LMFDB - Embedded newform 575.2.k.g.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09283 + 0.320885i) q^{2} +(1.07866 + 1.24484i) q^{3} +(-0.591189 + 0.379934i) q^{4} +(-1.57825 - 1.01428i) q^{6} +(0.643697 - 1.40950i) q^{7} +(2.01589 - 2.32646i) q^{8} +(0.0408222 - 0.283925i) q^{9} +O(q^{10})$	\(q+(-1.09283 + 0.320885i) q^{2} +(1.07866 + 1.24484i) q^{3} +(-0.591189 + 0.379934i) q^{4} +(-1.57825 - 1.01428i) q^{6} +(0.643697 - 1.40950i) q^{7} +(2.01589 - 2.32646i) q^{8} +(0.0408222 - 0.283925i) q^{9} +(-4.00579 - 1.17621i) q^{11} +(-1.11065 - 0.326117i) q^{12} +(-2.46165 - 5.39026i) q^{13} +(-0.251167 + 1.74690i) q^{14} +(-0.872642 + 1.91082i) q^{16} +(-1.24289 - 0.798760i) q^{17} +(0.0464953 + 0.323382i) q^{18} +(-6.07675 + 3.90529i) q^{19} +(2.44894 - 0.719074i) q^{21} +4.75509 q^{22} +(-2.79621 - 3.89631i) q^{23} +5.07055 q^{24} +(4.41983 + 5.10075i) q^{26} +(4.55453 - 2.92702i) q^{27} +(0.154970 + 1.07784i) q^{28} +(-2.24279 - 1.44135i) q^{29} +(0.638526 - 0.736898i) q^{31} +(-0.535690 + 3.72580i) q^{32} +(-2.85671 - 6.25531i) q^{33} +(1.61459 + 0.474086i) q^{34} +(0.0837390 + 0.183363i) q^{36} +(0.912338 - 6.34545i) q^{37} +(5.38773 - 6.21777i) q^{38} +(4.05474 - 8.87865i) q^{39} +(-0.434006 - 3.01857i) q^{41} +(-2.44555 + 1.57166i) q^{42} +(6.15639 + 7.10485i) q^{43} +(2.81506 - 0.826575i) q^{44} +(4.30606 + 3.36076i) q^{46} -3.03002 q^{47} +(-3.31996 + 0.974829i) q^{48} +(3.01168 + 3.47566i) q^{49} +(-0.346334 - 2.40881i) q^{51} +(3.50324 + 2.25140i) q^{52} +(-0.872932 + 1.91146i) q^{53} +(-4.03811 + 4.66022i) q^{54} +(-1.98152 - 4.33893i) q^{56} +(-11.4163 - 3.35212i) q^{57} +(2.91350 + 0.855482i) q^{58} +(1.42947 + 3.13011i) q^{59} +(-1.61183 + 1.86015i) q^{61} +(-0.461343 + 1.01020i) q^{62} +(-0.373915 - 0.240301i) q^{63} +(-1.20804 - 8.40212i) q^{64} +(5.12914 + 5.91934i) q^{66} +(3.43775 - 1.00941i) q^{67} +1.03826 q^{68} +(1.83413 - 7.68365i) q^{69} +(-6.31720 + 1.85490i) q^{71} +(-0.578247 - 0.667332i) q^{72} +(7.43453 - 4.77788i) q^{73} +(1.03913 + 7.22728i) q^{74} +(2.10875 - 4.61753i) q^{76} +(-4.23637 + 4.88904i) q^{77} +(-1.58214 + 11.0040i) q^{78} +(-2.53011 - 5.54018i) q^{79} +(7.73081 + 2.26997i) q^{81} +(1.44291 + 3.15953i) q^{82} +(-0.648601 + 4.51112i) q^{83} +(-1.17459 + 1.35554i) q^{84} +(-9.00775 - 5.78893i) q^{86} +(-0.624955 - 4.34666i) q^{87} +(-10.8116 + 6.94820i) q^{88} +(-5.73812 - 6.62215i) q^{89} -9.18213 q^{91} +(3.13343 + 1.24108i) q^{92} +1.60608 q^{93} +(3.31131 - 0.972287i) q^{94} +(-5.21588 + 3.35204i) q^{96} +(1.98507 + 13.8065i) q^{97} +(-4.40655 - 2.83192i) q^{98} +(-0.497479 + 1.08933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	−1.09283	+	0.320885i	−0.772750	+	0.226900i	−0.644256	−	0.764810i	$-0.722833\pi$
$2$	−1.09283	+	0.320885i	−0.772750	+	0.226900i	−0.128495	+	0.991710i	$0.541014\pi$
$3$	1.07866	+	1.24484i	0.622767	+	0.718712i	0.976230	−	0.216737i	$-0.0695414\pi$
$3$	1.07866	+	1.24484i	0.622767	+	0.718712i	−0.353463	+	0.935449i	$0.614996\pi$
$4$	−0.591189	+	0.379934i	−0.295594	+	0.189967i
$5$		0			0
$5$		0			0
$6$	−1.57825	−	1.01428i	−0.644319	−	0.414079i
$7$	0.643697	−	1.40950i	0.243295	−	0.532741i	−0.748110	−	0.663575i	$-0.769038\pi$
$7$	0.643697	−	1.40950i	0.243295	−	0.532741i	0.991404	+	0.130834i	$0.0417656\pi$
$8$	2.01589	−	2.32646i	0.712725	−	0.822528i
$9$	0.0408222	−	0.283925i	0.0136074	−	0.0946416i
$10$		0			0
$11$	−4.00579	−	1.17621i	−1.20779	−	0.354639i	−0.384964	−	0.922932i	$-0.625786\pi$
$11$	−4.00579	−	1.17621i	−1.20779	−	0.354639i	−0.822827	+	0.568293i	$0.807604\pi$
$12$	−1.11065	−	0.326117i	−0.320618	−	0.0941419i
$13$	−2.46165	−	5.39026i	−0.682739	−	1.49499i	−0.859715	−	0.510774i	$-0.829359\pi$
$13$	−2.46165	−	5.39026i	−0.682739	−	1.49499i	0.176976	−	0.984215i	$-0.443368\pi$
$14$	−0.251167	+	1.74690i	−0.0671271	+	0.466879i
$15$		0			0
$16$	−0.872642	+	1.91082i	−0.218161	+	0.477705i
$17$	−1.24289	−	0.798760i	−0.301446	−	0.193728i	0.381170	−	0.924505i	$-0.375521\pi$
$17$	−1.24289	−	0.798760i	−0.301446	−	0.193728i	−0.682616	+	0.730777i	$0.739158\pi$
$18$	0.0464953	+	0.323382i	0.0109590	+	0.0762218i
$19$	−6.07675	+	3.90529i	−1.39410	+	0.895935i	−0.999735	−	0.0230176i	$-0.992673\pi$
$19$	−6.07675	+	3.90529i	−1.39410	+	0.895935i	−0.394367	+	0.918953i	$0.629036\pi$
$20$		0			0
$21$	2.44894	−	0.719074i	0.534403	−	0.156915i
$22$	4.75509			1.01379
$23$	−2.79621	−	3.89631i	−0.583049	−	0.812437i
$23$	−2.79621	−	3.89631i	−0.583049	−	0.812437i
$24$	5.07055			1.03502
$25$		0			0
$26$	4.41983	+	5.10075i	0.866799	+	1.00034i
$27$	4.55453	−	2.92702i	0.876519	−	0.563305i
$28$	0.154970	+	1.07784i	0.0292867	+	0.203693i
$29$	−2.24279	−	1.44135i	−0.416475	−	0.267653i	0.315578	−	0.948900i	$-0.397802\pi$
$29$	−2.24279	−	1.44135i	−0.416475	−	0.267653i	−0.732054	+	0.681247i	$0.761438\pi$
$30$		0			0
$31$	0.638526	−	0.736898i	0.114683	−	0.132351i	−0.695505	−	0.718521i	$-0.744819\pi$
$31$	0.638526	−	0.736898i	0.114683	−	0.132351i	0.810188	+	0.586170i	$0.199365\pi$
$32$	−0.535690	+	3.72580i	−0.0946975	+	0.658635i
$33$	−2.85671	−	6.25531i	−0.497289	−	1.08891i
$34$	1.61459	+	0.474086i	0.276899	+	0.0813050i
$35$		0			0
$36$	0.0837390	+	0.183363i	0.0139565	+	0.0305605i
$37$	0.912338	−	6.34545i	0.149987	−	1.04319i	−0.766248	−	0.642545i	$-0.777878\pi$
