$993$	1.12268	+	5.16086i	0.0356271	+	0.163775i
$994$	−2.34391	−	0.887409i	−0.0743444	−	0.0281469i
$995$	24.2769	−	25.0422i	0.769628	−	0.793890i
$996$	7.11396	+	0.0700781i	0.225414	+	0.00222051i
$997$	−1.85024	+	25.8698i	−0.0585977	+	0.819303i	0.880149	+	0.474697i	$0.157442\pi$
$997$	−1.85024	+	25.8698i	−0.0585977	+	0.819303i	−0.938747	+	0.344607i	$0.888012\pi$
$998$	36.4935	−	31.3084i	1.15518	−	0.991050i
$999$	−0.857015	+	1.87660i	−0.0271148	+	0.0593730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bo.a.373.57	yes	2800
5.2	odd	4	inner	920.2.bo.a.557.127	yes	2800
8.5	even	2	inner	920.2.bo.a.373.103	yes	2800
23.14	odd	22	inner	920.2.bo.a.773.32	yes	2800
40.37	odd	4	inner	920.2.bo.a.557.32	yes	2800
115.37	even	44	inner	920.2.bo.a.37.103	yes	2800
184.37	odd	22	inner	920.2.bo.a.773.127	yes	2800
920.37	even	44	inner	920.2.bo.a.37.57	✓	2800

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bo.a.37.57	✓	2800	920.37	even	44	inner
920.2.bo.a.37.103	yes	2800	115.37	even	44	inner
920.2.bo.a.373.57	yes	2800	1.1	even	1	trivial
920.2.bo.a.373.103	yes	2800	8.5	even	2	inner
920.2.bo.a.557.32	yes	2800	40.37	odd	4	inner
920.2.bo.a.557.127	yes	2800	5.2	odd	4	inner
920.2.bo.a.773.32	yes	2800	23.14	odd	22	inner
920.2.bo.a.773.127	yes	2800	184.37	odd	22	inner

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bo (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.391742 - 1.35887i) q^{2} +(0.166783 + 2.33193i) q^{3} +(-1.69308 + 1.06466i) q^{4} +(0.194105 + 2.22763i) q^{5} +(3.10347 - 1.14015i) q^{6} +(-1.37657 + 3.69073i) q^{7} +(2.10998 + 1.88361i) q^{8} +(-2.44063 + 0.350910i) q^{9} +O(q^{10})\)	\(q+(-0.391742 - 1.35887i) q^{2} +(0.166783 + 2.33193i) q^{3} +(-1.69308 + 1.06466i) q^{4} +(0.194105 + 2.22763i) q^{5} +(3.10347 - 1.14015i) q^{6} +(-1.37657 + 3.69073i) q^{7} +(2.10998 + 1.88361i) q^{8} +(-2.44063 + 0.350910i) q^{9} +(2.95103 - 1.13642i) q^{10} +(5.24665 - 1.54056i) q^{11} +(-2.76508 - 3.77057i) q^{12} +(2.02042 + 5.41695i) q^{13} +(5.55450 + 0.424773i) q^{14} +(-5.16230 + 0.824171i) q^{15} +(1.73302 - 3.60509i) q^{16} +(1.29226 + 0.281114i) q^{17} +(1.43294 + 3.17904i) q^{18} +(0.790761 - 1.23045i) q^{19} +(-2.70029 - 3.56489i) q^{20} +(-8.83612 - 2.59452i) q^{21} +(-4.14875 - 6.52603i) q^{22} +(-4.15866 - 2.38863i) q^{23} +(-4.04054 + 5.23449i) q^{24} +(-4.92465 + 0.864788i) q^{25} +(6.56947 - 4.86754i) q^{26} +(0.265509 + 1.22052i) q^{27} +(-1.59872 - 7.71426i) q^{28} +(5.22979 - 3.36098i) q^{29} +(3.14224 + 6.69206i) q^{30} +(4.33286 + 5.00039i) q^{31} +(-5.57775 - 0.942685i) q^{32} +(4.46752 + 11.9779i) q^{33} +(-0.124234 - 1.86615i) q^{34} +(-8.48877 - 2.35010i) q^{35} +(3.75858 - 3.19255i) q^{36} +(1.32222 + 0.989802i) q^{37} +(-1.98180 - 0.592526i) q^{38} +(-12.2950 + 5.61493i) q^{39} +(-3.78642 + 5.06587i) q^{40} +(1.24547 - 8.66245i) q^{41} +(-0.0641446 + 13.0236i) q^{42} +(-7.42225 + 0.530850i) q^{43} +(-7.24282 + 8.19415i) q^{44} +(-1.25544 - 5.36870i) q^{45} +(-1.61672 + 6.58682i) q^{46} +(-4.40810 + 4.40810i) q^{47} +(8.69586 + 3.44001i) q^{48} +(-6.43629 - 5.57708i) q^{49} +(3.10433 + 6.35320i) q^{50} +(-0.440013 + 3.06035i) q^{51} +(-9.18791 - 7.02026i) q^{52} +(4.75649 - 12.7527i) q^{53} +(1.55453 - 0.838923i) q^{54} +(4.45018 + 11.3885i) q^{55} +(-9.85643 + 5.19446i) q^{56} +(3.00121 + 1.63878i) q^{57} +(-6.61588 - 5.78999i) q^{58} +(0.332903 - 0.728955i) q^{59} +(7.86272 - 6.89146i) q^{60} +(0.0557293 + 0.0643150i) q^{61} +(5.09753 - 7.84667i) q^{62} +(2.06459 - 9.49076i) q^{63} +(0.904051 + 7.94875i) q^{64} +(-11.6748 + 5.55220i) q^{65} +(14.5263 - 10.7630i) q^{66} +(-0.289707 + 0.158192i) q^{67} +(-2.48719 + 0.899867i) q^{68} +(4.87653 - 10.0961i) q^{69} +(0.131922 + 12.4558i) q^{70} +(-0.431678 - 0.126752i) q^{71} +(-5.81066 - 3.85678i) q^{72} +(-2.23979 - 10.2962i) q^{73} +(0.827046 - 2.18448i) q^{74} +(-2.83798 - 11.3397i) q^{75} +(-0.0288148 + 2.92513i) q^{76} +(-1.53661 + 21.4846i) q^{77} +(12.4465 + 14.5077i) q^{78} +(0.146226 - 0.320189i) q^{79} +(8.36718 + 3.16075i) q^{80} +(-9.89944 + 2.90674i) q^{81} +(-12.2591 + 1.70101i) q^{82} +(-0.911814 + 1.21804i) q^{83} +(17.7225 - 5.01471i) q^{84} +(-0.375383 + 2.93324i) q^{85} +(3.62896 + 9.87794i) q^{86} +(8.70983 + 11.6350i) q^{87} +(13.9721 + 6.63208i) q^{88} +(1.29494 - 1.49444i) q^{89} +(-6.80358 + 3.80912i) q^{90} -22.7737 q^{91} +(9.58400 - 0.383414i) q^{92} +(-10.9379 + 10.9379i) q^{93} +(7.71689 + 4.26321i) q^{94} +(2.89447 + 1.52268i) q^{95} +(1.26800 - 13.1642i) q^{96} +(8.74538 - 6.54671i) q^{97} +(-5.05718 + 10.9309i) q^{98} +(-12.2645 + 5.60103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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