LMFDB - Embedded newform 552.2.bf.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

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

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

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32050 + 0.506245i) q^{2} +(-0.661683 + 1.60068i) q^{3} +(1.48743 - 1.33699i) q^{4} +(3.61745 + 0.520111i) q^{5} +(0.0634149 - 2.44867i) q^{6} +(-0.429427 + 0.196113i) q^{7} +(-1.28731 + 2.51850i) q^{8} +(-2.12435 - 2.11829i) q^{9} +O(q^{10})$	\(q+(-1.32050 + 0.506245i) q^{2} +(-0.661683 + 1.60068i) q^{3} +(1.48743 - 1.33699i) q^{4} +(3.61745 + 0.520111i) q^{5} +(0.0634149 - 2.44867i) q^{6} +(-0.429427 + 0.196113i) q^{7} +(-1.28731 + 2.51850i) q^{8} +(-2.12435 - 2.11829i) q^{9} +(-5.04014 + 1.14451i) q^{10} +(1.16189 + 3.95704i) q^{11} +(1.15589 + 3.26557i) q^{12} +(-1.26973 - 0.579867i) q^{13} +(0.467776 - 0.476362i) q^{14} +(-3.22614 + 5.44623i) q^{15} +(0.424905 - 3.97737i) q^{16} +(1.14385 - 0.735106i) q^{17} +(3.87757 + 1.72175i) q^{18} +(6.41440 + 4.12229i) q^{19} +(6.07609 - 4.06287i) q^{20} +(-0.0297691 - 0.817139i) q^{21} +(-3.53751 - 4.63706i) q^{22} +(-4.11645 - 2.46067i) q^{23} +(-3.17952 - 3.72701i) q^{24} +(8.01797 + 2.35429i) q^{25} +(1.97023 + 0.122918i) q^{26} +(4.79634 - 1.99877i) q^{27} +(-0.376542 + 0.865844i) q^{28} +(-0.730219 + 0.469283i) q^{29} +(1.50298 - 8.82496i) q^{30} +(4.88523 + 5.63786i) q^{31} +(1.45244 + 5.46721i) q^{32} +(-7.10276 - 0.758490i) q^{33} +(-1.13830 + 1.54977i) q^{34} +(-1.65543 + 0.486078i) q^{35} +(-5.99196 - 0.310564i) q^{36} +(-0.586348 - 4.07814i) q^{37} +(-10.5571 - 2.19621i) q^{38} +(1.76834 - 1.64875i) q^{39} +(-5.96666 + 8.44101i) q^{40} +(-5.85594 - 0.841957i) q^{41} +(0.452983 + 1.06396i) q^{42} +(-2.94971 + 3.40414i) q^{43} +(7.01877 + 4.33239i) q^{44} +(-6.58299 - 8.76769i) q^{45} +(6.68146 + 1.16538i) q^{46} +2.60508i q^{47} +(6.08534 + 3.31189i) q^{48} +(-4.43808 + 5.12182i) q^{49} +(-11.7796 + 0.950225i) q^{50} +(0.419805 + 2.31734i) q^{51} +(-2.66392 + 0.835108i) q^{52} +(3.64897 - 1.66643i) q^{53} +(-5.32169 + 5.06750i) q^{54} +(2.14499 + 14.9187i) q^{55} +(0.0588935 - 1.33397i) q^{56} +(-10.8428 + 7.53976i) q^{57} +(0.726681 - 0.989358i) q^{58} +(-1.14863 + 2.51515i) q^{59} +(2.48291 + 12.4142i) q^{60} +(5.22227 + 6.02682i) q^{61} +(-9.30509 - 4.97166i) q^{62} +(1.32768 + 0.493036i) q^{63} +(-4.68569 - 6.48416i) q^{64} +(-4.29160 - 2.75804i) q^{65} +(9.76317 - 2.59415i) q^{66} +(-13.9853 - 4.10644i) q^{67} +(0.718563 - 2.62273i) q^{68} +(6.66252 - 4.96093i) q^{69} +(1.93992 - 1.47992i) q^{70} +(1.90546 - 6.48938i) q^{71} +(8.06959 - 2.62330i) q^{72} +(3.50996 + 2.25572i) q^{73} +(2.83881 + 5.08835i) q^{74} +(-9.07382 + 11.2764i) q^{75} +(15.0524 - 2.44439i) q^{76} +(-1.27497 - 1.47140i) q^{77} +(-1.50042 + 3.07238i) q^{78} +(-4.47549 - 2.04389i) q^{79} +(3.60575 - 14.1669i) q^{80} +(0.0257347 + 8.99996i) q^{81} +(8.15899 - 1.85274i) q^{82} +(-8.93096 + 1.28408i) q^{83} +(-1.13679 - 1.17564i) q^{84} +(4.52015 - 2.06428i) q^{85} +(2.17175 - 5.98844i) q^{86} +(-0.267999 - 1.47936i) q^{87} +(-11.4615 - 2.16769i) q^{88} +(8.42893 - 9.72751i) q^{89} +(13.1314 + 8.24511i) q^{90} +0.658976 q^{91} +(-9.41282 + 1.84358i) q^{92} +(-12.2569 + 4.08922i) q^{93} +(-1.31881 - 3.44001i) q^{94} +(21.0597 + 18.2484i) q^{95} +(-9.71231 - 1.29268i) q^{96} +(11.4993 + 1.65335i) q^{97} +(3.26758 - 9.01010i) q^{98} +(5.91388 - 10.8674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.32050	+	0.506245i	−0.933733	+	0.357969i
$2$	−1.32050	+	0.506245i	−0.933733	+	0.357969i
$3$	−0.661683	+	1.60068i	−0.382023	+	0.924153i
$3$	−0.661683	+	1.60068i	−0.382023	+	0.924153i
$4$	1.48743	−	1.33699i	0.743716	−	0.668496i
$5$	3.61745	+	0.520111i	1.61777	+	0.232601i	0.890909	−	0.454181i	$-0.150068\pi$
$5$	3.61745	+	0.520111i	1.61777	+	0.232601i	0.726864	+	0.686782i	$0.240977\pi$
$6$	0.0634149	−	2.44867i	0.0258890	−	0.999665i
$7$	−0.429427	+	0.196113i	−0.162308	+	0.0741236i	−0.494912	−	0.868943i	$-0.664800\pi$
$7$	−0.429427	+	0.196113i	−0.162308	+	0.0741236i	0.332604	+	0.943066i	$0.392073\pi$
$8$	−1.28731	+	2.51850i	−0.455131	+	0.890424i
$9$	−2.12435	−	2.11829i	−0.708117	−	0.706095i
$10$	−5.04014	+	1.14451i	−1.59383	+	0.361926i
$11$	1.16189	+	3.95704i	0.350324	+	1.19309i	0.926666	+	0.375885i	$0.122661\pi$
$11$	1.16189	+	3.95704i	0.350324	+	1.19309i	−0.576343	+	0.817208i	$0.695521\pi$
$12$	1.15589	+	3.26557i	0.333676	+	0.942688i
$13$	−1.26973	−	0.579867i	−0.352160	−	0.160826i	0.231478	−	0.972840i	$-0.425644\pi$
$13$	−1.26973	−	0.579867i	−0.352160	−	0.160826i	−0.583638	+	0.812014i	$0.698371\pi$
$14$	0.467776	−	0.476362i	0.125018	−	0.127313i
$15$	−3.22614	+	5.44623i	−0.832985	+	1.40621i
$16$	0.424905	−	3.97737i	0.106226	−	0.994342i
$17$	1.14385	−	0.735106i	0.277424	−	0.178289i	−0.394529	−	0.918883i	$-0.629092\pi$
$17$	1.14385	−	0.735106i	0.277424	−	0.178289i	0.671953	+	0.740594i	$0.265456\pi$
$18$	3.87757	+	1.72175i	0.913953	+	0.405820i
$19$	6.41440	+	4.12229i	1.47156	+	0.945717i	0.997884	+	0.0650206i	$0.0207113\pi$
$19$	6.41440	+	4.12229i	1.47156	+	0.945717i	0.473681	+	0.880697i	$0.342925\pi$
$20$	6.07609	−	4.06287i	1.35866	−	0.908486i
$21$	−0.0297691	−	0.817139i	−0.00649615	−	0.178314i
$22$	−3.53751	−	4.63706i	−0.754200	−	0.988626i
$23$	−4.11645	−	2.46067i	−0.858338	−	0.513084i
$23$	−4.11645	−	2.46067i	−0.858338	−	0.513084i
$24$	−3.17952	−	3.72701i	−0.649018	−	0.760773i
$25$	8.01797	+	2.35429i	1.60359	+	0.470858i
$26$	1.97023	+	0.122918i	0.386395	+	0.0241062i
$27$	4.79634	−	1.99877i	0.923057	−	0.384664i
$28$	−0.376542	+	0.865844i	−0.0711597	+	0.163629i
$29$	−0.730219	+	0.469283i	−0.135598	+	0.0871437i	−0.606681	−	0.794945i	$-0.707500\pi$
$29$	−0.730219	+	0.469283i	−0.135598	+	0.0871437i	0.471083	+	0.882089i	$0.343863\pi$
$30$	1.50298	−	8.82496i	0.274405	−	1.61121i
$31$	4.88523	+	5.63786i	0.877414	+	1.01259i	0.999798	+	0.0201070i	$0.00640069\pi$
$31$	4.88523	+	5.63786i	0.877414	+	1.01259i	−0.122384	+	0.992483i	$0.539054\pi$
$32$	1.45244	+	5.46721i	0.256757	+	0.966476i
$33$	−7.10276	−	0.758490i	−1.23643	−	0.132036i
$34$	−1.13830	+	1.54977i	−0.195218	+	0.265784i
$35$	−1.65543	+	0.486078i	−0.279819	+	0.0821622i
$36$	−5.99196	−	0.310564i	−0.998660	−	0.0517607i
$37$	−0.586348	−	4.07814i	−0.0963951	−	0.670443i	−0.979526	−	0.201316i	$-0.935478\pi$
$37$	−0.586348	−	4.07814i	−0.0963951	−	0.670443i	0.883131	−	0.469126i	$-0.155431\pi$
$38$	−10.5571	−	2.19621i	−1.71259	−	0.356273i
$39$	1.76834	−	1.64875i	0.283161	−	0.264011i
$40$	−5.96666	+	8.44101i	−0.943412	+	1.33464i
$41$	−5.85594	−	0.841957i	−0.914544	−	0.131492i	−0.331054	−	0.943612i	$-0.607404\pi$
$41$	−5.85594	−	0.841957i	−0.914544	−	0.131492i	−0.583490	+	0.812120i	$0.698313\pi$
$42$	0.452983	+	1.06396i	0.0698968	+	0.164173i
$43$	−2.94971	+	3.40414i	−0.449826	+	0.519127i	−0.934691	−	0.355462i	$-0.884323\pi$
$43$	−2.94971	+	3.40414i	−0.449826	+	0.519127i	0.484864	+	0.874589i	$0.338869\pi$
$44$	7.01877	+	4.33239i	1.05812	+	0.653132i
$45$	−6.58299	−	8.76769i	−0.981335	−	1.30701i
$46$	6.68146	+	1.16538i	0.985127	+	0.171825i
$47$			2.60508i			0.379990i	0.981785	+	0.189995i	$0.0608472\pi$
$47$			2.60508i			0.379990i	−0.981785	+	0.189995i	$0.939153\pi$
$48$	6.08534	+	3.31189i	0.878343	+	0.478031i
$49$	−4.43808	+	5.12182i	−0.634011	+	0.731688i
$50$	−11.7796	+	0.950225i	−1.66588	+	0.134382i
$51$	0.419805	+	2.31734i	0.0587844	+	0.324492i
$52$	−2.66392	+	0.835108i	−0.369419	+	0.115809i
$53$	3.64897	−	1.66643i	0.501225	−	0.228902i	−0.148726	−	0.988879i	$-0.547517\pi$
$53$	3.64897	−	1.66643i	0.501225	−	0.228902i	0.649950	+	0.759977i	$0.274790\pi$
$54$	−5.32169	+	5.06750i	−0.724191	+	0.689600i
$55$	2.14499	+	14.9187i	0.289230	+	2.01164i
$56$	0.0588935	−	1.33397i	0.00786998	−	0.178259i
$57$	−10.8428	+	7.53976i	−1.43616	+	0.998665i
$58$	0.726681	−	0.989358i	0.0954179	−	0.129909i
$59$	−1.14863	+	2.51515i	−0.149539	+	0.327445i	−0.969546	−	0.244908i	$-0.921242\pi$
$59$	−1.14863	+	2.51515i	−0.149539	+	0.327445i	0.820007	+	0.572353i	$0.193969\pi$
$60$	2.48291	+	12.4142i	0.320542	+	1.60267i
$61$	5.22227	+	6.02682i	0.668644	+	0.771656i	0.984163	−	0.177263i	$-0.0567244\pi$
$61$	5.22227	+	6.02682i	0.668644	+	0.771656i	−0.315520	+	0.948919i	$0.602179\pi$
$62$	−9.30509	−	4.97166i	−1.18175	−	0.631401i
$63$	1.32768	+	0.493036i	0.167271	+	0.0621167i
$64$	−4.68569	−	6.48416i	−0.585711	−	0.810520i
$65$	−4.29160	−	2.75804i	−0.532307	−	0.342093i
$66$	9.76317	−	2.59415i	1.20176	−	0.319318i
$67$	−13.9853	−	4.10644i	−1.70857	−	0.501682i	−0.726020	−	0.687673i	$-0.758632\pi$
$67$	−13.9853	−	4.10644i	−1.70857	−	0.501682i	−0.982551	+	0.185992i	$0.940450\pi$
$68$	0.718563	−	2.62273i	0.0871386	−	0.318053i
$69$	6.66252	−	4.96093i	0.802073	−	0.597226i
$70$	1.93992	−	1.47992i	0.231865	−	0.176884i
$71$	1.90546	−	6.48938i	0.226136	−	0.770148i	−0.765763	−	0.643122i	$-0.777639\pi$
$71$	1.90546	−	6.48938i	0.226136	−	0.770148i	0.991899	−	0.127026i	$-0.0405431\pi$
$72$	8.06959	−	2.62330i	0.951010	−	0.309159i
$73$	3.50996	+	2.25572i	0.410810	+	0.264012i	0.729683	−	0.683786i	$-0.239668\pi$
$73$	3.50996	+	2.25572i	0.410810	+	0.264012i	−0.318873	+	0.947798i	$0.603304\pi$
$74$	2.83881	+	5.08835i	0.330005	+	0.591508i
$75$	−9.07382	+	11.2764i	−1.04775	+	1.30209i
$76$	15.0524	−	2.44439i	1.72663	−	0.280390i
$77$	−1.27497	−	1.47140i	−0.145297	−	0.167681i