$37$	0.912338	−	6.34545i	0.149987	−	1.04319i	0.916235	−	0.400641i	$-0.131212\pi$
$38$	5.38773	−	6.21777i	0.874005	−	1.00866i
$39$	4.05474	−	8.87865i	0.649279	−	1.42172i
$40$		0			0
$41$	−0.434006	−	3.01857i	−0.0677803	−	0.471422i	−0.995236	−	0.0974903i	$-0.968918\pi$
$41$	−0.434006	−	3.01857i	−0.0677803	−	0.471422i	0.927456	−	0.373932i	$-0.121991\pi$
$42$	−2.44555	+	1.57166i	−0.377356	+	0.242512i
$43$	6.15639	+	7.10485i	0.938841	+	1.08348i	0.996369	+	0.0851361i	$0.0271325\pi$
$43$	6.15639	+	7.10485i	0.938841	+	1.08348i	−0.0575286	+	0.998344i	$0.518322\pi$
$44$	2.81506	−	0.826575i	0.424386	−	0.124611i
$45$		0			0
$46$	4.30606	+	3.36076i	0.634893	+	0.495517i
$47$	−3.03002			−0.441974			−0.220987	−	0.975277i	$-0.570928\pi$
$47$	−3.03002			−0.441974			−0.220987	+	0.975277i	$0.570928\pi$
$48$	−3.31996	+	0.974829i	−0.479195	+	0.140704i
$49$	3.01168	+	3.47566i	0.430240	+	0.496524i
$50$		0			0
$51$	−0.346334	−	2.40881i	−0.0484964	−	0.337300i
$52$	3.50324	+	2.25140i	0.485812	+	0.312213i
$53$	−0.872932	+	1.91146i	−0.119906	+	0.262559i	−0.960062	−	0.279787i	$-0.909736\pi$
$53$	−0.872932	+	1.91146i	−0.119906	+	0.262559i	0.840156	+	0.542345i	$0.182464\pi$
$54$	−4.03811	+	4.66022i	−0.549517	+	0.634176i
$55$		0			0
$56$	−1.98152	−	4.33893i	−0.264792	−	0.579814i
$57$	−11.4163	−	3.35212i	−1.51212	−	0.443999i
$58$	2.91350	+	0.855482i	0.382562	+	0.112330i
$59$	1.42947	+	3.13011i	0.186102	+	0.407506i	0.979569	−	0.201106i	$-0.0644537\pi$
$59$	1.42947	+	3.13011i	0.186102	+	0.407506i	−0.793468	+	0.608612i	$0.791726\pi$
$60$		0			0
$61$	−1.61183	+	1.86015i	−0.206374	+	0.238168i	−0.849495	−	0.527596i	$-0.823093\pi$
$61$	−1.61183	+	1.86015i	−0.206374	+	0.238168i	0.643122	+	0.765764i	$0.277639\pi$
$62$	−0.461343	+	1.01020i	−0.0585906	+	0.128296i
$63$	−0.373915	−	0.240301i	−0.0471088	−	0.0302750i
$64$	−1.20804	−	8.40212i	−0.151005	−	1.05026i
$65$		0			0
$66$	5.12914	+	5.91934i	0.631354	+	0.728621i
$67$	3.43775	−	1.00941i	0.419988	−	0.123320i	−0.0649084	−	0.997891i	$-0.520676\pi$
$67$	3.43775	−	1.00941i	0.419988	−	0.123320i	0.484896	+	0.874572i	$0.338857\pi$
$68$	1.03826			0.125908
$69$	1.83413	−	7.68365i	0.220804	−	0.925003i
$70$		0			0
$71$	−6.31720	+	1.85490i	−0.749714	+	0.220136i	−0.634199	−	0.773170i	$-0.718670\pi$
$71$	−6.31720	+	1.85490i	−0.749714	+	0.220136i	−0.115515	+	0.993306i	$0.536852\pi$
$72$	−0.578247	−	0.667332i	−0.0681470	−	0.0786459i
$73$	7.43453	−	4.77788i	0.870146	−	0.559209i	−0.0276515	−	0.999618i	$-0.508803\pi$
$73$	7.43453	−	4.77788i	0.870146	−	0.559209i	0.897797	+	0.440409i	$0.145167\pi$
$74$	1.03913	+	7.22728i	0.120796	+	0.840154i
$75$		0			0
$76$	2.10875	−	4.61753i	0.241891	−	0.529667i
$77$	−4.23637	+	4.88904i	−0.482780	+	0.557157i
$78$	−1.58214	+	11.0040i	−0.179142	+	1.24596i
$79$	−2.53011	−	5.54018i	−0.284660	−	0.623319i	0.712245	−	0.701931i	$-0.247678\pi$
$79$	−2.53011	−	5.54018i	−0.284660	−	0.623319i	−0.996905	+	0.0786121i	$0.974951\pi$
$80$		0			0
$81$	7.73081	+	2.26997i	0.858979	+	0.252219i
$82$	1.44291	+	3.15953i	0.159343	+	0.348912i
$83$	−0.648601	+	4.51112i	−0.0711932	+	0.495159i	0.922762	+	0.385371i	$0.125926\pi$
$83$	−0.648601	+	4.51112i	−0.0711932	+	0.495159i	−0.993955	+	0.109789i	$0.964983\pi$
$84$	−1.17459	+	1.35554i	−0.128158	+	0.147902i
$85$		0			0
$86$	−9.00775	−	5.78893i	−0.971331	−	0.624236i
$87$	−0.624955	−	4.34666i	−0.0670023	−	0.466011i
$88$	−10.8116	+	6.94820i	−1.15252	+	0.740681i
$89$	−5.73812	−	6.62215i	−0.608240	−	0.701946i	0.365190	−	0.930933i	$-0.381004\pi$
$89$	−5.73812	−	6.62215i	−0.608240	−	0.701946i	−0.973429	+	0.228987i	$0.926459\pi$
$90$		0			0
$91$	−9.18213			−0.962548
$92$	3.13343	+	1.24108i	0.326682	+	0.129392i
$93$	1.60608			0.166543
$94$	3.31131	−	0.972287i	0.341535	−	0.100284i
$95$		0			0
$96$	−5.21588	+	3.35204i	−0.532343	+	0.342116i
$97$	1.98507	+	13.8065i	0.201553	+	1.40183i	0.799678	+	0.600430i	$0.205004\pi$
$97$	1.98507	+	13.8065i	0.201553	+	1.40183i	−0.598124	+	0.801403i	$0.704087\pi$
$98$	−4.40655	−	2.83192i	−0.445129	−	0.286067i
$99$	−0.497479	+	1.08933i	−0.0499985	+	0.109481i
$100$		0			0
$101$	2.14777	−	14.9381i	0.213711	−	1.48639i	−0.546906	−	0.837194i	$-0.684194\pi$
$101$	2.14777	−	14.9381i	0.213711	−	1.48639i	0.760617	−	0.649201i	$-0.224897\pi$
$102$	1.15143	+	2.52129i	0.114009	+	0.249645i
$103$	−9.94787	−	2.92096i	−0.980193	−	0.287811i	−0.247889	−	0.968788i	$-0.579737\pi$
$103$	−9.94787	−	2.92096i	−0.980193	−	0.287811i	−0.732304	+	0.680978i	$0.761555\pi$
$104$	−17.5026	−	5.13924i	−1.71627	−	0.503944i
$105$		0			0
$106$	0.340613	−	2.36901i	0.0330832	−	0.230099i
$107$	8.36482	−	9.65352i	0.808658	−	0.933241i	−0.190165	−	0.981752i	$-0.560902\pi$
$107$	8.36482	−	9.65352i	0.808658	−	0.933241i	0.998823	+	0.0485111i	$0.0154476\pi$
$108$	−1.58051	+	3.46084i	−0.152085	+	0.333019i
$109$	12.4371	+	7.99285i	1.19126	+	0.765576i	0.977423	−	0.211294i	$-0.0677677\pi$
$109$	12.4371	+	7.99285i	1.19126	+	0.765576i	0.213836	+	0.976869i	$0.431404\pi$
$110$		0			0
$111$	8.88321	−	5.70889i	0.843157	−	0.541864i
$112$	2.13158	+	2.45998i	0.201416	+	0.232446i
$113$	−1.15434	+	0.338944i	−0.108591	+	0.0318852i	−0.335577	−	0.942013i	$-0.608931\pi$
$113$	−1.15434	+	0.338944i	−0.108591	+	0.0318852i	0.226986	+	0.973898i	$0.427113\pi$
$114$	13.5517			1.26923
$115$		0			0
$116$	1.87353			0.173953