$78$	−1.50042	+	3.07238i	−0.169889	+	0.347878i
$79$	−4.47549	−	2.04389i	−0.503532	−	0.229955i	0.147420	−	0.989074i	$-0.452903\pi$
$79$	−4.47549	−	2.04389i	−0.503532	−	0.229955i	−0.650952	+	0.759119i	$0.725630\pi$
$80$	3.60575	−	14.1669i	0.403135	−	1.58391i
$81$	0.0257347	+	8.99996i	0.00285942	+	0.999996i
$82$	8.15899	−	1.85274i	0.901010	−	0.204601i
$83$	−8.93096	+	1.28408i	−0.980300	+	0.140946i	−0.613791	−	0.789469i	$-0.710356\pi$
$83$	−8.93096	+	1.28408i	−0.980300	+	0.140946i	−0.366509	+	0.930415i	$0.619447\pi$
$84$	−1.13679	−	1.17564i	−0.124034	−	0.128273i
$85$	4.52015	−	2.06428i	0.490279	−	0.223903i
$86$	2.17175	−	5.98844i	0.234186	−	0.645750i
$87$	−0.267999	−	1.47936i	−0.0287325	−	0.158604i
$88$	−11.4615	−	2.16769i	−1.22180	−	0.231077i
$89$	8.42893	−	9.72751i	0.893465	−	1.03111i	−0.105860	−	0.994381i	$-0.533760\pi$
$89$	8.42893	−	9.72751i	0.893465	−	1.03111i	0.999325	−	0.0367327i	$-0.0116950\pi$
$90$	13.1314	+	8.24511i	1.38417	+	0.869111i
$91$	0.658976			0.0690794
$92$	−9.41282	+	1.84358i	−0.981354	+	0.192207i
$93$	−12.2569	+	4.08922i	−1.27098	+	0.424032i
$94$	−1.31881	−	3.44001i	−0.136025	−	0.354810i
$95$	21.0597	+	18.2484i	2.16068	+	1.87224i
$96$	−9.71231	−	1.29268i	−0.991259	−	0.131933i
$97$	11.4993	+	1.65335i	1.16758	+	0.167872i	0.698715	−	0.715400i	$-0.253755\pi$
$97$	11.4993	+	1.65335i	1.16758	+	0.167872i	0.468861	+	0.883272i	$0.344665\pi$
$98$	3.26758	−	9.01010i	0.330075	−	0.910158i
$99$	5.91388	−	10.8674i	0.594367	−	1.09221i
$100$	15.0738	−	7.21812i	1.50738	−	0.721812i
$101$	1.08487	+	7.54545i	0.107949	+	0.750800i	0.969846	+	0.243718i	$0.0783670\pi$
$101$	1.08487	+	7.54545i	0.107949	+	0.750800i	−0.861897	+	0.507083i	$0.830724\pi$
$102$	−1.72749	−	2.84752i	−0.171047	−	0.281946i
$103$	−5.24636	−	17.8675i	−0.516939	−	1.76053i	−0.640252	−	0.768165i	$-0.721170\pi$
$103$	−5.24636	−	17.8675i	−0.516939	−	1.76053i	0.123313	−	0.992368i	$-0.460648\pi$
$104$	3.09493	−	2.45135i	0.303483	−	0.240375i
$105$	0.317315	−	2.97144i	0.0309667	−	0.289983i
$106$	−3.97484	+	4.04779i	−0.386070	+	0.393156i
$107$	4.86506	−	4.21560i	0.470323	−	0.407537i	−0.387190	−	0.922000i	$-0.626554\pi$
$107$	4.86506	−	4.21560i	0.470323	−	0.407537i	0.857513	+	0.514463i	$0.172009\pi$
$108$	4.46189	−	9.38571i	0.429346	−	0.903140i
$109$	14.5386	−	9.34342i	1.39255	−	0.894937i	0.392853	−	0.919601i	$-0.371488\pi$
$109$	14.5386	−	9.34342i	1.39255	−	0.894937i	0.999696	+	0.0246642i	$0.00785165\pi$
$110$	−10.3850	−	18.6143i	−0.990169	−	1.77480i
$111$	6.91578	+	1.75988i	0.656417	+	0.167041i
$112$	0.597546	+	1.79132i	0.0564628	+	0.169264i
$113$	−6.13438	−	1.80122i	−0.577074	−	0.169444i	−0.0198448	−	0.999803i	$-0.506317\pi$
$113$	−6.13438	−	1.80122i	−0.577074	−	0.169444i	−0.557229	+	0.830359i	$0.688135\pi$
$114$	10.5009	−	15.4453i	0.983498	−	1.44659i
$115$	−13.6112	−	11.0423i	−1.26925	−	1.02970i
$116$	−0.458723	+	1.67432i	−0.0425914	+	0.155457i
$117$	1.46903	+	3.92149i	0.135812	+	0.362542i
$118$	0.243482	−	3.90275i	0.0224144	−	0.359277i
$119$	−0.347035	+	0.539997i	−0.0318126	+	0.0495014i
$120$	−9.56331	−	15.1360i	−0.873007	−	1.38172i
$121$	−5.05440	+	3.24827i	−0.459491	+	0.295297i
$122$	−9.94705	−	5.31466i	−0.900564	−	0.481167i
$123$	5.22248	−	8.81637i	0.470895	−	0.794945i
$124$	14.8042	+	1.85441i	1.32946	+	0.166531i
$125$	11.1582	+	5.09578i	0.998019	+	0.455780i
$126$	−2.00279	+	0.0210758i	−0.178423	+	0.00187758i
$127$	−1.01192	+	0.297125i	−0.0897930	+	0.0263656i	−0.326320	−	0.945259i	$-0.605809\pi$
$127$	−1.01192	+	0.297125i	−0.0897930	+	0.0263656i	0.236527	+	0.971625i	$0.423991\pi$
$128$	9.47002	+	6.19021i	0.837039	+	0.547143i
$129$	−3.49717	−	6.97400i	−0.307909	−	0.614027i
$130$	7.06329	+	1.46939i	0.619492	+	0.128874i
$131$	4.63895	+	10.1579i	0.405307	+	0.887499i	0.996704	+	0.0811184i	$0.0258492\pi$
$131$	4.63895	+	10.1579i	0.405307	+	0.887499i	−0.591397	+	0.806380i	$0.701424\pi$
$132$	−11.5790	+	8.36813i	−1.00782	+	0.728352i
$133$	−3.56295	−	0.512275i	−0.308947	−	0.0444198i
$134$	20.5464	−	1.65742i	1.77494	−	0.143179i
$135$	18.3901	−	4.73583i	1.58277	−	0.407595i
$136$	0.378884	+	3.82708i	0.0324891	+	0.328170i
$137$	−9.85433			−0.841912			−0.420956	−	0.907081i	$-0.638305\pi$
$137$	−9.85433			−0.841912			−0.420956	+	0.907081i	$0.638305\pi$
$138$	−6.28640	+	9.92377i	−0.535134	+	0.844767i
$139$			22.1669i			1.88017i	0.340935	+	0.940087i	$0.389256\pi$
$139$			22.1669i			1.88017i	−0.340935	+	0.940087i	$0.610744\pi$
$140$	−1.81246	+	2.93631i	−0.153181	+	0.248163i
$141$	−4.16990	−	1.72374i	−0.351169	−	0.145165i
$142$	0.769069	+	9.53385i	0.0645389	+	0.800063i
$143$	0.819267	−	5.69812i	0.0685105	−	0.476501i
$144$	−9.32785	+	7.54925i	−0.777321	+	0.629105i
$145$	−2.88561	+	1.31781i	−0.239637	+	0.109439i
$146$	−5.77684	−	1.20177i	−0.478095	−	0.0994590i
$147$	−5.26178	−	10.4930i	−0.433985	−	0.865445i
$148$	−6.32460	−	5.28202i	−0.519879	−	0.434179i
$149$	−4.02212	−	13.6981i	−0.329505	−	1.12219i	−0.943083	−	0.332557i	$-0.892089\pi$
$149$	−4.02212	−	13.6981i	−0.329505	−	1.12219i	0.613578	−	0.789634i	$-0.289730\pi$
$150$	6.27333	−	19.4841i	0.512215	−	1.59087i
$151$	4.59601	−	10.0639i	0.374018	−	0.818985i	−0.625239	−	0.780434i	$-0.714998\pi$
$151$	4.59601	−	10.0639i	0.374018	−	0.818985i	0.999257	−	0.0385513i	$-0.0122743\pi$
$152$	−18.6393	+	10.8480i	−1.51184	+	0.879892i
$153$	−3.98710	−	0.861371i	−0.322338	−	0.0696377i
$154$	2.42849	+	1.29753i	0.195693	+	0.104558i
$155$	14.7398	+	22.9356i	1.18393	+	1.84223i
$156$	0.425927	−	4.81665i	0.0341015	−	0.385641i
$157$	18.1884	+	11.6890i	1.45159	+	0.932880i	0.999156	+	0.0410825i	$0.0130806\pi$
$157$	18.1884	+	11.6890i	1.45159	+	0.932880i	0.452434	+	0.891798i	$0.350556\pi$
$158$	6.94458	+	0.433255i	0.552481	+	0.0344679i
$159$	0.252957	+	6.94348i	0.0200608	+	0.550654i
$160$	2.41056	+	20.5328i	0.190571	+	1.62326i
$161$	2.25028	+	0.249389i	0.177347	+	0.0196546i
$162$	−4.59017	−	11.8714i	−0.360638	−	0.932706i
$163$	2.36880	−	8.06738i	0.185538	−	0.631886i	−0.813215	−	0.581964i	$-0.802284\pi$
$163$	2.36880	−	8.06738i	0.185538	−	0.631886i	0.998753	−	0.0499221i	$-0.0158973\pi$
$164$	−9.83599	+	6.57699i	−0.768062	+	0.513576i
$165$	−25.2994	−	6.43802i	−1.96956	−	0.501200i
$166$	11.1433	−	6.21688i	0.864884	−	0.482523i
$167$	−0.955578	−	1.48691i	−0.0739448	−	0.115060i	0.802312	−	0.596905i	$-0.203603\pi$
$167$	−0.955578	−	1.48691i	−0.0739448	−	0.115060i	−0.876256	+	0.481845i	$0.839967\pi$
$168$	2.09629	+	0.976934i	0.161732	+	0.0753721i
$169$	−7.23722	−	8.35219i	−0.556709	−	0.642476i
$170$	−4.92381	+	5.01418i	−0.377639	+	0.384570i
$171$	−4.89426	−	22.3447i	−0.374274	−	1.70874i
$172$	0.163825	+	9.00717i	0.0124915	+	0.686790i
$173$	16.6714	−	4.89517i	1.26751	−	0.372173i	0.422223	−	0.906492i	$-0.361250\pi$
$173$	16.6714	−	4.89517i	1.26751	−	0.372173i	0.845283	+	0.534319i	$0.179432\pi$
$174$	1.10281	+	1.81782i	0.0836040	+	0.137809i
$175$	−3.90484	+	0.561431i	−0.295178	+	0.0424402i
$176$	16.2323	−	2.93990i	1.22356	−	0.221604i
$177$	−3.26593	−	3.50283i	−0.245482	−	0.263289i
$178$	−6.20589	+	17.1123i	−0.465151	+	1.28262i
$179$	3.55284	−	24.7106i	0.265552	−	1.84695i	−0.223506	−	0.974702i	$-0.571750\pi$
$179$	3.55284	−	24.7106i	0.265552	−	1.84695i	0.489058	−	0.872251i	$-0.337341\pi$
$180$	−21.5141	−	4.23993i	−1.60357	−	0.316026i
$181$	−6.61857	+	7.63824i	−0.491954	+	0.567746i	−0.946387	−	0.323036i	$-0.895297\pi$
$181$	−6.61857	+	7.63824i	−0.491954	+	0.567746i	0.454432	+	0.890781i	$0.349842\pi$
$182$	−0.870177	+	0.333603i	−0.0645018	+	0.0247283i
$183$	−13.1025	+	4.37134i	−0.968565	+	0.323139i
$184$	11.4963	−	7.19964i	0.847519	−	0.530765i
$185$		−	15.0574i		−	1.10705i
$186$	14.1151	−	11.6048i	1.03497	−	0.850905i
$187$	4.23787	+	3.67214i	0.309904	+	0.268533i
$188$	3.48297	+	3.87488i	0.254022	+	0.282605i
$189$	−1.66769	+	1.79895i	−0.121307	+	0.130854i
$190$	−37.0475	−	13.4355i	−2.68771	−	0.974717i
$191$	2.26959	+	4.96971i	0.164222	+	0.359595i	0.973796	−	0.227422i	$-0.0730295\pi$
$191$	2.26959	+	4.96971i	0.164222	+	0.359595i	−0.809575	+	0.587017i	$0.800302\pi$
$192$	13.4795	−	3.20983i	0.972799	−	0.231650i
$193$	−0.794736	−	5.52751i	−0.0572063	−	0.397879i	−0.998227	−	0.0595286i	$-0.981040\pi$
$193$	−0.794736	−	5.52751i	−0.0572063	−	0.397879i	0.941020	−	0.338350i	$-0.109869\pi$
$194$	−16.0218	+	3.63822i	−1.15030	+	0.261209i
$195$	7.25442	−	5.04452i	0.519500	−	0.361246i
$196$	0.246488	+	13.5520i	0.0176063	+	0.968002i
$197$	5.22958	−	11.4512i	0.372592	−	0.815863i	−0.626737	−	0.779231i	$-0.715610\pi$
$197$	5.22958	−	11.4512i	0.372592	−	0.815863i	0.999329	−	0.0366319i	$-0.0116629\pi$
$198$	−2.30771	+	17.3442i	−0.164002	+	1.23260i
$199$	1.85296	−	1.60560i	0.131353	−	0.113818i	−0.586707	−	0.809799i	$-0.699576\pi$
$199$	1.85296	−	1.60560i	0.131353	−	0.113818i	0.718060	+	0.695982i	$0.245030\pi$
$200$	−16.2509	+	17.1626i	−1.14911	+	1.21358i
$201$	15.8269	−	19.6688i	1.11634	−	1.38733i
$202$	−5.25242	−	9.41454i	−0.369559	−	0.662405i
$203$	0.221543	−	0.344728i	0.0155493	−	0.0241952i
$204$	3.72269	+	2.88561i	0.260641	+	0.202033i
$205$	−20.7457	−	6.09147i	−1.44894	−	0.425447i
$206$	15.9731	+	20.9380i	1.11290	+	1.45882i
$207$	3.53238	+	13.9471i	0.245517	+	0.969392i
$208$	−2.84586	+	4.80380i	−0.197325	+	0.333084i
$209$	−8.85921	+	30.1717i	−0.612805	+	2.08702i
$210$	1.08527	+	4.08443i	0.0748904	+	0.281852i
$211$	2.62336	−	4.08202i	0.180599	−	0.281018i	−0.739137	−	0.673555i	$-0.764766\pi$