$117$	−1.63092	+	0.478881i	−0.150778	+	0.0442726i
$118$	−2.56658	−	2.96200i	−0.236273	−	0.272674i
$119$	−1.92590	+	1.23770i	−0.176547	+	0.113460i
$120$		0			0
$121$	5.40908	+	3.47621i	0.491735	+	0.316019i
$122$	1.16457	−	2.55005i	0.105435	−	0.230870i
$123$	3.28951	−	3.79630i	0.296605	−	0.342301i
$124$	−0.0975167	+	0.678244i	−0.00875726	+	0.0609081i
$125$		0			0
$126$	0.485736	+	0.142625i	0.0432728	+	0.0127060i
$127$	−3.31075	−	0.972123i	−0.293781	−	0.0862620i	0.131521	−	0.991313i	$-0.458014\pi$
$127$	−3.31075	−	0.972123i	−0.293781	−	0.0862620i	−0.425302	+	0.905051i	$0.639832\pi$
$128$	0.888961	+	1.94655i	0.0785738	+	0.172053i
$129$	−2.20376	+	15.3275i	−0.194030	+	1.34951i
$130$		0			0
$131$	−4.46085	+	9.76790i	−0.389746	+	0.853426i	0.608461	+	0.793583i	$0.291787\pi$
$131$	−4.46085	+	9.76790i	−0.389746	+	0.853426i	−0.998208	+	0.0598422i	$0.980940\pi$
$132$	4.06546	+	2.61271i	0.353853	+	0.227407i
$133$	1.59292	+	11.0790i	0.138124	+	0.960672i
$134$	−3.43298	+	2.20624i	−0.296565	+	0.190590i
$135$		0			0
$136$	−4.36382	+	1.28133i	−0.374195	+	0.109873i
$137$	−6.58672			−0.562741			−0.281371	−	0.959599i	$-0.590789\pi$
$137$	−6.58672			−0.562741			−0.281371	+	0.959599i	$0.590789\pi$
$138$	0.461167	+	8.98550i	0.0392572	+	0.764897i
$139$	2.99730			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$139$	2.99730			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$140$		0			0
$141$	−3.26837	−	3.77190i	−0.275247	−	0.317652i
$142$	6.30844	−	4.05419i	0.529393	−	0.340220i
$143$	3.52079	+	24.4876i	0.294423	+	2.04776i
$144$	0.506906	+	0.325769i	0.0422422	+	0.0271474i
$145$		0			0
$146$	−6.59155	+	7.60706i	−0.545521	+	0.629565i
$147$	−1.07807	+	7.49815i	−0.0889178	+	0.618437i
$148$	1.87149	+	4.09799i	0.153835	+	0.336853i
$149$	−4.38329	−	1.28705i	−0.359093	−	0.105439i	0.0972094	−	0.995264i	$-0.469008\pi$
$149$	−4.38329	−	1.28705i	−0.359093	−	0.105439i	−0.456303	+	0.889825i	$0.650827\pi$
$150$		0			0
$151$	4.52490	+	9.90816i	0.368232	+	0.806315i	0.999526	+	0.0307717i	$0.00979649\pi$
$151$	4.52490	+	9.90816i	0.368232	+	0.806315i	−0.631295	+	0.775543i	$0.717476\pi$
$152$	−3.16455	+	22.0100i	−0.256679	+	1.78524i
$153$	−0.277526	+	0.320282i	−0.0224366	+	0.0258932i
$154$	3.06083	−	6.70229i	0.246649	−	0.540086i
$155$		0			0
$156$	0.976182	+	6.78949i	0.0781571	+	0.543595i
$157$	9.49978	−	6.10514i	0.758165	−	0.487243i	−0.103557	−	0.994624i	$-0.533022\pi$
$157$	9.49978	−	6.10514i	0.758165	−	0.487243i	0.861722	+	0.507380i	$0.169386\pi$
$158$	4.54275	+	5.24262i	0.361402	+	0.417080i
$159$	−3.32107	+	0.975153i	−0.263378	+	0.0773347i
$160$		0			0
$161$	−7.29176	+	1.43321i	−0.574671	+	0.112953i
$162$	−9.17689			−0.721005
$163$	7.95050	−	2.33448i	0.622731	−	0.182850i	0.0448798	−	0.998992i	$-0.485710\pi$
$163$	7.95050	−	2.33448i	0.622731	−	0.182850i	0.577851	+	0.816142i	$0.303891\pi$
$164$	1.40344	+	1.61965i	0.109590	+	0.126474i
$165$		0			0
$166$	−0.738737	−	5.13803i	−0.0573371	−	0.398788i
$167$	−20.5261	−	13.1914i	−1.58836	−	1.02078i	−0.972494	−	0.232927i	$-0.925170\pi$
$167$	−20.5261	−	13.1914i	−1.58836	−	1.02078i	−0.615866	−	0.787851i	$-0.711194\pi$
$168$	3.26390	−	7.14694i	0.251815	−	0.551398i
$169$	−14.4820	+	16.7131i	−1.11400	+	1.28562i
$170$		0			0
$171$	0.860743	+	1.88476i	0.0658226	+	0.144131i
$172$	−6.33896	−	1.86129i	−0.483341	−	0.141922i
$173$	−10.3061	−	3.02613i	−0.783555	−	0.230073i	−0.134601	−	0.990900i	$-0.542975\pi$
$173$	−10.3061	−	3.02613i	−0.783555	−	0.230073i	−0.648954	+	0.760827i	$0.724793\pi$
$174$	2.07775	+	4.54964i	0.157514	+	0.344907i
$175$		0			0
$176$	5.74313	−	6.62793i	0.432905	−	0.499599i
$177$	−2.35458	+	5.15582i	−0.176981	+	0.387535i
$178$	8.39576	+	5.39563i	0.629289	+	0.404419i
$179$	1.30715	+	9.09145i	0.0977012	+	0.679527i	0.978532	+	0.206095i	$0.0660757\pi$
$179$	1.30715	+	9.09145i	0.0977012	+	0.679527i	−0.880831	+	0.473431i	$0.843015\pi$
$180$		0			0
$181$	12.6057	+	14.5477i	0.936972	+	1.08132i	0.996541	+	0.0830995i	$0.0264819\pi$
$181$	12.6057	+	14.5477i	0.936972	+	1.08132i	−0.0595689	+	0.998224i	$0.518973\pi$
$182$	10.0345	−	2.94641i	0.743809	−	0.218402i
$183$	−4.05422			−0.299697
$184$	−14.7015	−	1.34926i	−1.08381	−	0.0994690i
$185$		0			0
$186$	−1.75518	+	0.515367i	−0.128696	+	0.0377885i
$187$	4.03927	+	4.66156i	0.295380	+	0.340887i
$188$	1.79131	−	1.15121i	0.130645	−	0.0839604i
$189$	−1.19389	−	8.30372i	−0.0868431	−	0.604007i
$190$		0			0
$191$	−0.519824	+	1.13826i	−0.0376132	+	0.0823614i	−0.927506	−	0.373808i	$-0.878052\pi$
$191$	−0.519824	+	1.13826i	−0.0376132	+	0.0823614i	0.889893	+	0.456170i	$0.150779\pi$
$192$	9.15626	−	10.5669i	0.660796	−	0.762600i
$193$	2.00269	−	13.9290i	0.144157	−	1.00263i	−0.781401	−	0.624029i	$-0.785495\pi$
$193$	2.00269	−	13.9290i	0.144157	−	1.00263i	0.925558	−	0.378605i	$-0.123596\pi$
$194$	−6.59963	−	14.4512i	−0.473826	−	1.03753i
$195$		0			0
$196$	−3.10099	−	0.910534i	−0.221500	−	0.0650382i
$197$	−9.36020	−	20.4960i	−0.666886	−	1.46028i	−0.875963	−	0.482378i	$-0.839773\pi$
$197$	−9.36020	−	20.4960i	−0.666886	−	1.46028i	0.209077	−	0.977899i	$-0.432954\pi$
$198$	0.194113	−	1.35009i	0.0137950	−	0.0959465i
$199$	0.972483	−	1.12230i	0.0689375	−	0.0795581i	−0.720233	−	0.693732i	$-0.755965\pi$
$199$	0.972483	−	1.12230i	0.0689375	−	0.0795581i	0.789171	+	0.614174i	$0.210511\pi$
$200$		0			0