$211$	2.62336	−	4.08202i	0.180599	−	0.281018i	0.919736	+	0.392537i	$0.128403\pi$
$212$	3.19959	−	7.35734i	0.219749	−	0.505304i
$213$	9.12662	+	7.34394i	0.625346	+	0.503198i
$214$	−4.29018	+	8.02961i	−0.293271	+	0.548893i
$215$	−12.4410	+	10.7801i	−0.848466	+	0.735200i
$216$	−1.14045	+	14.6526i	−0.0775977	+	0.996985i
$217$	−3.20351	−	1.46299i	−0.217468	−	0.0993144i
$218$	−14.4682	+	19.6981i	−0.979909	+	1.33412i
$219$	−5.93316	+	4.12576i	−0.400926	+	0.278793i
$220$	23.1367	+	19.3227i	1.55988	+	1.30274i
$221$	−1.87864	+	0.270108i	−0.126371	+	0.0181694i
$222$	−10.0232	+	1.17716i	−0.672713	+	0.0790057i
$223$	−5.42844	−	11.8866i	−0.363515	−	0.795987i	−0.999701	−	0.0244514i	$-0.992216\pi$
$223$	−5.42844	−	11.8866i	−0.363515	−	0.795987i	0.636186	−	0.771536i	$-0.280511\pi$
$224$	−1.69590	−	2.06293i	−0.113312	−	0.137835i
$225$	−12.0459	−	21.9857i	−0.803062	−	1.46571i
$226$	9.01229	−	0.726997i	0.599489	−	0.0483591i
$227$	10.3247	+	8.94637i	0.685272	+	0.593791i	0.926327	−	0.376720i	$-0.122948\pi$
$227$	10.3247	+	8.94637i	0.685272	+	0.593791i	−0.241055	+	0.970511i	$0.577494\pi$
$228$	−6.04727	+	25.7116i	−0.400490	+	1.70279i
$229$	−3.37847			−0.223256			−0.111628	−	0.993750i	$-0.535606\pi$
$229$	−3.37847			−0.223256			−0.111628	+	0.993750i	$0.535606\pi$
$230$	23.5637	+	7.69079i	1.55375	+	0.507116i
$231$	3.19887	−	1.06723i	0.210470	−	0.0702183i
$232$	−0.241876	−	2.44317i	−0.0158799	−	0.160402i
$233$	5.00933	+	4.34061i	0.328172	+	0.284363i	0.803326	−	0.595540i	$-0.203062\pi$
$233$	5.00933	+	4.34061i	0.328172	+	0.284363i	−0.475153	+	0.879903i	$0.657607\pi$
$234$	−3.92509	−	4.43464i	−0.256591	−	0.289901i
$235$	−1.35493	+	9.42376i	−0.0883860	+	0.614738i
$236$	1.65423	+	5.27683i	0.107681	+	0.343492i
$237$	6.23296	−	5.81142i	0.404875	−	0.377492i
$238$	0.184888	−	0.888750i	0.0119845	−	0.0576091i
$239$	29.2556	−	4.20632i	1.89239	−	0.272084i	0.904408	−	0.426670i	$-0.140313\pi$
$239$	29.2556	−	4.20632i	1.89239	−	0.272084i	0.987979	+	0.154585i	$0.0494042\pi$
$240$	20.2909	+	15.1457i	1.30977	+	0.977649i
$241$	−6.10849	−	20.8036i	−0.393482	−	1.34008i	−0.883527	−	0.468380i	$-0.844838\pi$
$241$	−6.10849	−	20.8036i	−0.393482	−	1.34008i	0.490045	−	0.871697i	$-0.336980\pi$
$242$	5.02991	−	6.84809i	0.323335	−	0.440212i
$243$	−14.4231	−	5.91393i	−0.925241	−	0.379379i
$244$	15.8256	+	1.98235i	1.01313	+	0.126907i
$245$	−18.7184	+	16.2196i	−1.19588	+	1.03623i
$246$	−2.43303	+	14.2859i	−0.155124	+	0.910833i
$247$	−5.75419	−	8.95370i	−0.366130	−	0.569710i
$248$	−20.4877	+	5.04582i	−1.30097	+	0.320410i
$249$	3.85406	−	15.1453i	0.244241	−	0.959791i
$250$	−17.3141	−	1.08018i	−1.09504	−	0.0683167i
$251$	5.39775	−	18.3830i	0.340703	−	1.16033i	−0.593872	−	0.804560i	$-0.702401\pi$
$251$	5.39775	−	18.3830i	0.340703	−	1.16033i	0.934574	−	0.355768i	$-0.115781\pi$
$252$	2.63401	−	1.04173i	0.165927	−	0.0656231i
$253$	4.95410	−	19.1480i	0.311461	−	1.20382i
$254$	1.18581	−	0.904631i	0.0744046	−	0.0567616i
$255$	0.313349	+	8.60121i	0.0196227	+	0.538628i
$256$	−15.6389	−	3.38001i	−0.977432	−	0.211251i
$257$	−0.239131	+	0.372094i	−0.0149166	+	0.0232106i	−0.848632	−	0.528984i	$-0.822573\pi$
$257$	−0.239131	+	0.372094i	−0.0149166	+	0.0232106i	0.833715	+	0.552195i	$0.186209\pi$
$258$	8.14857	+	7.43873i	0.507308	+	0.463115i
$259$	1.05157	+	1.63627i	0.0653413	+	0.101673i
$260$	−10.0709	+	1.63543i	−0.624573	+	0.101425i
$261$	2.54532	+	0.549890i	0.157551	+	0.0340373i
$262$	−11.2681	−	11.0650i	−0.696146	−	0.683600i
$263$	6.95367	−	15.2264i	0.428782	−	0.938901i	−0.564741	−	0.825268i	$-0.691024\pi$
$263$	6.95367	−	15.2264i	0.428782	−	0.938901i	0.993523	−	0.113633i	$-0.0362488\pi$
$264$	11.0537	−	16.9119i	0.680307	−	1.04086i
$265$	14.0667	−	4.13035i	0.864110	−	0.253726i
$266$	4.96420	−	1.12727i	0.304375	−	0.0691172i
$267$	9.99334	+	19.9285i	0.611583	+	1.21961i
$268$	−26.2924	+	12.5901i	−1.60606	+	0.769064i
$269$	−8.64985	−	18.9405i	−0.527391	−	1.15482i	−0.966565	−	0.256422i	$-0.917456\pi$
$269$	−8.64985	−	18.9405i	−0.527391	−	1.15482i	0.439174	−	0.898402i	$-0.355271\pi$
$270$	−21.8866	+	15.5636i	−1.33198	+	0.947168i
$271$	−0.419511	+	2.91777i	−0.0254835	+	0.177242i	−0.998588	−	0.0531225i	$-0.983083\pi$
$271$	−0.419511	+	2.91777i	−0.0254835	+	0.177242i	0.973105	+	0.230364i	$0.0739917\pi$
$272$	−2.43776	−	4.86185i	−0.147811	−	0.294793i
$273$	−0.436033	+	1.05481i	−0.0263899	+	0.0638400i
$274$	13.0126	−	4.98871i	0.786122	−	0.301379i
$275$			34.4629i			2.07819i
$276$	3.27732	−	16.2868i	0.197272	−	0.980349i
$277$			12.2143i			0.733885i	0.930244	+	0.366942i	$0.119595\pi$
$277$			12.2143i			0.733885i	−0.930244	+	0.366942i	$0.880405\pi$
$278$	−11.2219	−	29.2714i	−0.673045	−	1.75558i
$279$	1.56465	−	22.3251i	0.0936729	−	1.33657i
$280$	0.906856	−	4.79493i	0.0541950	−	0.286552i
$281$	1.01448	−	7.05583i	0.0605185	−	0.420916i	−0.936929	−	0.349518i	$-0.886345\pi$
$281$	1.01448	−	7.05583i	0.0605185	−	0.420916i	0.997448	−	0.0713970i	$-0.0227457\pi$
$282$	6.37898	+	0.165201i	0.379863	+	0.00983759i
$283$	3.06983	+	6.72199i	0.182482	+	0.399581i	0.978661	−	0.205481i	$-0.0658758\pi$
$283$	3.06983	+	6.72199i	0.182482	+	0.399581i	−0.796179	+	0.605061i	$0.793149\pi$
$284$	−5.84202	−	12.2001i	−0.346660	−	0.723942i
$285$	−43.1447	+	21.6353i	−2.55567	+	1.28156i
$286$	1.80281	+	7.93911i	0.106602	+	0.469450i
$287$	2.67981	−	0.786864i	0.158184	−	0.0464471i
$288$	8.49563	−	14.6910i	0.500610	−	0.865673i
$289$	−6.29405	+	13.7820i	−0.370238	+	0.810709i
$290$	3.14331	−	3.20100i	0.184581	−	0.187969i
$291$	−10.2554	+	17.3127i	−0.601180	+	1.01489i
$292$	8.23670	−	1.33757i	0.482017	−	0.0782753i
$293$	7.85508	+	12.2227i	0.458899	+	0.714060i	0.991182	−	0.132506i	$-0.0423024\pi$
$293$	7.85508	+	12.2227i	0.458899	+	0.714060i	−0.532284	+	0.846566i	$0.678666\pi$
$294$	12.2602	+	11.1922i	0.715029	+	0.652741i
$295$	−5.46328	+	8.50103i	−0.318084	+	0.494949i
$296$	11.0256	+	3.77310i	0.640851	+	0.219307i
$297$	13.4821	+	16.6570i	0.782308	+	0.966536i
$298$	12.2458	+	16.0521i	0.709380	+	0.929874i
$299$	3.79992	+	5.51138i	0.219755	+	0.318731i
$300$	1.57979	+	28.9045i	0.0912090	+	1.66880i
$301$	0.599088	−	2.04031i	0.0345308	−	0.117601i
$302$	−0.974243	+	15.6160i	−0.0560614	+	0.898600i
$303$	−12.7957	−	3.25616i	−0.735093	−	0.187062i
$304$	19.1214	−	23.7609i	1.09669	−	1.36278i
$305$	15.7567	+	24.5179i	0.902226	+	1.40389i
$306$	5.70102	−	0.881009i	0.325906	−	0.0503639i
$307$	−14.8755	+	12.8897i	−0.848990	+	0.735654i	−0.966294	−	0.257442i	$-0.917120\pi$
$307$	−14.8755	+	12.8897i	−0.848990	+	0.735654i	0.117304	+	0.993096i	$0.462575\pi$
$308$	−3.86368	−	0.483974i	−0.220154	−	0.0275770i
$309$	32.0715	+	3.42485i	1.82448	+	0.194833i
$310$	−31.0749	−	22.8244i	−1.76493	−	1.29634i
$311$	−5.09792	−	17.3619i	−0.289076	−	0.984504i	−0.968137	−	0.250422i	$-0.919431\pi$
$311$	−5.09792	−	17.3619i	−0.289076	−	0.984504i	0.679060	−	0.734082i	$-0.262387\pi$
$312$	1.87597	+	6.57601i	0.106206	+	0.372293i
$313$	15.2071	−	2.18644i	0.859554	−	0.123585i	0.301577	−	0.953442i	$-0.402487\pi$
$313$	15.2071	−	2.18644i	0.859554	−	0.123585i	0.557977	+	0.829857i	$0.311578\pi$
$314$	−29.9352	−	6.22747i	−1.68934	−	0.351437i
$315$	4.54637	+	2.47407i	0.256159	+	0.139398i
$316$	−9.38965	+	2.94355i	−0.528209	+	0.165588i
$317$	−3.00617	+	20.9084i	−0.168843	+	1.17433i	0.712437	+	0.701736i	$0.247591\pi$
$317$	−3.00617	+	20.9084i	−0.168843	+	1.17433i	−0.881280	+	0.472594i	$0.843318\pi$
$318$	−3.84913	−	9.04079i	−0.215849	−	0.506983i
$319$	−2.70541	−	2.34425i	−0.151474	−	0.131253i
$320$	−13.5778	−	25.8932i	−0.759021	−	1.44747i
$321$	3.52870	+	10.5768i	0.196953	+	0.590339i
$322$	−3.09774	+	0.809875i	−0.172630	+	0.0451326i
$323$	10.3674			0.576858
$324$	12.0712	+	13.3524i	0.670620	+	0.741801i
$325$	−8.81550	−	7.63867i	−0.488996	−	0.423717i
$326$	0.956081	+	11.8522i	0.0529524	+	0.656430i
$327$	5.33585	+	29.4541i	0.295073	+	1.62881i
$328$	9.65885	−	13.6643i	0.533321	−	0.754486i
$329$	−0.510890	−	1.11869i	−0.0281663	−	0.0616755i
$330$	36.6670	−	4.30630i	2.01845	−	0.237054i
$331$	−19.8516	+	2.85422i	−1.09114	+	0.156882i	−0.664316	−	0.747452i	$-0.731277\pi$
$331$	−19.8516	+	2.85422i	−1.09114	+	0.156882i	−0.426825	+	0.904334i	$0.640368\pi$
$332$	−11.5674	+	13.8506i	−0.634843	+	0.760150i
$333$	−7.39306	+	9.90546i	−0.405137	+	0.542816i
$334$	2.01458	+	1.47970i	0.110233	+	0.0809657i
$335$	−48.4552	−	22.1287i	−2.64739	−	1.20902i
$336$	−3.26271	−	0.228804i	−0.177996	−	0.0124823i
$337$	−7.72058	+	6.68992i	−0.420567	+	0.364423i	−0.839284	−	0.543694i	$-0.817025\pi$
$337$	−7.72058	+	6.68992i	−0.420567	+	0.364423i	0.418717	+	0.908117i	$0.362480\pi$
$338$	13.7850	+	7.36525i	0.749805	+	0.400617i
$339$	6.94218	−	8.62734i	0.377048	−	0.468573i
$340$	3.96348	−	9.11388i	0.214950	−	0.494269i
$341$	−16.6331	+	25.8817i	−0.900735	+	1.40157i
$342$	17.7748	+	27.0285i	0.961150	+	1.46153i
$343$	1.83240	−	6.24057i	0.0989401	−	0.336959i
$344$	−4.77617	−	11.8110i	−0.257514	−	0.636807i
$345$	26.6816	−	14.4807i	1.43649	−	0.779613i
$346$	−19.5364	+	14.9039i	−1.05029	+	0.801239i
$347$	−24.9371	−	7.32218i	−1.33869	−	0.393075i	−0.467489	−	0.883999i	$-0.654841\pi$
$347$	−24.9371	−	7.32218i	−1.33869	−	0.393075i	−0.871203	+	0.490923i	$0.836659\pi$
$348$	−2.37653	−	1.84214i	−0.127395	−	0.0987491i
$349$	15.3055	−	23.8158i	0.819285	−	1.27483i	−0.139363	−	0.990241i	$-0.544506\pi$
$349$	15.3055	−	23.8158i	0.819285	−	1.27483i	0.958649	−	0.284592i	$-0.0918580\pi$