$201$	4.96474	+	3.19065i	0.350186	+	0.225051i
$202$	2.44625	+	17.0140i	0.172117	+	1.19710i
$203$	−3.47526	+	2.23342i	−0.243916	+	0.156755i
$204$	1.11994	+	1.29247i	0.0784112	+	0.0904913i
$205$		0			0
$206$	11.8087			0.822748
$207$	−1.22041	+	0.634857i	−0.0848241	+	0.0441256i
$208$	12.4480			0.863110
$209$	28.9356	−	8.49626i	2.00152	−	0.587698i
$210$		0			0
$211$	10.4138	−	6.69256i	0.716917	−	0.460734i	−0.130646	−	0.991429i	$-0.541705\pi$
$211$	10.4138	−	6.69256i	0.716917	−	0.460734i	0.847563	+	0.530695i	$0.178069\pi$
$212$	−0.210159	−	1.46169i	−0.0144338	−	0.100389i
$213$	−9.12320	−	5.86312i	−0.625111	−	0.401735i
$214$	−6.04369	+	13.2338i	−0.413138	+	0.904647i
$215$		0			0
$216$	2.37183	−	16.4965i	0.161383	−	1.12244i
$217$	−0.627641	−	1.37434i	−0.0426070	−	0.0932964i
$218$	−16.1565	−	4.74397i	−1.09425	−	0.321302i
$219$	13.9671	+	4.10111i	0.943808	+	0.277127i
$220$		0			0
$221$	−1.24595	+	8.66579i	−0.0838119	+	0.582924i
$222$	−7.87597	+	9.08936i	−0.528601	+	0.610038i
$223$	2.32052	−	5.08124i	0.155394	−	0.340265i	−0.815883	−	0.578217i	$-0.803749\pi$
$223$	2.32052	−	5.08124i	0.155394	−	0.340265i	0.971277	+	0.237952i	$0.0764761\pi$
$224$	4.90670	+	3.15334i	0.327843	+	0.210692i
$225$		0			0
$226$	1.15274	−	0.740819i	0.0766789	−	0.0492786i
$227$	0.207283	+	0.239218i	0.0137579	+	0.0158774i	0.762587	−	0.646886i	$-0.223929\pi$
$227$	0.207283	+	0.239218i	0.0137579	+	0.0158774i	−0.748829	+	0.662763i	$0.769384\pi$
$228$	8.02274	−	2.35569i	0.531319	−	0.156009i
$229$	11.8915			0.785810			0.392905	−	0.919579i	$-0.371470\pi$
$229$	11.8915			0.785810			0.392905	+	0.919579i	$0.371470\pi$
$230$		0			0
$231$	−10.6557			−0.701095
$232$	−7.87447	+	2.31215i	−0.516984	+	0.151800i
$233$	−18.6840	−	21.5625i	−1.22403	−	1.41261i	−0.880887	−	0.473326i	$-0.843053\pi$
$233$	−18.6840	−	21.5625i	−1.22403	−	1.41261i	−0.343145	−	0.939282i	$-0.611492\pi$
$234$	1.62866	−	1.04667i	0.106469	−	0.0684232i
$235$		0			0
$236$	−2.03433	−	1.30738i	−0.132423	−	0.0851033i
$237$	4.16752	−	9.12559i	0.270709	−	0.592771i
$238$	1.70753	−	1.97059i	0.110683	−	0.127735i
$239$	2.64917	−	18.4254i	0.171361	−	1.19184i	−0.704653	−	0.709552i	$-0.748897\pi$
$239$	2.64917	−	18.4254i	0.171361	−	1.19184i	0.876014	−	0.482287i	$-0.160194\pi$
$240$		0			0
$241$	−25.8171	−	7.58060i	−1.66303	−	0.488309i	−0.690937	−	0.722915i	$-0.742802\pi$
$241$	−25.8171	−	7.58060i	−1.66303	−	0.488309i	−0.972091	+	0.234605i	$0.924620\pi$
$242$	−7.02669	−	2.06322i	−0.451693	−	0.132629i
$243$	−1.23395	−	2.70198i	−0.0791581	−	0.173332i
$244$	0.246161	−	1.71209i	0.0157589	−	0.109605i
$245$		0			0
$246$	−2.37671	+	5.20428i	−0.151534	+	0.331813i
$247$	36.0094	+	23.1418i	2.29122	+	1.47248i
$248$	−0.427167	−	2.97101i	−0.0271251	−	0.188659i
$249$	−6.31526	+	4.05857i	−0.400214	+	0.257202i
$250$		0			0
$251$	11.5799	−	3.40017i	0.730918	−	0.214617i	0.104963	−	0.994476i	$-0.466528\pi$
$251$	11.5799	−	3.40017i	0.730918	−	0.214617i	0.625955	+	0.779859i	$0.284709\pi$
$252$	0.312353			0.0196764
$253$	6.61815	+	18.8967i	0.416080	+	1.18803i
$254$	3.93004			0.246592
$255$		0			0
$256$	9.52149	+	10.9884i	0.595093	+	0.686774i
$257$	5.66657	−	3.64168i	0.353471	−	0.227162i	−0.351840	−	0.936060i	$-0.614444\pi$
$257$	5.66657	−	3.64168i	0.353471	−	0.227162i	0.705311	+	0.708898i	$0.250808\pi$
$258$	−2.51002	−	17.4576i	−0.156267	−	1.08686i
$259$	−8.35665	−	5.37049i	−0.519257	−	0.333706i
$260$		0			0
$261$	−0.500792	+	0.577944i	−0.0309982	+	0.0357739i
$262$	1.74060	−	12.1061i	0.107534	−	0.747918i
$263$	7.08264	+	15.5088i	0.436734	+	0.956315i	0.992186	+	0.124766i	$0.0398181\pi$
$263$	7.08264	+	15.5088i	0.436734	+	0.956315i	−0.555452	+	0.831549i	$0.687455\pi$
$264$	−20.3115	−	5.96401i	−1.25009	−	0.367059i
$265$		0			0
$266$	−5.29588	−	11.5964i	−0.324711	−	0.711019i
$267$	2.05404	−	14.2861i	0.125705	−	0.874298i
$268$	−1.64885	+	1.90287i	−0.100719	+	0.116236i
$269$	5.60123	−	12.2650i	0.341513	−	0.747810i	−0.658475	−	0.752602i	$-0.728798\pi$
$269$	5.60123	−	12.2650i	0.341513	−	0.747810i	0.999989	+	0.00479268i	$0.00152556\pi$
$270$		0			0
$271$	−2.61458	−	18.1848i	−0.158825	−	1.10465i	−0.900804	−	0.434226i	$-0.857022\pi$
$271$	−2.61458	−	18.1848i	−0.158825	−	1.10465i	0.741979	−	0.670423i	$-0.233887\pi$
$272$	2.61089	−	1.67792i	0.158308	−	0.101739i
$273$	−9.90443	−	11.4303i	−0.599444	−	0.691795i
$274$	7.19819	−	2.11358i	0.434858	−	0.127686i
$275$		0			0
$276$	1.83496	+	5.23934i	0.110452	+	0.315371i
$277$	22.0544			1.32512			0.662561	−	0.749008i	$-0.269469\pi$
$277$	22.0544			1.32512			0.662561	+	0.749008i	$0.269469\pi$
$278$	−3.27555	+	0.961790i	−0.196455	+	0.0576843i
$279$	−0.183158	−	0.211375i	−0.0109654	−	0.0126547i
$280$		0			0
$281$	0.477468	+	3.32086i	0.0284834	+	0.198106i	0.999094	−	0.0425474i	$-0.0135474\pi$
$281$	0.477468	+	3.32086i	0.0284834	+	0.198106i	−0.970611	+	0.240653i	$0.922638\pi$
$282$	4.78213	+	3.07329i	0.284772	+	0.183012i
$283$	3.89580	−	8.53060i	0.231581	−	0.507092i	−0.757791	−	0.652497i	$-0.773721\pi$
$283$	3.89580	−	8.53060i	0.231581	−	0.507092i	0.989372	+	0.145406i	$0.0464487\pi$
$284$	3.02992	−	3.49671i	0.179793	−	0.207492i
$285$		0			0
$286$	−11.7054	−	25.6311i	−0.692152	−	1.51560i
$287$	−4.53405	−	1.33132i	−0.267636	−	0.0785852i
$288$	1.03598	+	0.304191i	0.0610457	+	0.0179246i
$289$	−6.15529	−	13.4782i	−0.362076	−	0.792835i
$290$		0			0
$291$	−15.0457	+	17.3636i	−0.881993	+	1.01787i
$292$	−2.57993	+	5.64926i	−0.150979	+	0.330598i
$293$	−3.42210	−	2.19925i	−0.199921	−	0.128482i	0.436850	−	0.899534i	$-0.356094\pi$
$293$	−3.42210	−	2.19925i	−0.199921	−	0.128482i	−0.636771	+	0.771053i	$0.719730\pi$
$294$	−1.22789	−	8.54017i	−0.0716121	−	0.498073i
$295$		0			0
$296$	−12.9233	−	14.9142i	−0.751150	−	0.866873i
$297$	−21.6872	+	6.36795i	−1.25842	+	0.369506i
$298$	5.20320			0.301413
$299$	−14.1188	+	24.6636i	−0.816513	+	1.42633i
$300$		0			0
$301$	13.9771	−	4.10406i	0.805629	−	0.236554i
$302$	−8.12435	−	9.37600i	−0.467504	−	0.539528i
$303$	20.9123	−	13.4395i	1.20138	−	0.772081i
$304$	−2.15948	−	15.0195i	−0.123855	−	0.861427i
$305$		0			0
$306$	0.200516	−	0.439068i	0.0114627	−	0.0250999i
$307$	−11.3315	+	13.0772i	−0.646721	+	0.746356i	−0.980548	−	0.196278i	$-0.937114\pi$
$307$	−11.3315	+	13.0772i	−0.646721	+	0.746356i	0.333827	+	0.942634i	$0.391660\pi$
$308$	0.646986	−	4.49989i	0.0368654	−	0.256405i
$309$	−7.09427	−	15.5343i	−0.403579	−	0.883715i
$310$		0			0
$311$	5.99870	+	1.76138i	0.340155	+	0.0998785i	0.447349	−	0.894360i	$-0.352368\pi$
$311$	5.99870	+	1.76138i	0.340155	+	0.0998785i	−0.107194	+	0.994238i	$0.534186\pi$
$312$	−12.4819	−	27.3316i	−0.706649	−	1.54735i
$313$	2.16968	−	15.0905i	0.122638	−	0.852964i	−0.831911	−	0.554909i	$-0.812753\pi$
$313$	2.16968	−	15.0905i	0.122638	−	0.852964i	0.954549	−	0.298055i	$-0.0963378\pi$
$314$	−8.42264	+	9.72024i	−0.475317	+	0.548545i
$315$		0			0
$316$	3.60068	+	2.31401i	0.202554	+	0.130173i
$317$	−2.49041	−	17.3212i	−0.139876	−	0.972856i	−0.931990	−	0.362483i	$-0.881929\pi$
$317$	−2.49041	−	17.3212i	−0.139876	−	0.972856i	0.792115	−	0.610372i	$-0.208980\pi$
$318$	3.31646	−	2.13136i	0.185978	−	0.119521i
$319$	7.28881	+	8.41173i	0.408095	+	0.470967i
$320$		0			0
$321$	21.0400			1.17434
$322$	7.50878	−	3.90608i	0.418448	−	0.217677i
$323$	10.6722			0.593815
$324$	−5.43281	+	1.59522i	−0.301823	+	0.0886232i
$325$		0			0
$326$	−7.93947	+	5.10239i	−0.439727	+	0.282595i
$327$	3.46561	+	24.1039i	0.191649	+	1.33295i
$328$	−7.89750	−	5.07542i	−0.436067	−	0.280243i
$329$	−1.95041	+	4.27081i	−0.107530	+	0.235457i
$330$		0			0
$331$	−3.74185	+	26.0252i	−0.205671	+	1.43047i	0.581404	+	0.813615i	$0.302503\pi$
$331$	−3.74185	+	26.0252i	−0.205671	+	1.43047i	−0.787075	+	0.616857i	$0.788406\pi$
$332$	−1.33048	−	2.91335i	−0.0730196	−	0.159891i
$333$	−1.76439	−	0.518071i	−0.0966879	−	0.0283901i
$334$	26.6646	+	7.82942i	1.45902	+	0.428407i
$335$		0			0
$336$	−0.763029	+	5.30698i	−0.0416266	+	0.289520i
$337$	3.25210	−	3.75313i	0.177153	−	0.204446i	−0.660228	−	0.751066i	$-0.729540\pi$
$337$	3.25210	−	3.75313i	0.177153	−	0.204446i	0.837381	+	0.546620i	$0.184086\pi$
$338$	10.4634	−	22.9117i	0.569135	−	1.24623i
$339$	−1.66708	−	1.07136i	−0.0905431	−	0.0581885i
$340$		0			0
$341$	−3.42454	+	2.20082i	−0.185449	+	0.119181i
$342$	−1.54544	−	1.78353i	−0.0835679	−	0.0964424i
$343$	17.2449	−	5.06356i	0.931136	−	0.273406i
$344$	28.9398			1.56033
$345$		0			0
$346$	12.2338			0.657696
$347$	12.6440	−	3.71262i	0.678767	−	0.199304i	0.0758639	−	0.997118i	$-0.475829\pi$
$347$	12.6440	−	3.71262i	0.678767	−	0.199304i	0.602904	+	0.797814i	$0.294010\pi$
$348$	2.02091	+	2.33225i	0.108332	+	0.125022i
$349$	1.54418	−	0.992384i	0.0826580	−	0.0531211i	−0.498659	−	0.866798i	$-0.666174\pi$
$349$	1.54418	−	0.992384i	0.0826580	−	0.0531211i	0.581317	+	0.813677i	$0.302538\pi$
$350$		0			0
$351$	−26.9890	−	17.3448i	−1.44057	−	0.925797i
$352$	6.52817	−	14.2947i	0.347953	−	0.761910i
$353$	−20.9166	+	24.1390i	−1.11328	+	1.28479i	−0.158537	+	0.987353i	$0.550678\pi$
$353$	−20.9166	+	24.1390i	−1.11328	+	1.28479i	−0.954741	+	0.297438i	$0.903868\pi$
$354$	0.918743	−	6.39000i	0.0488306	−	0.339625i
$355$		0			0
$356$	5.90829	+	1.73483i	0.313139	+	0.0919459i
$357$	−3.61815	−	1.06238i	−0.191493	−	0.0562273i
$358$	−4.34581	−	9.51599i	−0.229683	−	0.502936i
$359$	−3.10723	+	21.6113i	−0.163993	+	1.14060i	0.727018	+	0.686618i	$0.240905\pi$
$359$	−3.10723	+	21.6113i	−0.163993	+	1.14060i	−0.891012	+	0.453980i	$0.850004\pi$
$360$		0			0
$361$	13.7827	−	30.1800i	0.725407	−	1.58842i
$362$	−18.4440	−	11.8533i	−0.969398	−	0.622994i
$363$	1.50725	+	10.4831i	0.0791099	+	0.550221i
$364$	5.42837	−	3.48860i	0.284524	−	0.182852i
$365$		0			0
$366$	4.43059	−	1.30094i	0.231591	−	0.0680011i
$367$	−4.69179			−0.244909			−0.122455	−	0.992474i	$-0.539077\pi$
$367$	−4.69179			−0.244909			−0.122455	+	0.992474i	$0.539077\pi$
$368$	9.88523	−	1.94296i	0.515303	−	0.101284i
$369$	−0.874765			−0.0455385
$370$		0			0
$371$	2.13229	+	2.46080i	0.110703	+	0.127758i
$372$	−0.949496	+	0.610204i	−0.0492291	+	0.0316376i
$373$	1.03085	+	7.16970i	0.0533752	+	0.371233i	0.998949	+	0.0458263i	$0.0145921\pi$
$373$	1.03085	+	7.16970i	0.0533752	+	0.371233i	−0.945574	+	0.325407i	$0.894499\pi$
$374$	−5.91007	−	3.79817i	−0.305603	−	0.196399i
$375$		0			0
$376$	−6.10818	+	7.04922i	−0.315005	+	0.363536i
$377$	−2.24831	+	15.6373i	−0.115794	+	0.805363i
$378$	3.96927	+	8.69148i	0.204157	+	0.447042i
$379$	−15.6248	−	4.58785i	−0.802592	−	0.235662i	−0.145388	−	0.989375i	$-0.546443\pi$
$379$	−15.6248	−	4.58785i	−0.802592	−	0.235662i	−0.657204	+	0.753713i	$0.728261\pi$
$380$		0			0