$350$	4.87211	−	2.71817i	0.260425	−	0.145292i
$351$	−7.24909	−	0.243337i	−0.386928	−	0.0129884i
$352$	−19.9464	+	12.0997i	−1.06315	+	0.644914i
$353$	11.1956	−	9.70100i	0.595879	−	0.516332i	−0.303885	−	0.952709i	$-0.598284\pi$
$353$	11.1956	−	9.70100i	0.595879	−	0.516332i	0.899764	+	0.436377i	$0.143738\pi$
$354$	6.08594	+	2.97212i	0.323464	+	0.157966i
$355$	10.2681	−	22.4840i	0.544974	−	1.19333i
$356$	−0.468137	−	25.7384i	−0.0248112	−	1.36413i
$357$	−0.634735	−	0.912798i	−0.0335937	−	0.0483104i
$358$	7.81808	+	34.4289i	0.413198	+	1.81962i
$359$	−1.62531	−	11.3043i	−0.0857807	−	0.596618i	−0.986690	−	0.162611i	$-0.948008\pi$
$359$	−1.62531	−	11.3043i	−0.0857807	−	0.596618i	0.900910	−	0.434007i	$-0.142901\pi$
$360$	30.5558	−	5.29258i	1.61043	−	0.278943i
$361$	16.2584	+	35.6010i	0.855707	+	1.87374i
$362$	4.87299	−	13.4369i	0.256119	−	0.706228i
$363$	−1.85502	−	10.2398i	−0.0973634	−	0.537450i
$364$	0.980182	−	0.881045i	0.0513755	−	0.0461793i
$365$	11.5239	+	9.98551i	0.603188	+	0.522666i
$366$	15.0889	−	12.4054i	0.788708	−	0.648442i
$367$		−	18.9944i		−	0.991498i	−0.868466	−	0.495749i	$-0.834894\pi$
$367$		−	18.9944i		−	0.991498i	0.868466	−	0.495749i	$-0.165106\pi$
$368$	−11.5361	+	15.3271i	−0.601360	+	0.798979i
$369$	10.6566	+	14.1932i	0.554758	+	0.738866i
$370$	7.62276	+	19.8833i	0.396288	+	1.03369i
$371$	−1.24016	+	1.43122i	−0.0643858	+	0.0743051i
$372$	−12.7640	+	22.4698i	−0.661784	+	1.16500i
$373$	1.56279	−	10.8694i	0.0809180	−	0.562797i	−0.908520	−	0.417841i	$-0.862787\pi$
$373$	1.56279	−	10.8694i	0.0809180	−	0.562797i	0.989438	−	0.144956i	$-0.0463040\pi$
$374$	−7.45510	−	2.70365i	−0.385494	−	0.139802i
$375$	−15.5399	+	14.4889i	−0.802477	+	0.748204i
$376$	−6.56090	−	3.35354i	−0.338353	−	0.172945i
$377$	1.19930	−	0.172434i	0.0617673	−	0.00888080i
$378$	1.29148	−	3.21977i	0.0664264	−	0.165607i
$379$	−18.6594	+	5.47889i	−0.958468	+	0.281432i	−0.723308	−	0.690525i	$-0.757379\pi$
$379$	−18.6594	+	5.47889i	−0.958468	+	0.281432i	−0.235159	+	0.971957i	$0.575561\pi$
$380$	55.7228	−	1.01350i	2.85852	−	0.0519915i
$381$	0.193965	−	1.81636i	0.00993713	−	0.0930547i
$382$	−5.51288	−	5.41352i	−0.282063	−	0.276980i
$383$	11.6057	+	13.3937i	0.593023	+	0.684385i	0.970352	−	0.241694i	$-0.0777031\pi$
$383$	11.6057	+	13.3937i	0.593023	+	0.684385i	−0.377330	+	0.926079i	$0.623158\pi$
$384$	−16.1747	+	11.0625i	−0.825412	+	0.564531i
$385$	−3.84686	−	5.98584i	−0.196054	−	0.305067i
$386$	3.84772	+	6.89674i	0.195844	+	0.351035i
$387$	13.4772	−	0.983275i	0.685083	−	0.0499827i
$388$	19.3149	−	12.9152i	0.980567	−	0.655671i
$389$	3.32149	−	11.3120i	0.168406	−	0.573540i	−0.831433	−	0.555625i	$-0.812479\pi$
$389$	3.32149	−	11.3120i	0.168406	−	0.573540i	0.999840	−	0.0179148i	$-0.00570275\pi$
$390$	−7.02568	+	10.3338i	−0.355759	+	0.523272i
$391$	−6.51743	+	0.211397i	−0.329601	+	0.0106908i
$392$	−7.18613	−	17.7706i	−0.362955	−	0.897553i
$393$	−19.3290	+	0.704174i	−0.975021	+	0.0355209i
$394$	−1.10855	+	17.7687i	−0.0558477	+	0.895175i
$395$	−15.1268	−	9.72141i	−0.761113	−	0.489137i
$396$	−5.73309	−	24.0713i	−0.288099	−	1.20963i
$397$	15.3244	+	23.8452i	0.769110	+	1.19676i	0.975867	+	0.218366i	$0.0700726\pi$
$397$	15.3244	+	23.8452i	0.769110	+	1.19676i	−0.206757	+	0.978392i	$0.566291\pi$
$398$	−1.63400	+	3.05824i	−0.0819051	+	0.153296i
$399$	3.17753	−	5.36418i	0.159075	−	0.268545i
$400$	12.7708	−	30.8901i	0.638538	−	1.54450i
$401$	−7.05987	+	15.4590i	−0.352553	+	0.771984i	0.647398	+	0.762152i	$0.275857\pi$
$401$	−7.05987	+	15.4590i	−0.352553	+	0.771984i	−0.999952	+	0.00983213i	$0.996870\pi$
$402$	−10.9422	+	33.9849i	−0.545747	+	1.69501i
$403$	−2.93373	−	9.99136i	−0.146139	−	0.497705i
$404$	11.7019	+	9.77288i	0.582190	+	0.486219i
$405$	−4.58789	+	32.5703i	−0.227974	+	1.61843i
$406$	−0.118031	+	0.567368i	−0.00585776	+	0.0281580i
$407$	15.4561	−	7.05857i	0.766131	−	0.349880i
$408$	−6.37664	−	1.92584i	−0.315691	−	0.0953435i
$409$	2.27648	−	15.8333i	0.112565	−	0.782906i	−0.852844	−	0.522166i	$-0.825124\pi$
$409$	2.27648	−	15.8333i	0.112565	−	0.782906i	0.965409	−	0.260740i	$-0.0839667\pi$
$410$	30.4784	−	2.45861i	1.50522	−	0.121422i
$411$	6.52044	−	15.7736i	0.321630	−	0.778056i
$412$	−31.6922	−	19.5623i	−1.56137	−	0.963765i
$413$		−	1.30534i		−	0.0642314i
$414$	−11.7252	−	16.6289i	−0.576261	−	0.817266i
$415$	−32.9752			−1.61869
$416$	1.32605	−	7.78411i	0.0650151	−	0.381648i
$417$	−35.4821	−	14.6675i	−1.73757	−	0.718269i
$418$	−3.57571	−	44.3266i	−0.174894	−	2.16809i
$419$	0.915083	+	0.131569i	0.0447047	+	0.00642757i	0.164631	−	0.986355i	$-0.447357\pi$
$419$	0.915083	+	0.131569i	0.0447047	+	0.00642757i	−0.119926	+	0.992783i	$0.538266\pi$
$420$	−3.50081	−	4.84407i	−0.170822	−	0.236366i
$421$	−12.8058	−	28.0408i	−0.624117	−	1.36663i	−0.912487	−	0.409106i	$-0.865840\pi$
$421$	−12.8058	−	28.0408i	−0.624117	−	1.36663i	0.288370	−	0.957519i	$-0.406887\pi$
$422$	−1.39763	+	6.71837i	−0.0680358	+	0.327045i
$423$	5.51831	−	5.53411i	0.268309	−	0.269078i
$424$	−0.500436	+	11.3351i	−0.0243033	+	0.550483i
$425$	10.9020	−	3.20111i	0.528824	−	0.155277i
$426$	−15.7695	−	5.07735i	−0.764036	−	0.245999i
$427$	−3.42452	−	1.56393i	−0.165724	−	0.0756837i
$428$	1.60022	−	12.7750i	0.0773497	−	0.617501i
$429$	8.57878	+	5.08174i	0.414187	+	0.245349i
$430$	10.9709	−	20.5333i	0.529062	−	0.990206i
$431$	−28.4479	+	18.2823i	−1.37029	+	0.880629i	−0.998855	−	0.0478318i	$-0.984769\pi$
$431$	−28.4479	+	18.2823i	−1.37029	+	0.880629i	−0.371430	+	0.928461i	$0.621132\pi$
$432$	−5.91186	−	19.9261i	−0.284434	−	0.958695i
$433$	−2.87169	+	4.46844i	−0.138005	+	0.214740i	−0.903376	−	0.428849i	$-0.858919\pi$
$433$	−2.87169	+	4.46844i	−0.138005	+	0.214740i	0.765371	+	0.643589i	$0.222555\pi$
$434$	4.97086	+	0.310119i	0.238609	+	0.0148862i
$435$	−0.200039	−	5.49092i	−0.00959113	−	0.263269i
$436$	9.13316	−	33.3357i	0.437399	−	1.59649i
$437$	−16.2610	−	32.7529i	−0.777867	−	1.56678i
$438$	5.74609	−	8.45169i	0.274559	−	0.403837i
$439$	−3.48068	−	1.02202i	−0.166124	−	0.0487783i	0.197613	−	0.980280i	$-0.436681\pi$
$439$	−3.48068	−	1.02202i	−0.166124	−	0.0487783i	−0.363737	+	0.931502i	$0.618499\pi$
$440$	−40.3341	−	13.8028i	−1.92285	−	0.658022i
$441$	20.2775	−	1.47942i	0.965595	−	0.0704485i
$442$	2.34400	−	1.30773i	0.111493	−	0.0622024i
$443$	−7.55181	+	4.85326i	−0.358798	+	0.230585i	−0.707603	−	0.706610i	$-0.750224\pi$
$443$	−7.55181	+	4.85326i	−0.358798	+	0.230585i	0.348806	+	0.937195i	$0.386587\pi$
$444$	12.6397	−	6.62863i	0.599853	−	0.314581i
$445$	35.5506	−	30.8048i	1.68526	−	1.46029i
$446$	13.1858	+	12.9481i	0.624365	+	0.613112i
$447$	24.5876	+	2.62566i	1.16295	+	0.124190i
$448$	3.28379	+	1.86555i	0.155144	+	0.0881388i
$449$	−4.86804	−	16.5790i	−0.229737	−	0.782412i	−0.990987	−	0.133954i	$-0.957232\pi$
$449$	−4.86804	−	16.5790i	−0.229737	−	0.782412i	0.761251	−	0.648458i	$-0.224586\pi$
$450$	27.0368	+	22.9339i	1.27453	+	1.08111i
$451$	−3.47231	−	24.1505i	−0.163505	−	1.13720i
$452$	−11.5327	+	5.52243i	−0.542451	+	0.259753i
$453$	13.0679	+	14.0158i	0.613984	+	0.658521i
$454$	−18.1628	−	6.58686i	−0.852420	−	0.309136i
$455$	2.38381	+	0.342741i	0.111755	+	0.0160679i
$456$	−5.03094	−	37.0135i	−0.235595	−	1.73331i
$457$	9.40723	+	8.15141i	0.440052	+	0.381307i	0.846519	−	0.532358i	$-0.178694\pi$
$457$	9.40723	+	8.15141i	0.440052	+	0.381307i	−0.406467	+	0.913665i	$0.633240\pi$
$458$	4.46127	−	1.71034i	0.208461	−	0.0799188i
$459$	4.01697	−	5.81211i	0.187496	−	0.271286i
$460$	−35.0093	+	1.77335i	−1.63232	+	0.0826829i
$461$	−37.6758			−1.75474			−0.877368	−	0.479817i	$-0.840703\pi$
$461$	−37.6758			−1.75474			−0.877368	+	0.479817i	$0.840703\pi$
$462$	−3.68382	+	3.02868i	−0.171387	+	0.140907i
$463$	6.90680	−	7.97087i	0.320986	−	0.370438i	−0.572208	−	0.820108i	$-0.693913\pi$
$463$	6.90680	−	7.97087i	0.320986	−	0.370438i	0.893195	+	0.449670i	$0.148459\pi$
$464$	1.55624	+	3.10375i	0.0722466	+	0.144088i
$465$	−46.4655	+	8.41761i	−2.15479	+	0.390357i
$466$	−8.81223	−	3.19582i	−0.408219	−	0.148043i
$467$	33.6619	−	15.3729i	1.55769	−	0.711372i	0.564235	−	0.825614i	$-0.309171\pi$
$467$	33.6619	−	15.3729i	1.55769	−	0.711372i	0.993453	+	0.114242i	$0.0364438\pi$
$468$	7.42809	+	3.86887i	0.343364	+	0.178839i
$469$	6.81097	−	0.979270i	0.314501	−	0.0452185i
$470$	−2.98155	−	13.1300i	−0.137529	−	0.605641i
$471$	−30.7452	+	21.3794i	−1.41666	+	0.985109i
$472$	−4.85578	−	6.13060i	−0.223505	−	0.282184i
$473$	−16.8976	−	7.71687i	−0.776952	−	0.354822i
$474$	−5.28862	+	10.8294i	−0.242914	+	0.497410i
$475$	41.7254	+	48.1537i	1.91449	+	2.20944i
$476$	0.205781	+	1.26719i	0.00943194	+	0.0580816i
$477$	−11.2817	−	4.18948i	−0.516552	−	0.191823i
$478$	−36.5025	+	20.3649i	−1.66959	+	0.931471i
$479$	−4.50393	−	2.89450i	−0.205790	−	0.132253i	0.433687	−	0.901064i	$-0.357212\pi$
$479$	−4.50393	−	2.89450i	−0.205790	−	0.132253i	−0.639476	+	0.768811i	$0.720849\pi$
$480$	−34.4615	−	9.72768i	−1.57294	−	0.444006i
$481$	−1.62028	+	5.51815i	−0.0738782	+	0.251606i
$482$	18.5980	+	24.3787i	0.847114	+	1.11042i
$483$	−1.88816	+	3.43696i	−0.0859144	+	0.156387i
$484$	−3.17517	+	11.5893i	−0.144326	+	0.526785i
$485$	40.7382	+	11.9618i	1.84983	+	0.543158i
$486$	22.0396	+	0.507716i	0.999735	+	0.0230305i
$487$	8.08415	+	5.19537i	0.366328	+	0.235425i	0.710835	−	0.703359i	$-0.248317\pi$
$487$	8.08415	+	5.19537i	0.366328	+	0.235425i	−0.344507	+	0.938784i	$0.611954\pi$
$488$	−21.9012	+	5.39394i	−0.991422	+	0.244172i
$489$	11.3459	+	9.12973i	0.513079	+	0.412861i
$490$	16.5066	−	30.8941i	0.745691	−	1.39565i
$491$	−6.63891	−	7.66171i	−0.299610	−	0.345768i	0.585905	−	0.810380i	$-0.300739\pi$
$491$	−6.63891	−	7.66171i	−0.299610	−	0.345768i	−0.885514	+	0.464612i	$0.846194\pi$
$492$	−4.01934	−	20.0962i	−0.181206	−	0.906005i
$493$	−0.490286	+	1.07358i	−0.0220814	+	0.0483515i
$494$	12.1312	+	8.91031i	0.545807	+	0.400894i
$495$	27.0454	−	36.2363i	1.21560	−	1.62870i
$496$	24.4996	−	17.0348i	1.10007	−	0.764886i
$497$	0.454397	+	3.16040i	0.0203825	+	0.141763i
$498$	2.57792	+	21.9504i	0.115520	+	0.983620i
$499$	13.9876	−	6.38794i	0.626173	−	0.285964i	−0.0769466	−	0.997035i	$-0.524517\pi$
$499$	13.9876	−	6.38794i	0.626173	−	0.285964i	0.703120	+	0.711072i	$0.251790\pi$
$500$	23.4101	−	7.33879i	1.04693	−	0.328201i
$501$	3.01235	−	0.545712i	0.134582	−	0.0243806i
$502$	2.17861	+	27.0074i	0.0972361	+	1.20540i
$503$	−12.3576	+	14.2615i	−0.551000	+	0.635888i	−0.961116	−	0.276145i	$-0.910943\pi$
$503$	−12.3576	+	14.2615i	−0.551000	+	0.635888i	0.410116	+	0.912034i	$0.365488\pi$
$504$	−2.95084	+	2.70906i	−0.131441	+	0.120671i
$505$			27.8596i			1.23973i
$506$	3.15170	+	27.7929i	0.140110	+	1.23554i
$507$	18.1579	−	6.05796i	0.806422	−	0.269044i
$508$	−1.10790	+	1.79488i	−0.0491552	+	0.0796348i
$509$	15.0381	−	17.3549i	0.666553	−	0.769243i	−0.317280	−	0.948332i	$-0.602770\pi$
$509$	15.0381	−	17.3549i	0.666553	−	0.769243i	0.983833	+	0.179089i	$0.0573150\pi$
$510$	−4.76810	−	11.1992i	−0.211135	−	0.495911i
$511$	−1.94965	−	0.280317i	−0.0862473	−	0.0124005i
$512$	22.3623	−	3.45382i	0.988282	−	0.152639i
$513$	39.0052	+	6.95097i	1.72212	+	0.306893i
$514$	0.127400	−	0.612409i	0.00561939	−	0.0270122i
$515$	−9.68539	−	67.3633i	−0.426789	−	2.96838i
$516$	−14.5260	−	5.69766i	−0.639471	−	0.250825i
$517$	−10.3084	+	3.02683i	−0.453364	+	0.133120i
$518$	−2.21695	−	1.62834i	−0.0974072	−	0.0715454i
$519$	−3.19560	+	29.9247i	−0.140271	+	1.31355i
$520$	12.4707	−	7.25795i	0.546877	−	0.318282i
$521$	22.8652	+	26.3878i	1.00174	+	1.15607i	0.987730	+	0.156169i	$0.0499145\pi$
$521$	22.8652	+	26.3878i	1.00174	+	1.15607i	0.0140108	+	0.999902i	$0.495540\pi$
$522$	−3.63947	+	0.562426i	−0.159295	+	0.0246167i
$523$	−9.03672	+	5.80755i	−0.395148	+	0.253946i	−0.723093	−	0.690750i	$-0.757280\pi$
$523$	−9.03672	+	5.80755i	−0.395148	+	0.253946i	0.327945	+	0.944697i	$0.393644\pi$
$524$	20.4811	+	8.90692i	0.894723	+	0.389101i
$525$	1.68509	−	6.62188i	0.0735435	−	0.289003i
$526$	−1.47401	+	23.6267i	−0.0642699	+	1.03017i
$527$	9.73238	+	2.85769i	0.423949	+	0.124483i
$528$	−6.03480	+	27.9280i	−0.262631	+	1.21541i
$529$	10.8902	+	20.2584i	0.473489	+	0.880800i
$530$	−16.4841	+	12.5753i	−0.716023	+	0.546237i
$531$	7.76791	−	2.90994i	0.337099	−	0.126281i
$532$	−5.98455	+	4.00166i	−0.259463	+	0.173494i
$533$	6.94724	+	4.46472i	0.300919	+	0.193389i
$534$	−23.2849	−	21.2565i	−1.00764	−	0.919860i
$535$	19.7917	−	12.7194i	0.855670	−	0.549906i
$536$	28.3454	−	29.9356i	1.22433	−	1.29302i
$537$	37.2028	+	22.0375i	1.60542	+	0.950989i
$538$	21.0107	+	20.6320i	0.905834	+	0.889508i
$539$	−25.4238	−	11.6107i	−1.09508	−	0.500107i
$540$	21.0223	−	31.6317i	0.904655	−	1.36121i
$541$	6.02404	+	20.5160i	0.258994	+	0.882052i	0.981625	+	0.190819i	$0.0611142\pi$
$541$	6.02404	+	20.5160i	0.258994	+	0.882052i	−0.722631	+	0.691234i	$0.757068\pi$
$542$	−0.923141	−	4.06528i	−0.0396523	−	0.174619i
$543$	−7.84697	−	15.6483i	−0.336746	−	0.671533i
$544$	5.68034	+	5.18596i	0.243543	+	0.222346i
$545$	57.4524	−	26.2376i	2.46099	−	1.12390i
$546$	0.0417889	−	1.61361i	0.00178840	−	0.0690563i
$547$	−24.3523	−	3.50133i	−1.04123	−	0.149706i	−0.399575	−	0.916701i	$-0.630842\pi$
$547$	−24.3523	−	3.50133i	−1.04123	−	0.149706i	−0.641653	+	0.766995i	$0.721751\pi$
$548$	−14.6576	+	13.1752i	−0.626143	+	0.562815i
$549$	1.67259	−	23.8654i	0.0713845	−	1.01855i
$550$	−17.4467	−	45.5082i	−0.743928	−	1.94048i
$551$	−6.61844			−0.281955
$552$	3.91740	+	23.1658i	0.166736	+	0.986002i
$553$	2.32273			0.0987724
$554$	−6.18342	−	16.1289i	−0.262708	−	0.685253i
$555$	24.1022	+	9.96326i	1.02308	+	0.422917i
$556$	29.6370	+	32.9718i	1.25689	+	1.39831i
$557$	−17.2578	−	2.48130i	−0.731238	−	0.105136i	−0.233369	−	0.972388i	$-0.574975\pi$
$557$	−17.2578	−	2.48130i	−0.731238	−	0.105136i	−0.497869	+	0.867252i	$0.665884\pi$
$558$	9.23587	+	30.2724i	0.390986	+	1.28153i
$559$	5.71929	−	2.61191i	0.241900	−	0.110472i
$560$	1.22991	+	6.79079i	0.0519732	+	0.286963i
$561$	−8.68204	+	4.35368i	−0.366556	+	0.183813i
$562$	2.23237	+	9.83078i	0.0941667	+	0.414687i
$563$	−1.16089	−	3.95363i	−0.0489257	−	0.166626i	0.931406	−	0.363981i	$-0.118583\pi$
$563$	−1.16089	−	3.95363i	−0.0489257	−	0.166626i	−0.980332	+	0.197356i	$0.936765\pi$
$564$	−8.50707	+	3.01118i	−0.358212	+	0.126794i
$565$	−21.2540	−	9.70636i	−0.894161	−	0.408350i
$566$	−7.45668	−	7.32228i	−0.313427	−	0.307779i
$567$	−1.77606	−	3.85978i	−0.0745874	−	0.162095i
$568$	13.8906	+	13.1527i	0.582837	+	0.551875i
$569$	−6.05078	+	3.88860i	−0.253662	+	0.163019i	−0.661292	−	0.750128i	$-0.729992\pi$
$569$	−6.05078	+	3.88860i	−0.253662	+	0.163019i	0.407630	+	0.913147i	$0.366355\pi$
$570$	46.0197	−	50.4111i	1.92755	−	2.11149i
$571$	19.2572	+	12.3758i	0.805888	+	0.517913i	0.877532	−	0.479517i	$-0.159188\pi$
$571$	19.2572	+	12.3758i	0.805888	+	0.517913i	−0.0716443	+	0.997430i	$0.522825\pi$
$572$	−6.39974	−	9.57092i	−0.267587	−	0.400180i
$573$	−9.45666	+	0.344514i	−0.395057	+	0.0143923i
$574$	−3.14034	+	2.39570i	−0.131075	+	0.0999944i
$575$	−27.2124	−	29.4209i	−1.13484	−	1.22693i
$576$	−3.78124	+	23.7003i	−0.157552	+	0.987511i
$577$	−41.4696	−	12.1766i	−1.72640	−	0.506917i	−0.740188	−	0.672400i	$-0.765264\pi$
$577$	−41.4696	−	12.1766i	−1.72640	−	0.506917i	−0.986213	+	0.165483i	$0.947082\pi$
$578$	1.33419	−	21.3855i	0.0554949	−	0.889520i
$579$	9.37364	+	2.38534i	0.389555	+	0.0991314i
$580$	−2.53024	+	5.81820i	−0.105063	+	0.241588i
$581$	3.58337	−	2.30289i	0.148663	−	0.0955400i
$582$	4.77773	−	28.0531i	0.198043	−	1.16284i
$583$	10.8338	+	12.5029i	0.448692	+	0.517818i
$584$	−10.1994	+	5.93605i	−0.422055	+	0.245635i
$585$	3.27454	+	14.9499i	0.135386	+	0.618101i
$586$	−16.5603	−	12.1635i	−0.684101	−	0.502470i
$587$	−10.1888	+	2.99170i	−0.420537	+	0.123481i	−0.485153	−	0.874429i	$-0.661236\pi$
$587$	−10.1888	+	2.99170i	−0.420537	+	0.123481i	0.0646157	+	0.997910i	$0.479418\pi$
$588$	−21.8555	−	8.57260i	−0.901308	−	0.353528i
$589$	8.09498	+	56.3018i	0.333548	+	2.31988i
$590$	2.91065	−	13.9914i	0.119829	−	0.576015i
$591$	14.8694	+	15.9479i	0.611643	+	0.656010i
$592$	−16.4694	+	0.599298i	−0.676889	+	0.0246310i
$593$	15.3438	+	2.20611i	0.630095	+	0.0905940i	0.449961	−	0.893048i	$-0.351438\pi$
$593$	15.3438	+	2.20611i	0.630095	+	0.0905940i	0.180134	+	0.983642i	$0.442347\pi$
$594$	−26.2356	−	15.1703i	−1.07646	−	0.622444i
$595$	−1.53624	+	1.77292i	−0.0629797	+	0.0726824i
$596$	−24.2969	−	14.9974i	−0.995238	−	0.614318i
$597$	1.34398	+	4.02839i	0.0550053	+	0.164871i
$598$	−7.80790	−	5.35407i	−0.319289	−	0.218944i
$599$			3.81121i			0.155722i	0.996964	+	0.0778609i	$0.0248090\pi$
$599$			3.81121i			0.155722i	−0.996964	+	0.0778609i	$0.975191\pi$
$600$	−16.7189	−	37.3686i	−0.682545	−	1.52557i
$601$	−21.5111	+	24.8251i	−0.877455	+	1.01264i	0.122342	+	0.992488i	$0.460959\pi$
$601$	−21.5111	+	24.8251i	−0.877455	+	1.01264i	−0.999797	+	0.0201489i	$0.993586\pi$
$602$	0.241801	+	2.99751i	0.00985505	+	0.122169i
$603$	21.0110	+	38.3483i	0.855633	+	1.56166i
$604$	−6.61904	−	21.1141i	−0.269325	−	0.859121i
$605$	−19.9735	+	9.12159i	−0.812038	+	0.370845i
$606$	18.5451	−	2.17800i	0.753343	−	0.0884751i
$607$	4.83060	+	33.5976i	0.196068	+	1.36368i	0.815556	+	0.578678i	$0.196431\pi$
$607$	4.83060	+	33.5976i	0.196068	+	1.36368i	−0.619488	+	0.785006i	$0.712660\pi$
$608$	−13.2209	+	41.0563i	−0.536179	+	1.66505i
$609$	0.405208	+	0.582721i	0.0164198	+	0.0236130i
$610$	−33.2188	−	24.3991i	−1.34499	−	0.987891i
$611$	1.51060	−	3.30776i	0.0611124	−	0.133817i
$612$	−7.08218	+	4.04948i	−0.286280	+	0.163691i
$613$	4.27999	+	4.93937i	0.172867	+	0.199499i	0.835571	−	0.549382i	$-0.185137\pi$
$613$	4.27999	+	4.93937i	0.172867	+	0.199499i	−0.662704	+	0.748881i	$0.730591\pi$
$614$	13.1177	−	24.5515i	0.529389	−	0.990817i
$615$	23.4775	−	29.1765i	0.946706	−	1.17651i
$616$	5.34700	−	1.31688i	0.215437	−	0.0530588i
$617$	−26.9984	−	17.3508i	−1.08691	−	0.698518i	−0.130770	−	0.991413i	$-0.541745\pi$
$617$	−26.9984	−	17.3508i	−1.08691	−	0.698518i	−0.956145	+	0.292895i	$0.905381\pi$
$618$	−44.0842	+	11.7135i	−1.77333	+	0.471187i
$619$	34.8807	+	10.2419i	1.40197	+	0.411656i	0.893361	−	0.449340i	$-0.148341\pi$
$619$	34.8807	+	10.2419i	1.40197	+	0.411656i	0.508611	+	0.860996i	$0.330159\pi$
$620$	52.5891	+	14.4081i	2.11203	+	0.578643i
$621$	−24.6622	−	3.57437i	−0.989660	−	0.143434i
$622$	15.5212	+	20.3456i	0.622343	+	0.815784i
$623$	−1.71192	+	5.83027i	−0.0685867	+	0.233585i
$624$	−5.80629	−	7.73390i	−0.232438	−	0.309604i
$625$	2.56431	+	1.64798i	0.102572	+	0.0659193i
$626$	−18.9740	+	10.5857i	−0.758354	+	0.423089i
$627$	−42.4333	−	34.1449i	−1.69462	−	1.36361i
$628$	42.6820	−	6.93118i	1.70320	−	0.276584i
$629$	−3.66856	−	4.23374i	−0.146275	−	0.168810i
$630$	−7.25596	−	0.965433i	−0.289084	−	0.0384638i