$381$	−2.36104	−	5.16996i	−0.120960	−	0.264865i
$382$	0.202832	−	1.41073i	0.0103778	−	0.0721792i
$383$	17.4013	−	20.0821i	0.889163	−	1.02615i	−0.110317	−	0.993896i	$-0.535187\pi$
$383$	17.4013	−	20.0821i	0.889163	−	1.02615i	0.999480	−	0.0322519i	$-0.0102679\pi$
$384$	−1.46427	+	3.20629i	−0.0747230	+	0.163621i
$385$		0			0
$386$	2.28101	+	15.8648i	0.116100	+	0.807495i
$387$	2.26856	−	1.45792i	0.115317	−	0.0741100i
$388$	−6.41909	−	7.40802i	−0.325880	−	0.376085i
$389$	−15.4843	+	4.54660i	−0.785086	+	0.230522i	−0.649619	−	0.760260i	$-0.725072\pi$
$389$	−15.4843	+	4.54660i	−0.785086	+	0.230522i	−0.135467	+	0.990782i	$0.543253\pi$
$390$		0			0
$391$	0.363175	+	7.07620i	0.0183666	+	0.357859i
$392$	14.1572			0.715047
$393$	−16.9713	+	4.98322i	−0.856088	+	0.251370i
$394$	16.8060	+	19.3951i	0.846673	+	0.977113i
$395$		0			0
$396$	−0.119768	−	0.833007i	−0.00601858	−	0.0418602i
$397$	−6.82699	−	4.38744i	−0.342637	−	0.220199i	0.357993	−	0.933724i	$-0.383461\pi$
$397$	−6.82699	−	4.38744i	−0.342637	−	0.220199i	−0.700630	+	0.713525i	$0.747097\pi$
$398$	−0.702631	+	1.53855i	−0.0352197	+	0.0771204i
$399$	−12.0734	+	13.9335i	−0.604427	+	0.697546i
$400$		0			0
$401$	11.1440	+	24.4020i	0.556506	+	1.21858i	0.953677	+	0.300833i	$0.0972646\pi$
$401$	11.1440	+	24.4020i	0.556506	+	1.21858i	−0.397171	+	0.917744i	$0.630008\pi$
$402$	−6.44947	−	1.89373i	−0.321670	−	0.0944509i
$403$	−5.54390	−	1.62784i	−0.276161	−	0.0810883i
$404$	4.40575	+	9.64724i	0.219194	+	0.479968i
$405$		0			0
$406$	3.08122	−	3.55591i	0.152918	−	0.176477i
$407$	−11.1182	+	24.3454i	−0.551108	+	1.20676i
$408$	−6.30216	−	4.05015i	−0.312003	−	0.200512i
$409$	−5.50570	−	38.2930i	−0.272239	−	1.89347i	−0.424984	−	0.905201i	$-0.639720\pi$
$409$	−5.50570	−	38.2930i	−0.272239	−	1.89347i	0.152744	−	0.988266i	$-0.451189\pi$
$410$		0			0
$411$	−7.10486	−	8.19944i	−0.350457	−	0.404449i
$412$	6.99084	−	2.05270i	0.344414	−	0.101129i
$413$	5.33204			0.262373
$414$	1.12999	−	1.08540i	0.0555357	−	0.0533446i
$415$		0			0
$416$	21.4017	−	6.28412i	1.04931	−	0.308104i
$417$	3.23308	+	3.73118i	0.158325	+	0.182717i
$418$	−28.8955	+	18.5700i	−1.41332	+	0.908288i
$419$	−0.00995759	−	0.0692566i	−0.000486460	−	0.00338340i	0.989577	−	0.144006i	$-0.0459986\pi$
$419$	−0.00995759	−	0.0692566i	−0.000486460	−	0.00338340i	−0.990063	+	0.140623i	$0.955089\pi$
$420$		0			0
$421$	−10.6053	+	23.2223i	−0.516869	+	1.13179i	0.453742	+	0.891133i	$0.350089\pi$
$421$	−10.6053	+	23.2223i	−0.516869	+	1.13179i	−0.970611	+	0.240653i	$0.922639\pi$
$422$	−9.23303	+	10.6555i	−0.449457	+	0.518701i
$423$	−0.123692	+	0.860297i	−0.00601412	+	0.0418291i
$424$	2.68719	+	5.88412i	0.130501	+	0.285758i
$425$		0			0
$426$	11.8515	+	3.47992i	0.574208	+	0.168603i
$427$	1.58435	+	3.46925i	0.0766722	+	0.167889i
$428$	−1.27749	+	8.88513i	−0.0617498	+	0.429479i
$429$	−26.6856	+	30.7968i	−1.28839	+	1.48688i
$430$		0			0
$431$	−1.50664	−	0.968256i	−0.0725721	−	0.0466392i	0.503852	−	0.863790i	$-0.331916\pi$
$431$	−1.50664	−	0.968256i	−0.0725721	−	0.0466392i	−0.576424	+	0.817151i	$0.695552\pi$
$432$	1.61853	+	11.2571i	0.0778715	+	0.541608i
$433$	12.6245	−	8.11329i	0.606696	−	0.389900i	−0.200921	−	0.979607i	$-0.564393\pi$
$433$	12.6245	−	8.11329i	0.606696	−	0.389900i	0.807617	+	0.589708i	$0.200757\pi$
$434$	1.12691	+	1.30053i	0.0540935	+	0.0624273i
$435$		0			0
$436$	−10.3894			−0.497564
$437$	32.2081	+	12.7569i	1.54072	+	0.610245i
$438$	−16.5797			−0.792208
$439$	−0.281430	+	0.0826353i	−0.0134319	+	0.00394397i	−0.288442	−	0.957497i	$-0.593137\pi$
$439$	−0.281430	+	0.0826353i	−0.0134319	+	0.00394397i	0.275010	+	0.961441i	$0.411319\pi$
$440$		0			0
$441$	1.10977	−	0.713207i	0.0528462	−	0.0339622i
$442$	−1.41910	−	9.87008i	−0.0674998	−	0.469472i
$443$	14.6283	+	9.40101i	0.695010	+	0.446656i	0.839864	−	0.542797i	$-0.182635\pi$
$443$	14.6283	+	9.40101i	0.695010	+	0.446656i	−0.144854	+	0.989453i	$0.546271\pi$
$444$	−3.08265	+	6.75007i	−0.146296	+	0.320344i
$445$		0			0
$446$	−0.905454	+	6.29757i	−0.0428745	+	0.298198i
$447$	−3.12592	−	6.84481i	−0.147851	−	0.323749i
$448$	−12.6204	−	3.70568i	−0.596258	−	0.175077i
$449$	25.0112	+	7.34396i	1.18035	+	0.346583i	0.812310	−	0.583226i	$-0.198210\pi$
$449$	25.0112	+	7.34396i	1.18035	+	0.346583i	0.368042	+	0.929809i	$0.380028\pi$
$450$		0			0
$451$	−1.81193	+	12.6022i	−0.0853204	+	0.593417i
$452$	0.553655	−	0.638952i	0.0260417	−	0.0300538i
$453$	−7.45327	+	16.3204i	−0.350185	+	0.766798i
$454$	−0.303288	−	0.194911i	−0.0142340	−	0.00914764i
$455$		0			0
$456$	−30.8125	+	19.8020i	−1.44293	+	0.927312i
$457$	−7.22935	−	8.34312i	−0.338175	−	0.390274i	0.561035	−	0.827792i	$-0.310403\pi$
$457$	−7.22935	−	8.34312i	−0.338175	−	0.390274i	−0.899210	+	0.437518i	$0.855858\pi$
$458$	−12.9954	+	3.81579i	−0.607235	+	0.178300i
$459$	−7.99878			−0.373351
$460$		0			0
$461$	8.98684			0.418559			0.209279	−	0.977856i	$-0.432888\pi$
$461$	8.98684			0.418559			0.209279	+	0.977856i	$0.432888\pi$
$462$	11.6449	−	3.41926i	0.541771	−	0.159078i
$463$	20.3749	+	23.5138i	0.946900	+	1.09278i	0.995575	+	0.0939666i	$0.0299547\pi$
$463$	20.3749	+	23.5138i	0.946900	+	1.09278i	−0.0486750	+	0.998815i	$0.515500\pi$
$464$	4.71132	−	3.02778i	0.218717	−	0.140561i
$465$		0			0
$466$	27.3376	+	17.5688i	1.26639	+	0.813861i
$467$	−8.97557	+	19.6538i	−0.415340	+	0.909468i	0.580142	+	0.814515i	$0.302997\pi$
$467$	−8.97557	+	19.6538i	−0.415340	+	0.909468i	−0.995482	+	0.0949522i	$0.969730\pi$
$468$	0.782237	−	0.902750i	0.0361589	−	0.0417296i
$469$	0.790100	−	5.49527i	0.0364834	−	0.253748i
$470$		0			0
$471$	17.8470	+	5.24036i	0.822348	+	0.241463i
$472$	10.1637	+	2.98435i	0.467824	+	0.137366i
$473$	−16.3044	−	35.7017i	−0.749678	−	1.64157i
$474$	−1.62614	+	11.3100i	−0.0746910	+	0.519488i
$475$		0			0
$476$	0.668326	−	1.46343i	0.0306327	−	0.0670762i
$477$	0.507075	+	0.325877i	0.0232173	+	0.0149209i
$478$	3.01732	+	20.9860i	0.138009	+	0.959875i
$479$	32.8334	−	21.1007i	1.50019	−	0.964117i	0.505328	−	0.862928i	$-0.331372\pi$
$479$	32.8334	−	21.1007i	1.50019	−	0.964117i	0.994867	−	0.101189i	$-0.0322647\pi$
$480$		0			0
$481$	−36.4495	+	10.7025i	−1.66195	+	0.487994i
$482$	30.6463			1.39590
$483$	−9.64948	−	7.53115i	−0.439067	−	0.342679i
$484$	−4.51852			−0.205387
$485$		0			0
$486$	2.21553	+	2.55686i	0.100499	+	0.115981i
$487$	17.1454	−	11.0187i	0.776930	−	0.499303i	−0.0910833	−	0.995843i	$-0.529033\pi$
$487$	17.1454	−	11.0187i	0.776930	−	0.499303i	0.868014	+	0.496541i	$0.165397\pi$
$488$	1.07830	+	7.49971i	0.0488122	+	0.339496i
$489$	11.4820	+	7.37902i	0.519233	+	0.333691i
$490$		0			0
$491$	11.2576	−	12.9920i	0.508050	−	0.586321i	−0.442548	−	0.896745i	$-0.645926\pi$
$491$	11.2576	−	12.9920i	0.508050	−	0.586321i	0.950598	+	0.310424i	$0.100471\pi$
$492$	−0.502379	+	3.49413i	−0.0226490	+	0.157527i
$493$	1.63626	+	3.58290i	0.0736933	+	0.161366i
$494$	−46.7781	−	13.7353i	−2.10465	−	0.617980i
$495$		0			0
$496$	0.850875	+	1.86316i	0.0382054	+	0.0836582i
$497$	−1.45189	+	10.0981i	−0.0651260	+	0.452961i
$498$	5.59920	−	6.46182i	0.250906	−	0.289561i
$499$	−4.07726	+	8.92796i	−0.182523	+	0.399670i	−0.978672	−	0.205431i	$-0.934140\pi$
$499$	−4.07726	+	8.92796i	−0.182523	+	0.399670i	0.796148	+	0.605102i	$0.206868\pi$
$500$		0			0
$501$	−5.71963	−	39.7809i	−0.255534	−	1.77728i
$502$	−11.5639	+	7.43164i	−0.516120	+	0.331690i
$503$	5.89248	+	6.80028i	0.262733	+	0.303210i	0.871754	−	0.489944i	$-0.162983\pi$
$503$	5.89248	+	6.80028i	0.262733	+	0.303210i	−0.609021	+	0.793154i	$0.708438\pi$
$504$	−1.31282	+	0.385479i	−0.0584777	+	0.0171706i
$505$		0			0
$506$	−13.2962	−	18.5273i	−0.591088	−	0.823638i
$507$	−36.4264			−1.61775
$508$	2.32662	−	0.683157i	0.103227	−	0.0303102i
$509$	23.1725	+	26.7425i	1.02710	+	1.18534i	0.982486	+	0.186334i	$0.0596608\pi$
$509$	23.1725	+	26.7425i	1.02710	+	1.18534i	0.0446155	+	0.999004i	$0.485794\pi$
$510$		0			0
$511$	−1.94884	−	13.5545i	−0.0862116	−	0.599615i
$512$	−17.5319	−	11.2670i	−0.774806	−	0.497938i
$513$	−16.2459	+	35.5735i	−0.717273	+	1.57061i
$514$	−5.02405	+	5.79807i	−0.221602	+	0.255742i
$515$		0			0
$516$	−4.52060	−	9.89873i	−0.199008	−	0.435767i
$517$	12.1376	+	3.56392i	0.533811	+	0.156741i
$518$	10.8557	+	3.18753i	0.476974	+	0.140052i
$519$	−7.34971	−	16.0936i	−0.322617	−	0.706432i
$520$		0			0
$521$	1.01673	−	1.17337i	0.0445439	−	0.0514064i	−0.733040	−	0.680185i	$-0.761899\pi$
$521$	1.01673	−	1.17337i	0.0445439	−	0.0514064i	0.777584	+	0.628779i	$0.216445\pi$
$522$	0.361828	−	0.792293i	0.0158368	−	0.0346777i
$523$	14.7917	+	9.50603i	0.646794	+	0.415670i	0.822494	−	0.568774i	$-0.192582\pi$
$523$	14.7917	+	9.50603i	0.646794	+	0.415670i	−0.175699	+	0.984444i	$0.556219\pi$
$524$	−1.07395	−	7.46950i	−0.0469158	−	0.326307i
$525$		0			0
$526$	−12.7167	−	14.6759i	−0.554474	−	0.639898i
$527$	−1.38223	+	0.405858i	−0.0602107	+	0.0176795i
$528$	14.4457			0.628667
$529$	−7.36245	+	21.7898i	−0.320107	+	0.947382i
$530$		0			0
$531$	0.947071	−	0.278085i	0.0410994	−	0.0120679i
$532$	−5.15101	−	5.94458i	−0.223324	−	0.257730i
$533$	−15.2025	+	9.77007i	−0.658495	+	0.423189i
$534$	2.33949	+	16.2715i	0.101240	+	0.704136i
$535$		0			0
$536$	4.58176	−	10.0327i	0.197902	−	0.433345i
$537$	−9.90746	+	11.4338i	−0.427538	+	0.493406i
$538$	−2.18557	+	15.2009i	−0.0942264	+	0.655359i
$539$	−7.97606	−	17.4651i	−0.343553	−	0.752276i
$540$		0			0
$541$	−33.3293	−	9.78638i	−1.43294	−	0.420749i	−0.529078	−	0.848573i	$-0.677462\pi$
$541$	−33.3293	−	9.78638i	−1.43294	−	0.420749i	−0.903862	+	0.427824i	$0.859280\pi$
$542$	8.69254	+	19.0340i	0.373376	+	0.817580i
$543$	−4.51237	+	31.3842i	−0.193644	+	1.34683i
$544$	3.64183	−	4.20290i	0.156142	−	0.180198i
$545$		0			0
$546$	14.4917	+	9.31326i	0.620188	+	0.398571i
$547$	3.98753	+	27.7339i	0.170495	+	1.18582i	0.877842	+	0.478950i	$0.158983\pi$
$547$	3.98753	+	27.7339i	0.170495	+	1.18582i	−0.707347	+	0.706866i	$0.750108\pi$
$548$	3.89399	−	2.50252i	0.166343	−	0.106902i
$549$	0.462344	+	0.533574i	0.0197324	+	0.0227724i
$550$		0			0
$551$	19.2578			0.820409
$552$	−14.1783	−	19.7564i	−0.603469	−	0.840890i
$553$	−9.43751			−0.401324
$554$	−24.1018	+	7.07694i	−1.02399	+	0.300670i
$555$		0			0
$556$	−1.77197	+	1.13878i	−0.0751484	+	0.0482949i
$557$	−0.0693439	−	0.482297i	−0.00293820	−	0.0204356i	0.988300	−	0.152525i	$-0.0487405\pi$
$557$	−0.0693439	−	0.482297i	−0.00293820	−	0.0204356i	−0.991238	+	0.132089i	$0.957831\pi$
$558$	0.267988	+	0.172225i	0.0113448	+	0.00729088i
$559$	23.1421	−	50.6742i	0.978808	−	2.14329i
$560$		0			0
$561$	−1.44591	+	10.0565i	−0.0610463	+	0.424587i
$562$	−1.58741	−	3.47594i	−0.0669608	−	0.146624i