$631$	−31.9803	−	14.6049i	−1.27312	−	0.581413i	−0.339811	−	0.940494i	$-0.610363\pi$
$631$	−31.9803	−	14.6049i	−1.27312	−	0.581413i	−0.933307	+	0.359081i	$0.883090\pi$
$632$	10.9089	−	8.64042i	0.433931	−	0.343697i
$633$	4.79818	+	6.90016i	0.190711	+	0.274257i
$634$	−6.61512	−	29.1313i	−0.262720	−	1.15695i
$635$	−3.81509	+	0.548528i	−0.151397	+	0.0217677i
$636$	9.65963	+	9.98975i	0.383029	+	0.396119i
$637$	8.60514	−	3.92984i	0.340948	−	0.155706i
$638$	4.75926	+	1.72598i	0.188421	+	0.0683322i
$639$	−17.7942	+	9.74943i	−0.703929	+	0.385682i
$640$	31.0377	+	27.3182i	1.22687	+	1.07985i
$641$	−13.3681	+	15.4276i	−0.528007	+	0.609353i	−0.955617	−	0.294610i	$-0.904810\pi$
$641$	−13.3681	+	15.4276i	−0.528007	+	0.609353i	0.427610	+	0.903963i	$0.359356\pi$
$642$	−10.0141	−	12.1803i	−0.395225	−	0.480716i
$643$	−12.5271			−0.494019			−0.247010	−	0.969013i	$-0.579448\pi$
$643$	−12.5271			−0.494019			−0.247010	+	0.969013i	$0.579448\pi$
$644$	3.68057	−	2.63766i	0.145035	−	0.103938i
$645$	−9.02360	−	27.0470i	−0.355304	−	1.06498i
$646$	−13.6901	+	5.24845i	−0.538632	+	0.206498i
$647$	−8.14962	−	7.06169i	−0.320395	−	0.277624i	0.479782	−	0.877388i	$-0.340716\pi$
$647$	−8.14962	−	7.06169i	−0.320395	−	0.277624i	−0.800177	+	0.599764i	$0.795261\pi$
$648$	−22.6995	−	11.5209i	−0.891722	−	0.452583i
$649$	−11.2872	−	1.62285i	−0.443060	−	0.0637024i
$650$	15.5079	+	5.62405i	0.608269	+	0.220593i
$651$	4.46149	−	4.15975i	0.174860	−	0.163033i
$652$	−7.26260	−	15.1667i	−0.284425	−	0.593975i
$653$	3.52866	+	24.5423i	0.138087	+	0.960416i	0.934576	+	0.355763i	$0.115779\pi$
$653$	3.52866	+	24.5423i	0.138087	+	0.960416i	−0.796489	+	0.604653i	$0.793312\pi$
$654$	−21.9570	−	36.1928i	−0.858585	−	1.41525i
$655$	11.4980	+	39.1584i	0.449262	+	1.53005i
$656$	−5.83699	+	22.9335i	−0.227896	+	0.895401i
$657$	−2.67814	−	12.2270i	−0.104484	−	0.477022i
$658$	1.24096	+	1.21860i	0.0483777	+	0.0475058i
$659$	−12.7238	+	11.0252i	−0.495647	+	0.429481i	−0.866475	−	0.499221i	$-0.833620\pi$
$659$	−12.7238	+	11.0252i	−0.495647	+	0.429481i	0.370828	+	0.928702i	$0.379074\pi$
$660$	−46.2387	+	24.2490i	−1.79984	+	0.943889i
$661$	−5.63248	+	3.61977i	−0.219078	+	0.140793i	−0.645577	−	0.763695i	$-0.723383\pi$
$661$	−5.63248	+	3.61977i	−0.219078	+	0.140793i	0.426499	+	0.904488i	$0.359747\pi$
$662$	24.7690	−	13.8188i	0.962675	−	0.537081i
$663$	0.810709	−	3.18583i	0.0314853	−	0.123727i
$664$	8.26291	−	24.1456i	0.320663	−	0.937032i
$665$	−12.6224	−	3.70626i	−0.489474	−	0.143722i
$666$	4.74793	−	16.8228i	0.183979	−	0.651872i
$667$	4.16066	−	0.134953i	0.161101	−	0.00522541i
$668$	−3.40934	−	0.934074i	−0.131911	−	0.0361404i
$669$	22.6186	−	0.824015i	0.874485	−	0.0318583i
$670$	75.1876	+	4.69076i	2.90475	+	0.181220i
$671$	−17.7807	+	27.6673i	−0.686415	+	1.06808i
$672$	4.42424	−	1.34960i	0.170669	−	0.0520618i
$673$	22.9054	−	14.7204i	0.882939	−	0.567431i	−0.0187457	−	0.999824i	$-0.505967\pi$
$673$	22.9054	−	14.7204i	0.882939	−	0.567431i	0.901685	+	0.432394i	$0.142331\pi$
$674$	6.80827	−	12.7425i	0.262245	−	0.490824i
$675$	43.1626	−	4.73412i	1.66133	−	0.182216i
$676$	−21.9317	−	2.74722i	−0.843526	−	0.105662i
$677$	3.37589	+	1.54172i	0.129746	+	0.0592530i	0.479230	−	0.877689i	$-0.340916\pi$
$677$	3.37589	+	1.54172i	0.129746	+	0.0592530i	−0.349484	+	0.936942i	$0.613643\pi$
$678$	−4.79959	+	14.9068i	−0.184327	+	0.572493i
$679$	−5.26235	+	1.54516i	−0.201950	+	0.0592980i
$680$	−0.619913	+	14.0414i	−0.0237726	+	0.538461i
$681$	−21.1519	+	10.6068i	−0.810544	+	0.406454i
$682$	8.86156	−	42.5971i	0.339327	−	1.63113i
$683$	10.2971	+	22.5475i	0.394007	+	0.862756i	0.997843	+	0.0656467i	$0.0209110\pi$
$683$	10.2971	+	22.5475i	0.394007	+	0.862756i	−0.603836	+	0.797109i	$0.706362\pi$
$684$	−37.1546	−	26.6926i	−1.42064	−	1.02062i
$685$	−35.6476	−	5.12534i	−1.36202	−	0.195829i
$686$	0.739581	+	9.16830i	0.0282374	+	0.350047i
$687$	2.23548	−	5.40786i	0.0852889	−	0.206323i
$688$	12.2862	+	13.1785i	0.468406	+	0.502426i
$689$	−5.59952			−0.213325
$690$	−27.9022	+	32.6291i	−1.06222	+	1.24217i
$691$			23.1401i			0.880291i	0.897927	+	0.440145i	$0.145073\pi$
$691$			23.1401i			0.880291i	−0.897927	+	0.440145i	$0.854927\pi$
$692$	18.2528	−	29.5708i	0.693868	−	1.12411i
$693$	−0.408349	+	5.82652i	−0.0155119	+	0.221331i
$694$	36.6362	−	2.95534i	1.39069	−	0.112183i
$695$	−11.5293	+	80.1878i	−0.437330	+	3.04169i
$696$	4.07078	+	1.22944i	0.154302	+	0.0466017i
$697$	−7.31722	+	3.34166i	−0.277160	+	0.126575i
$698$	−8.15425	+	39.1971i	−0.308643	+	1.48363i
$699$	−10.2625	+	5.14623i	−0.388164	+	0.194648i
$700$	−5.05755	+	6.05583i	−0.191157	+	0.228889i
$701$	4.23586	+	14.4260i	0.159986	+	0.544863i	0.999997	+	0.00229407i	$0.000730224\pi$
$701$	4.23586	+	14.4260i	0.159986	+	0.544863i	−0.840011	+	0.542569i	$0.817452\pi$
$702$	9.69560	−	3.34849i	0.365937	−	0.126381i
$703$	13.0502	−	28.5759i	0.492197	−	1.07776i
$704$	20.2138	−	26.0754i	0.761837	−	0.982752i
$705$	−14.1879	−	8.40435i	−0.534347	−	0.316526i
$706$	−9.87262	+	18.4778i	−0.371561	+	0.695423i
$707$	−1.94563	−	3.02746i	−0.0731730	−	0.113859i
$708$	−9.54109	−	0.843700i	−0.358576	−	0.0317082i
$709$	−12.4312	−	7.98903i	−0.466863	−	0.300034i	0.285979	−	0.958236i	$-0.407681\pi$
$709$	−12.4312	−	7.98903i	−0.466863	−	0.300034i	−0.752842	+	0.658201i	$0.771318\pi$
$710$	−2.17659	+	34.8882i	−0.0816859	+	1.30933i
$711$	5.17797	+	13.8223i	0.194189	+	0.518377i
$712$	13.6481	+	33.7505i	0.511485	+	1.26486i
$713$	−6.23690	−	35.2289i	−0.233574	−	1.31933i
$714$	1.30027	+	0.884017i	0.0486612	+	0.0330835i
$715$	5.92731	−	20.1866i	0.221669	−	0.754935i
$716$	−27.7532	−	41.5054i	−1.03719	−	1.55113i
$717$	−12.6250	+	49.6121i	−0.471488	+	1.85280i
$718$	7.86897	+	14.1045i	0.293667	+	0.526375i
$719$	−19.6622	−	30.5950i	−0.733278	−	1.14100i	−0.984891	−	0.173175i	$-0.944598\pi$
$719$	−19.6622	−	30.5950i	−0.733278	−	1.14100i	0.251613	−	0.967828i	$-0.419039\pi$
$720$	−37.6695	+	22.4575i	−1.40386	+	0.836943i
$721$	5.75696	+	6.64389i	0.214400	+	0.247431i
$722$	−39.4921	−	38.7803i	−1.46974	−	1.44325i
$723$	37.3418	+	3.98766i	1.38876	+	0.148302i
$724$	0.367591	+	20.2103i	0.0136614	+	0.751111i
$725$	−6.95971	+	2.04355i	−0.258477	+	0.0758957i
$726$	7.63340	+	12.5825i	0.283302	+	0.466982i
$727$	−38.4500	+	5.52828i	−1.42603	+	0.205033i	−0.811728	−	0.584036i	$-0.801473\pi$
$727$	−38.4500	+	5.52828i	−1.42603	+	0.205033i	−0.614305	+	0.789069i	$0.710564\pi$
$728$	−0.848303	+	1.65963i	−0.0314402	+	0.0615100i
$729$	19.0098	−	19.1736i	0.704067	−	0.710133i
$730$	−20.2724	−	7.35193i	−0.750315	−	0.272107i
$731$	−0.871608	+	6.06217i	−0.0322376	+	0.224217i
$732$	−13.6446	+	24.0200i	−0.504320	+	0.887805i
$733$	−24.1196	+	27.8356i	−0.890879	+	1.02813i	0.108541	+	0.994092i	$0.465382\pi$
$733$	−24.1196	+	27.8356i	−0.890879	+	1.02813i	−0.999421	+	0.0340378i	$0.989163\pi$
$734$	9.61581	+	25.0820i	0.354926	+	0.925795i
$735$	−13.5767	−	40.6945i	−0.500786	−	1.50104i
$736$	7.47412	−	26.0794i	0.275500	−	0.961301i
$737$		−	60.1115i		−	2.21424i
$738$	−21.2572	−	13.3472i	−0.782488	−	0.491317i
$739$	−33.7620	−	29.2549i	−1.24195	−	1.07616i	−0.994223	−	0.107331i	$-0.965769\pi$
$739$	−33.7620	−	29.2549i	−1.24195	−	1.07616i	−0.247732	−	0.968829i	$-0.579685\pi$
$740$	−20.1317	−	22.3969i	−0.740056	−	0.823327i
$741$	18.1395	−	3.28611i	0.666369	−	0.120718i
$742$	0.913079	−	2.51774i	0.0335202	−	0.0924293i
$743$	18.3492	+	40.1791i	0.673166	+	1.47403i	0.869726	+	0.493535i	$0.164296\pi$
$743$	18.3492	+	40.1791i	0.673166	+	1.47403i	−0.196560	+	0.980492i	$0.562977\pi$
$744$	5.47966	−	36.1331i	0.200894	−	1.32470i
$745$	−7.42530	−	51.6441i	−0.272042	−	1.89209i
$746$	3.43893	+	15.1442i	0.125908	+	0.554468i
$747$	21.6925	+	16.1905i	0.793688	+	0.592379i
$748$	11.2132	−	0.203948i	0.409994	−	0.00745707i
$749$	−1.26246	+	2.76439i	−0.0461291	+	0.101009i
$750$	13.1855	−	26.9996i	0.481465	−	0.985885i
$751$	−1.75038	+	1.51671i	−0.0638723	+	0.0553457i	−0.686212	−	0.727402i	$-0.740728\pi$
$751$	−1.75038	+	1.51671i	−0.0638723	+	0.0553457i	0.622340	+	0.782747i	$0.286182\pi$
$752$	10.3614	+	1.10691i	0.377840	+	0.0403650i
$753$	25.8538	+	20.8038i	0.942164	+	0.758133i
$754$	−1.49639	+	0.834841i	−0.0544951	+	0.0304031i
$755$	21.8602	−	34.0151i	0.795573	−	1.23793i
$756$	−0.0753992	+	4.90551i	−0.00274224	+	0.178412i
$757$	12.9285	+	3.79614i	0.469893	+	0.137973i	0.508102	−	0.861297i	$-0.330347\pi$
$757$	12.9285	+	3.79614i	0.469893	+	0.137973i	−0.0382092	+	0.999270i	$0.512165\pi$
$758$	21.8660	−	16.6811i	0.794209	−	0.605884i
$759$	27.3717	+	20.5998i	0.993531	+	0.747726i
$760$	−73.0688	+	29.5477i	−2.65049	+	1.07181i
$761$	−8.59157	+	29.2602i	−0.311444	+	1.06068i	0.643881	+	0.765125i	$0.277323\pi$
$761$	−8.59157	+	29.2602i	−0.311444	+	1.06068i	−0.955325	+	0.295556i	$0.904495\pi$
$762$	0.663391	+	2.49669i	0.0240321	+	0.0904455i
$763$	−4.41092	+	6.86352i	−0.159686	+	0.248476i
$764$	10.0203	+	4.35768i	0.362522	+	0.157655i
$765$	−13.9751	−	5.18970i	−0.505271	−	0.187634i
$766$	−22.1058	−	11.8110i	−0.798714	−	0.426749i
$767$	2.91691	−	2.52752i	0.105323	−	0.0912633i
$768$	15.7583	−	22.7964i	0.568629	−	0.822594i
$769$	47.2493	+	21.5780i	1.70385	+	0.778123i	0.997531	+	0.0702316i	$0.0223738\pi$
$769$	47.2493	+	21.5780i	1.70385	+	0.778123i	0.706321	+	0.707891i	$0.250353\pi$
$770$	8.11008	+	5.95683i	0.292267	+	0.214669i
$771$	−0.437375	−	0.628980i	−0.0157517	−	0.0226522i
$772$	−8.57235	−	7.15924i	−0.308526	−	0.257667i
$773$	−47.9097	+	6.88838i	−1.72319	+	0.247758i	−0.931650	−	0.363356i	$-0.881631\pi$
$773$	−47.9097	+	6.88838i	−1.72319	+	0.247758i	−0.791543	+	0.611114i	$0.790722\pi$
$774$	−17.2988	+	8.12116i	−0.621792	+	0.291909i
$775$	25.8965	+	56.7055i	0.930230	+	2.03692i
$776$	−18.9671	+	26.8326i	−0.680878	+	0.963235i
$777$	−3.31496	+	0.600531i	−0.118923	+	0.0215439i
$778$	1.34060	+	16.6189i	0.0480630	+	0.595817i
$779$	−34.0915	−	29.5405i	−1.22146	−	1.05840i
$780$	4.04597	−	17.2025i	0.144869	−	0.615948i
$781$	27.8927			0.998079
$782$	8.49924	−	3.57857i	0.303932	−	0.127969i
$783$	−2.56439	+	3.71039i	−0.0916439	+	0.132598i
$784$	18.4856	+	19.8282i	0.660199	+	0.708148i
$785$	59.7160	+	51.7442i	2.13135	+	1.84683i
$786$	25.1675	−	10.7151i	0.897694	−	0.382195i
$787$	6.28965	−	43.7455i	0.224202	−	1.55936i	−0.497691	−	0.867354i	$-0.665819\pi$
$787$	6.28965	−	43.7455i	0.224202	−	1.55936i	0.721893	−	0.692005i	$-0.243272\pi$
$788$	−7.53150	−	24.0248i	−0.268298	−	0.855847i
$789$	19.7715	+	21.2057i	0.703884	+	0.754942i
$790$	24.8964	+	5.17923i	0.885772	+	0.184269i
$791$	2.98751	−	0.429539i	0.106224	−	0.0152726i
$792$	19.7565	+	28.8837i	0.702017	+	1.02634i
$793$	−3.13613	−	10.6807i	−0.111367	−	0.379282i
$794$	−32.3074	−	23.7297i	−1.14655	−	0.842135i
$795$	−2.69632	+	25.2493i	−0.0956286	+	0.895499i
$796$	0.609478	−	4.86560i	0.0216024	−	0.172457i
$797$	26.7242	−	23.1567i	0.946621	−	0.820252i	−0.0372176	−	0.999307i	$-0.511849\pi$
$797$	26.7242	−	23.1567i	0.946621	−	0.820252i	0.983839	+	0.179055i	$0.0573040\pi$
$798$	−1.48033	+	8.69199i	−0.0524033	+	0.307693i
$799$	1.91501	+	2.97982i	0.0677482	+	0.105418i
$800$	−1.22581	+	47.2554i	−0.0433388	+	1.67073i
$801$	−38.5116	+	2.80976i	−1.36074	+	0.0992778i
$802$	1.49652	−	23.9876i	0.0528441	−	0.847030i
$803$	−4.84776	+	16.5100i	−0.171074	+	0.582624i
$804$	−2.75552	−	50.4164i	−0.0971799	−	1.77805i
$805$	8.01057	+	2.07255i	0.282335	+	0.0730477i
$806$	8.93206	+	11.7084i	0.314618	+	0.412410i
$807$	36.0412	−	1.31301i	1.26871	−	0.0462202i
$808$	−20.3998	−	6.98105i	−0.717662	−	0.245592i
$809$	−13.2156	+	20.5639i	−0.464637	+	0.722989i	−0.991943	−	0.126686i	$-0.959566\pi$
$809$	−13.2156	+	20.5639i	−0.464637	+	0.722989i	0.527306	+	0.849675i	$0.323202\pi$
$810$	−10.4303	−	45.3316i	−0.366482	−	1.59279i
$811$	−1.92253	−	2.99151i	−0.0675091	−	0.105046i	0.805858	−	0.592109i	$-0.201705\pi$
$811$	−1.92253	−	2.99151i	−0.0675091	−	0.105046i	−0.873367	+	0.487063i	$0.838068\pi$
$812$	−0.131368	−	0.808961i	−0.00461012	−	0.0283890i
$813$	−4.39283	−	2.60214i	−0.154063	−	0.0912610i
$814$	−16.8364	+	17.1454i	−0.590116	+	0.600946i
$815$	12.7649	−	27.9513i	0.447136	−	0.979092i
$816$	9.39529	−	0.685068i	0.328901	−	0.0239822i
$817$	−32.9535	+	9.67601i	−1.15290	+	0.338521i
$818$	5.00944	+	22.0603i	0.175151	+	0.771320i
$819$	−1.39990	−	1.39590i	−0.0489163	−	0.0487767i
$820$	−39.0020	+	18.6761i	−1.36201	+	0.652198i
$821$	13.2925	+	29.1066i	0.463913	+	1.01583i	0.986578	+	0.163289i	$0.0522103\pi$
$821$	13.2925	+	29.1066i	0.463913	+	1.01583i	−0.522666	+	0.852538i	$0.675062\pi$
$822$	−0.624912	+	24.1300i	−0.0217963	+	0.841630i
$823$	4.69524	−	32.6561i	0.163666	−	1.13832i	−0.727984	−	0.685594i	$-0.759542\pi$
$823$	4.69524	−	32.6561i	0.163666	−	1.13832i	0.891650	−	0.452726i	$-0.149548\pi$
$824$	51.7529	+	9.78791i	1.80290	+	0.340978i
$825$	−55.1640	−	22.8035i	−1.92057	−	0.793916i
$826$	0.660820	+	1.72369i	0.0229929	+	0.0599750i
$827$			21.6881i			0.754170i	0.926179	+	0.377085i	$0.123074\pi$
$827$			21.6881i			0.754170i	−0.926179	+	0.377085i	$0.876926\pi$
$828$	23.9014	+	16.0226i	0.830630	+	0.556825i
$829$		−	28.4535i		−	0.988230i	−0.869397	−	0.494115i	$-0.835492\pi$
$829$		−	28.4535i		−	0.988230i	0.869397	−	0.494115i	$-0.164508\pi$
$830$	43.5436	−	16.6935i	1.51142	−	0.579440i
$831$	−19.5511	−	8.08198i	−0.678222	−	0.280361i
$832$	2.18962	+	10.9502i	0.0759114	+	0.379630i
$833$	−1.31141	+	9.12103i	−0.0454375	+	0.316025i
$834$	54.2794	+	1.40571i	1.87954	+	0.0486759i
$835$	−2.68340	−	5.87582i	−0.0928628	−	0.203341i
$836$	27.1619	+	56.7231i	0.939412	+	1.96181i
$837$	34.7001	+	17.2766i	1.19941	+	0.597168i
$838$	−1.27497	+	0.289520i	−0.0440432	+	0.0100013i
$839$	1.48759	−	0.436797i	0.0513574	−	0.0150799i	−0.255953	−	0.966689i	$-0.582389\pi$
$839$	1.48759	−	0.436797i	0.0513574	−	0.0150799i	0.307310	+	0.951609i	$0.400571\pi$
$840$	7.07510	+	4.62431i	0.244114	+	0.159554i
$841$	−11.7340	+	25.6940i	−0.404622	+	0.885999i
$842$	31.1056	+	30.5450i	1.07197	+	1.05265i
$843$	10.6229	+	6.29257i	0.365871	+	0.216728i
$844$	−1.55557	−	9.57914i	−0.0535449	−	0.329728i
$845$	−21.8362	−	33.9778i	−0.751188	−	1.16887i
$846$	−4.48530	+	10.1014i	−0.154208	+	0.347293i
$847$	1.53347	−	2.38612i	0.0526906	−	0.0819882i
$848$	−5.07753	−	15.2214i	−0.174363	−	0.522704i
$849$	−12.7910	+	0.465987i	−0.438986	+	0.0159926i
$850$	−12.7755	+	9.74614i	−0.438196	+	0.334290i
$851$	−7.62128	+	18.2303i	−0.261254	+	0.624925i
$852$	23.3940	−	1.27861i	0.801465	−	0.0438044i
$853$	−1.82616	+	6.21933i	−0.0625265	+	0.212946i	−0.984830	−	0.173520i	$-0.944486\pi$
$853$	−1.82616	+	6.21933i	−0.0625265	+	0.212946i	0.922304	+	0.386465i	$0.126304\pi$
$854$	5.31380	+	0.331515i	0.181835	+	0.0113442i
$855$	−6.08303	−	83.3765i	−0.208035	−	2.85142i
$856$	4.35417	+	17.6794i	0.148823	+	0.604270i
$857$	−10.7969	−	16.8003i	−0.368815	−	0.573888i	0.606396	−	0.795163i	$-0.292615\pi$
$857$	−10.7969	−	16.8003i	−0.368815	−	0.573888i	−0.975211	+	0.221275i	$0.928978\pi$
$858$	−13.9009	−	2.36746i	−0.474568	−	0.0808237i
$859$	−12.3925	+	10.7382i	−0.422828	+	0.366383i	−0.840130	−	0.542385i	$-0.817521\pi$
$859$	−12.3925	+	10.7382i	−0.422828	+	0.366383i	0.417302	+	0.908768i	$0.362976\pi$
$860$	−4.09210	+	32.6682i	−0.139539	+	1.11398i
$861$	−0.513670	+	4.81018i	−0.0175058	+	0.163930i
$862$	28.3100	−	38.5434i	0.964243	−	1.31279i
$863$	2.82994	+	9.63788i	0.0963322	+	0.328077i	0.993533	−	0.113546i	$-0.0362209\pi$
$863$	2.82994	+	9.63788i	0.0963322	+	0.328077i	−0.897201	+	0.441623i	$0.854403\pi$
$864$	17.8941	+	23.3195i	0.608770	+	0.793347i
$865$	62.8541	−	9.03706i	2.13710	−	0.307269i
$866$	1.52994	−	7.35435i	0.0519894	−	0.249911i
$867$	−17.8960	−	19.1941i	−0.607779	−	0.651866i
$868$	−6.72101	+	2.10696i	−0.228126	+	0.0715149i
$869$	2.88771	−	20.0845i	0.0979589	−	0.681319i
$870$	3.04390	+	7.14948i	0.103198	+	0.242390i
$871$	15.3763	+	13.3237i	0.521007	+	0.451455i
$872$	4.81573	+	48.6434i	0.163081	+	1.64727i
$873$	−20.9263	−	27.8711i	−0.708247	−	0.943293i
$874$	38.0536	+	35.0181i	1.28718	+	1.18450i
$875$	−5.79097			−0.195771
$876$	−3.30907	+	14.0694i	−0.111803	+	0.475360i
$877$	3.39164	+	2.93887i	0.114527	+	0.0992385i	0.710242	−	0.703958i	$-0.248586\pi$
$877$	3.39164	+	2.93887i	0.114527	+	0.0992385i	−0.595714	+	0.803196i	$0.703131\pi$
$878$	5.11362	−	0.412502i	0.172576	−	0.0139213i
$879$	−24.7623	+	4.48588i	−0.835210	+	0.151305i
$880$	60.2486	−	2.19236i	2.03098	−	0.0739045i
$881$	1.03968	+	2.27658i	0.0350278	+	0.0767001i	0.926337	−	0.376696i	$-0.122940\pi$
$881$	1.03968	+	2.27658i	0.0350278	+	0.0767001i	−0.891309	+	0.453396i	$0.850212\pi$
$882$	−26.0275	+	12.2190i	−0.876390	+	0.411434i
$883$	3.74732	−	0.538783i	0.126107	−	0.0181315i	−0.0789721	−	0.996877i	$-0.525164\pi$
$883$	3.74732	−	0.538783i	0.126107	−	0.0181315i	0.205079	+	0.978745i	$0.434255\pi$
$884$	−2.43322	+	2.91350i	−0.0818380	+	0.0979915i
$885$	−9.99247	−	14.3699i	−0.335893	−	0.483041i
$886$	7.51522	−	10.2318i	0.252479	−	0.343744i
$887$	−0.696567	−	0.318112i	−0.0233884	−	0.0106811i	0.403686	−	0.914897i	$-0.367729\pi$
$887$	−0.696567	−	0.318112i	−0.0233884	−	0.0106811i	−0.427075	+	0.904216i	$0.640456\pi$
$888$	−13.3350	+	15.1519i	−0.447493	+	0.508464i
$889$	0.376274	−	0.326043i	0.0126198	−	0.0109351i
$890$	−31.3498	+	58.6750i	−1.05085	+	1.96679i
$891$	−35.5833	+	10.5588i	−1.19209	+	0.353734i
$892$	−23.9668	−	10.4228i	−0.802466	−	0.348980i
$893$	−10.7389	+	16.7100i	−0.359363	+	0.559180i
$894$	−33.7971	+	8.98018i	−1.13035	+	0.300342i
$895$	25.7045	−	87.5413i	0.859205	−	2.92618i
$896$	−5.28066	−	0.801052i	−0.176414	−	0.0267613i
$897$	−11.3363	+	2.43567i	−0.378508	+	0.0813247i
$898$	14.8213	+	19.4281i	0.494593	+	0.648326i
$899$	−6.21305	−	1.82432i	−0.207217	−	0.0608443i
$900$	−47.3122	−	16.5969i	−1.57707	−	0.553230i
$901$	2.94886	−	4.58852i	0.0982408	−	0.152866i
$902$	16.8112	+	30.1328i	0.559753	+	1.00331i
$903$	2.86947	+	2.30898i	0.0954900	+	0.0768381i
$904$	12.4332	−	13.1307i	0.413521	−	0.436721i
$905$	−27.9151	+	24.1886i	−0.927929	+	0.804055i
$906$	−24.3516	−	11.8923i	−0.809027	−	0.395095i
$907$	10.1064	−	22.1300i	0.335579	−	0.734816i	−0.664341	−	0.747429i	$-0.731288\pi$
$907$	10.1064	−	22.1300i	0.335579	−	0.734816i	0.999920	+	0.0126136i	$0.00401513\pi$
$908$	27.3185	−	0.496875i	0.906595	−	0.0164894i
$909$	13.6788	−	18.3273i	0.453696	−	0.607877i
$910$	−3.32133	+	0.754206i	−0.110101	+	0.0250017i
$911$	−4.69618	−	32.6626i	−0.155591	−	1.08216i	−0.906637	−	0.421911i	$-0.861359\pi$
$911$	−4.69618	−	32.6626i	−0.155591	−	1.08216i	0.751046	−	0.660250i	$-0.229550\pi$
$912$	25.3812	+	46.3293i	0.840457	+	1.53412i
$913$	−15.4580	−	33.8482i	−0.511584	−	1.12021i
$914$	−16.5488	−	6.00156i	−0.547387	−	0.198514i
$915$	−49.6712	+	8.99835i	−1.64208	+	0.297476i
$916$	−5.02525	+	4.51699i	−0.166039	+	0.149246i
$917$	−3.98418	−	3.45231i	−0.131569	−	0.114005i
$918$	−2.36205	+	9.70845i	−0.0779594	+	0.320427i
$919$		−	15.4076i		−	0.508250i	−0.967171	−	0.254125i	$-0.918212\pi$
$919$		−	15.4076i		−	0.508250i	0.967171	−	0.254125i	$-0.0817875\pi$
$920$	45.3320	−	20.0650i	1.49455	−	0.661523i
$921$	−10.7894	−	32.3398i	−0.355523	−	1.06563i
$922$	49.7508	−	19.0732i	1.63846	−	0.628142i
$923$	−6.18240	+	7.13487i	−0.203496	+	0.234847i
$924$	3.33122	−	5.86428i	0.109589	−	0.192921i
$925$	4.89980	−	34.0789i	0.161104	−	1.12051i
$926$	−5.08520	+	14.0221i	−0.167110	+	0.460794i
$927$	−26.7033	+	49.0700i	−0.877050	+	1.61167i
$928$	−3.62627	−	3.31066i	−0.119038	−	0.108678i
$929$	33.1744	−	4.76975i	1.08842	−	0.156490i	0.425333	−	0.905037i	$-0.360157\pi$
$929$	33.1744	−	4.76975i	1.08842	−	0.156490i	0.663082	+	0.748546i	$0.269248\pi$
$930$	57.0963	−	34.6384i	1.87226	−	1.13584i
$931$	−49.5812	+	14.5584i	−1.62496	+	0.477131i
$932$	13.2544	−	0.241074i	0.434162	−	0.00789666i
$933$	31.1641	+	3.32795i	1.02027	+	0.108952i
$934$	−36.6681	+	37.3411i	−1.19982	+	1.22184i
$935$	13.4204	+	15.4879i	0.438893	+	0.506510i
$936$	−11.7674	−	1.34840i	−0.384629	−	0.0440739i
$937$	−10.3016	−	16.0297i	−0.336540	−	0.523667i	0.631199	−	0.775621i	$-0.282563\pi$
$937$	−10.3016	−	16.0297i	−0.336540	−	0.523667i	−0.967739	+	0.251954i	$0.918927\pi$
$938$	−8.49812	+	4.74115i	−0.277474	+	0.154804i
$939$	−6.56245	+	25.7884i	−0.214158	+	0.841571i
$940$	10.5841	+	15.8287i	0.345216	+	0.516276i
$941$	−4.69490	+	15.9894i	−0.153049	+	0.521239i	−0.999945	−	0.0105212i	$-0.996651\pi$
$941$	−4.69490	+	15.9894i	−0.153049	+	0.521239i	0.846895	+	0.531760i	$0.178469\pi$
$942$	29.7758	−	43.7960i	0.970148	−	1.42695i
$943$	22.0339	+	17.8754i	0.717521	+	0.582102i
$944$	9.51563	+	5.63724i	0.309707	+	0.183476i
$945$	−6.96845	+	5.64023i	−0.226684	+	0.183477i
$946$	26.2199	+	1.63579i	0.852481	+	0.0531841i
$947$	2.89653	+	1.86148i	0.0941244	+	0.0604901i	0.586856	−	0.809691i	$-0.300365\pi$
$947$	2.89653	+	1.86148i	0.0941244	+	0.0604901i	−0.492732	+	0.870181i	$0.664002\pi$
$948$	1.50129	−	16.9775i	0.0487596	−	0.551404i
$949$	−3.14869	−	4.89946i	−0.102211	−	0.159043i
$950$	−79.4760	−	42.4636i	−2.57854	−	1.37770i
$951$	−31.4785	−	18.6466i	−1.02076	−	0.604658i
$952$	−0.913243	−	1.56915i	−0.0295984	−	0.0508564i
$953$	−13.3754	+	29.2881i	−0.433272	+	0.948733i	0.559513	+	0.828822i	$0.310988\pi$
$953$	−13.3754	+	29.2881i	−0.433272	+	0.948733i	−0.992785	+	0.119911i	$0.961739\pi$
$954$	17.0183	−	0.179088i	0.550988	−	0.00579817i
$955$	5.62533	+	19.1581i	0.182031	+	0.619942i
$956$	37.8919	−	45.3711i	1.22551	−	1.46741i
$957$	5.54252	−	2.77934i	0.179164	−	0.0898434i
$958$	7.41275	+	1.54209i	0.239495	+	0.0498226i
$959$	4.23171	−	1.93256i	0.136649	−	0.0624056i
$960$	50.4309	−	4.60058i	1.62765	−	0.148483i
$961$	−3.50820	+	24.4001i	−0.113168	+	0.787100i
$962$	−0.653967	−	8.10697i	−0.0210847	−	0.261379i
$963$	−19.2649	−	1.35017i	−0.620804	−	0.0435088i
$964$	−36.9002	−	22.7769i	−1.18848	−	0.733595i
$965$		−	20.4088i		−	0.656984i
$966$	0.753373	−	5.49437i	0.0242394	−	0.176779i
$967$	34.8651			1.12118			0.560592	−	0.828092i	$-0.310573\pi$
$967$	34.8651			1.12118			0.560592	+	0.828092i	$0.310573\pi$
$968$	−1.67420	−	16.9110i	−0.0538109	−	0.543541i
$969$	−6.85994	+	16.5949i	−0.220373	+	0.533105i
$970$	−59.8503	+	4.82796i	−1.92168	+	0.155017i
$971$	42.3355	+	6.08693i	1.35861	+	0.195339i	0.782816	−	0.622254i	$-0.213783\pi$
$971$	42.3355	+	6.08693i	1.35861	+	0.195339i	0.575797	+	0.817593i	$0.304692\pi$
$972$	−29.3602	+	10.4870i	−0.941730	+	0.336370i
$973$	−4.34721	−	9.51907i	−0.139365	−	0.305167i
$974$	−13.3052	−	2.76791i	−0.426327	−	0.0886897i
$975$	18.0601	−	9.05641i	0.578387	−	0.290037i
$976$	26.1899	−	18.2101i	0.838317	−	0.582890i
$977$	−14.3358	+	4.20938i	−0.458644	+	0.134670i	−0.502890	−	0.864351i	$-0.667730\pi$
$977$	−14.3358	+	4.20938i	−0.458644	+	0.134670i	0.0442456	+	0.999021i	$0.485912\pi$
$978$	−19.6041	−	6.31199i	−0.626871	−	0.201835i
$979$	48.2857	+	22.0513i	1.54322	+	0.704763i
$980$	−6.15690	+	49.1520i	−0.196675	+	1.57010i
$981$	−50.6772	−	10.9483i	−1.61800	−	0.349552i
$982$	12.6454	+	6.75636i	0.403530	+	0.215604i
$983$	18.1746	−	11.6801i	0.579679	−	0.372537i	−0.217700	−	0.976016i	$-0.569855\pi$
$983$	18.1746	−	11.6801i	0.579679	−	0.372537i	0.797379	+	0.603479i	$0.206219\pi$
$984$	15.4811	+	24.5022i	0.493520	+	0.781101i
$985$	24.8736	−	38.7041i	0.792540	−	1.23322i
$986$	0.103929	−	1.66586i	0.00330977	−	0.0530518i
$987$	2.12872	−	0.0775510i	0.0677577	−	0.00246847i
$988$	−20.5300	−	5.62470i	−0.653146	−	0.178946i
$989$	20.5188	−	6.75473i	0.652459	−	0.214788i
$990$	−17.3689	+	61.5416i	−0.552021	+	1.95592i
$991$	16.9546	+	4.97832i	0.538581	+	0.158142i	0.539700	−	0.841858i	$-0.318538\pi$
$991$	16.9546	+	4.97832i	0.538581	+	0.158142i	−0.00111844	+	0.999999i	$0.500356\pi$
$992$	−23.7279	+	34.8973i	−0.753362	+	1.10799i
$993$	8.56675	−	33.6646i	0.271858	−	1.06831i
$994$	−2.19997	−	3.94327i	−0.0697787	−	0.125073i
$995$	7.53807	−	4.84442i	0.238973	−	0.153579i
$996$	−14.5164	−	27.6804i	−0.459970	−	0.877086i
$997$	−7.93149	+	6.87267i	−0.251193	+	0.217660i	−0.771351	−	0.636410i	$-0.780419\pi$
$997$	−7.93149	+	6.87267i	−0.251193	+	0.217660i	0.520158	+	0.854070i	$0.325873\pi$
$998$	−15.2368	+	15.5164i	−0.482312	+	0.491165i
$999$	−10.9636	−	18.3882i	−0.346873	−	0.581777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.10	✓	920
3.2	odd	2	inner	552.2.bf.a.5.83	yes	920
8.5	even	2	inner	552.2.bf.a.5.65	yes	920
23.14	odd	22	inner	552.2.bf.a.221.28	yes	920
24.5	odd	2	inner	552.2.bf.a.5.28	yes	920
69.14	even	22	inner	552.2.bf.a.221.65	yes	920
184.37	odd	22	inner	552.2.bf.a.221.83	yes	920
552.221	even	22	inner	552.2.bf.a.221.10	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.10	✓	920	1.1	even	1	trivial
552.2.bf.a.5.28	yes	920	24.5	odd	2	inner
552.2.bf.a.5.65	yes	920	8.5	even	2	inner
552.2.bf.a.5.83	yes	920	3.2	odd	2	inner
552.2.bf.a.221.10	yes	920	552.221	even	22	inner
552.2.bf.a.221.28	yes	920	23.14	odd	22	inner
552.2.bf.a.221.65	yes	920	69.14	even	22	inner
552.2.bf.a.221.83	yes	920	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32050 + 0.506245i) q^{2} +(-0.661683 + 1.60068i) q^{3} +(1.48743 - 1.33699i) q^{4} +(3.61745 + 0.520111i) q^{5} +(0.0634149 - 2.44867i) q^{6} +(-0.429427 + 0.196113i) q^{7} +(-1.28731 + 2.51850i) q^{8} +(-2.12435 - 2.11829i) q^{9} +O(q^{10})\)	\(q+(-1.32050 + 0.506245i) q^{2} +(-0.661683 + 1.60068i) q^{3} +(1.48743 - 1.33699i) q^{4} +(3.61745 + 0.520111i) q^{5} +(0.0634149 - 2.44867i) q^{6} +(-0.429427 + 0.196113i) q^{7} +(-1.28731 + 2.51850i) q^{8} +(-2.12435 - 2.11829i) q^{9} +(-5.04014 + 1.14451i) q^{10} +(1.16189 + 3.95704i) q^{11} +(1.15589 + 3.26557i) q^{12} +(-1.26973 - 0.579867i) q^{13} +(0.467776 - 0.476362i) q^{14} +(-3.22614 + 5.44623i) q^{15} +(0.424905 - 3.97737i) q^{16} +(1.14385 - 0.735106i) q^{17} +(3.87757 + 1.72175i) q^{18} +(6.41440 + 4.12229i) q^{19} +(6.07609 - 4.06287i) q^{20} +(-0.0297691 - 0.817139i) q^{21} +(-3.53751 - 4.63706i) q^{22} +(-4.11645 - 2.46067i) q^{23} +(-3.17952 - 3.72701i) q^{24} +(8.01797 + 2.35429i) q^{25} +(1.97023 + 0.122918i) q^{26} +(4.79634 - 1.99877i) q^{27} +(-0.376542 + 0.865844i) q^{28} +(-0.730219 + 0.469283i) q^{29} +(1.50298 - 8.82496i) q^{30} +(4.88523 + 5.63786i) q^{31} +(1.45244 + 5.46721i) q^{32} +(-7.10276 - 0.758490i) q^{33} +(-1.13830 + 1.54977i) q^{34} +(-1.65543 + 0.486078i) q^{35} +(-5.99196 - 0.310564i) q^{36} +(-0.586348 - 4.07814i) q^{37} +(-10.5571 - 2.19621i) q^{38} +(1.76834 - 1.64875i) q^{39} +(-5.96666 + 8.44101i) q^{40} +(-5.85594 - 0.841957i) q^{41} +(0.452983 + 1.06396i) q^{42} +(-2.94971 + 3.40414i) q^{43} +(7.01877 + 4.33239i) q^{44} +(-6.58299 - 8.76769i) q^{45} +(6.68146 + 1.16538i) q^{46} +2.60508i q^{47} +(6.08534 + 3.31189i) q^{48} +(-4.43808 + 5.12182i) q^{49} +(-11.7796 + 0.950225i) q^{50} +(0.419805 + 2.31734i) q^{51} +(-2.66392 + 0.835108i) q^{52} +(3.64897 - 1.66643i) q^{53} +(-5.32169 + 5.06750i) q^{54} +(2.14499 + 14.9187i) q^{55} +(0.0588935 - 1.33397i) q^{56} +(-10.8428 + 7.53976i) q^{57} +(0.726681 - 0.989358i) q^{58} +(-1.14863 + 2.51515i) q^{59} +(2.48291 + 12.4142i) q^{60} +(5.22227 + 6.02682i) q^{61} +(-9.30509 - 4.97166i) q^{62} +(1.32768 + 0.493036i) q^{63} +(-4.68569 - 6.48416i) q^{64} +(-4.29160 - 2.75804i) q^{65} +(9.76317 - 2.59415i) q^{66} +(-13.9853 - 4.10644i) q^{67} +(0.718563 - 2.62273i) q^{68} +(6.66252 - 4.96093i) q^{69} +(1.93992 - 1.47992i) q^{70} +(1.90546 - 6.48938i) q^{71} +(8.06959 - 2.62330i) q^{72} +(3.50996 + 2.25572i) q^{73} +(2.83881 + 5.08835i) q^{74} +(-9.07382 + 11.2764i) q^{75} +(15.0524 - 2.44439i) q^{76} +(-1.27497 - 1.47140i) q^{77} +(-1.50042 + 3.07238i) q^{78} +(-4.47549 - 2.04389i) q^{79} +(3.60575 - 14.1669i) q^{80} +(0.0257347 + 8.99996i) q^{81} +(8.15899 - 1.85274i) q^{82} +(-8.93096 + 1.28408i) q^{83} +(-1.13679 - 1.17564i) q^{84} +(4.52015 - 2.06428i) q^{85} +(2.17175 - 5.98844i) q^{86} +(-0.267999 - 1.47936i) q^{87} +(-11.4615 - 2.16769i) q^{88} +(8.42893 - 9.72751i) q^{89} +(13.1314 + 8.24511i) q^{90} +0.658976 q^{91} +(-9.41282 + 1.84358i) q^{92} +(-12.2569 + 4.08922i) q^{93} +(-1.31881 - 3.44001i) q^{94} +(21.0597 + 18.2484i) q^{95} +(-9.71231 - 1.29268i) q^{96} +(11.4993 + 1.65335i) q^{97} +(3.26758 - 9.01010i) q^{98} +(5.91388 - 10.8674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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