$563$	37.4866	+	11.0071i	1.57987	+	0.463892i	0.949856	−	0.312689i	$-0.101230\pi$
$563$	37.4866	+	11.0071i	1.57987	+	0.463892i	0.630017	+	0.776581i	$0.283048\pi$
$564$	3.36530	+	0.988141i	0.141705	+	0.0416082i
$565$		0			0
$566$	−1.52011	+	10.5726i	−0.0638952	+	0.444401i
$567$	8.17583	−	9.43541i	0.343353	−	0.396250i
$568$	−8.41943	+	18.4360i	−0.353272	+	0.773557i
$569$	−29.2483	−	18.7968i	−1.22615	−	0.788001i	−0.242866	−	0.970060i	$-0.578088\pi$
$569$	−29.2483	−	18.7968i	−1.22615	−	0.788001i	−0.983288	+	0.182059i	$0.941724\pi$
$570$		0			0
$571$	23.1655	−	14.8876i	0.969448	−	0.623026i	0.0428504	−	0.999082i	$-0.486356\pi$
$571$	23.1655	−	14.8876i	0.969448	−	0.623026i	0.926597	+	0.376055i	$0.122720\pi$
$572$	−11.3851	−	13.1391i	−0.476036	−	0.549375i
$573$	−1.97767	+	0.580696i	−0.0826183	+	0.0242589i
$574$	5.38216			0.224647
$575$		0			0
$576$	−2.43488			−0.101454
$577$	−32.3598	+	9.50169i	−1.34716	+	0.395561i	−0.874217	−	0.485535i	$-0.838625\pi$
$577$	−32.3598	+	9.50169i	−1.34716	+	0.395561i	−0.472938	+	0.881096i	$0.656807\pi$
$578$	11.0517	+	12.7543i	0.459688	+	0.530508i
$579$	19.4997	−	12.5317i	0.810381	−	0.520800i
$580$		0			0
$581$	5.94092	+	3.81800i	0.246471	+	0.158397i
$582$	10.8707	−	23.8035i	0.450605	−	0.986686i
$583$	5.74504	−	6.63014i	0.237935	−	0.274592i
$584$	3.87164	−	26.9278i	0.160209	−	1.11428i
$585$		0			0
$586$	4.44549	+	1.30532i	0.183642	+	0.0539221i
$587$	−7.08767	−	2.08113i	−0.292540	−	0.0858974i	0.132170	−	0.991227i	$-0.457806\pi$
$587$	−7.08767	−	2.08113i	−0.292540	−	0.0858974i	−0.424709	+	0.905330i	$0.639624\pi$
$588$	−2.21146	−	4.84242i	−0.0911990	−	0.199698i
$589$	−1.00236	+	6.97158i	−0.0413016	+	0.287259i
$590$		0			0
$591$	15.4178	−	33.7603i	0.634203	−	1.38871i
$592$	11.3289	+	7.28062i	0.465614	+	0.299232i
$593$	−3.68749	−	25.6470i	−0.151427	−	1.05320i	−0.913831	−	0.406095i	$-0.866890\pi$
$593$	−3.68749	−	25.6470i	−0.151427	−	1.05320i	0.762404	−	0.647102i	$-0.224019\pi$
$594$	21.6572	−	13.9182i	0.888605	−	0.571071i
$595$		0			0
$596$	3.08035	−	0.904471i	0.126176	−	0.0370486i
$597$	2.44608			0.100111
$598$	7.51535	−	31.4838i	0.307326	−	1.28747i
$599$	39.7801			1.62537			0.812686	−	0.582702i	$-0.198004\pi$
$599$	39.7801			1.62537			0.812686	+	0.582702i	$0.198004\pi$
$600$		0			0
$601$	−19.8051	−	22.8563i	−0.807865	−	0.932326i	0.190920	−	0.981606i	$-0.438853\pi$
$601$	−19.8051	−	22.8563i	−0.807865	−	0.932326i	−0.998785	+	0.0492793i	$0.984308\pi$
$602$	−13.9578	+	8.97011i	−0.568876	+	0.365594i
$603$	−0.146261	−	1.01727i	−0.00595622	−	0.0414264i
$604$	−6.43952	−	4.13843i	−0.262020	−	0.168390i
$605$		0			0
$606$	−18.5411	+	21.3976i	−0.753183	+	0.869219i
$607$	2.74002	−	19.0572i	0.111214	−	0.773509i	−0.855528	−	0.517756i	$-0.826767\pi$
$607$	2.74002	−	19.0572i	0.111214	−	0.773509i	0.966742	−	0.255753i	$-0.0823235\pi$
$608$	−11.2951	−	24.7328i	−0.458077	−	1.00305i
$609$	−6.52890	−	1.91706i	−0.264564	−	0.0776831i
$610$		0			0
$611$	7.45884	+	16.3326i	0.301752	+	0.660746i
$612$	0.0423841	−	0.294788i	0.00171328	−	0.0119161i
$613$	−14.3261	+	16.5332i	−0.578626	+	0.667770i	−0.967309	−	0.253602i	$-0.918385\pi$
$613$	−14.3261	+	16.5332i	−0.578626	+	0.667770i	0.388683	+	0.921372i	$0.372930\pi$
$614$	8.18713	−	17.9273i	0.330406	−	0.723488i
$615$		0			0
$616$	2.83409	+	19.7115i	0.114189	+	0.794200i
$617$	4.36367	−	2.80436i	0.175675	−	0.112899i	−0.449848	−	0.893105i	$-0.648522\pi$
$617$	4.36367	−	2.80436i	0.175675	−	0.112899i	0.625523	+	0.780206i	$0.284886\pi$
$618$	12.7376	+	14.7000i	0.512381	+	0.591319i
$619$	−42.6842	+	12.5332i	−1.71562	+	0.503752i	−0.984032	−	0.177993i	$-0.943040\pi$
$619$	−42.6842	+	12.5332i	−1.71562	+	0.503752i	−0.731590	+	0.681745i	$0.761221\pi$
$620$		0			0
$621$	−24.1400	−	9.56130i	−0.968704	−	0.383682i
$622$	−7.12078			−0.285517
$623$	−13.0275	+	3.82523i	−0.521937	+	0.153255i
$624$	13.4272	+	15.4958i	0.537517	+	0.620327i
$625$		0			0
$626$	2.47120	+	17.1876i	0.0987691	+	0.686954i
$627$	41.7883	+	26.8557i	1.66886	+	1.07251i
$628$	−3.29662	+	7.21858i	−0.131549	+	0.288053i
$629$	−6.20243	+	7.15799i	−0.247307	+	0.285408i
$630$		0			0
$631$	−0.390162	−	0.854336i	−0.0155321	−	0.0340106i	0.901707	−	0.432348i	$-0.142315\pi$
$631$	−0.390162	−	0.854336i	−0.0155321	−	0.0340106i	−0.917239	+	0.398337i	$0.869587\pi$
$632$	−17.9894	−	5.28217i	−0.715581	−	0.210114i
$633$	19.5642	+	5.74457i	0.777607	+	0.228326i
$634$	8.27972	+	18.1301i	0.328830	+	0.720036i
$635$		0			0
$636$	1.59288	−	1.83829i	0.0631619	−	0.0728928i
$637$	11.3210	−	24.7896i	0.448556	−	0.982200i
$638$	−10.6647	−	6.85376i	−0.422218	−	0.271343i
$639$	0.268769	+	1.86933i	0.0106323	+	0.0739496i
$640$		0			0
$641$	−0.287210	−	0.331458i	−0.0113441	−	0.0130918i	0.750049	−	0.661382i	$-0.230030\pi$
$641$	−0.287210	−	0.331458i	−0.0113441	−	0.0130918i	−0.761393	+	0.648290i	$0.775484\pi$
$642$	−22.9932	+	6.75141i	−0.907469	+	0.266457i
$643$	−30.1871			−1.19046			−0.595232	−	0.803554i	$-0.702940\pi$
$643$	−30.1871			−1.19046			−0.595232	+	0.803554i	$0.702940\pi$
$644$	3.76628	−	3.61768i	0.148412	−	0.142557i
$645$		0			0
$646$	−11.6629	+	3.42453i	−0.458870	+	0.134736i
$647$	15.8888	+	18.3366i	0.624651	+	0.720886i	0.976583	−	0.215139i	$-0.0690206\pi$
$647$	15.8888	+	18.3366i	0.624651	+	0.720886i	−0.351932	+	0.936026i	$0.614475\pi$
$648$	20.8655	−	13.4094i	0.819673	−	0.526772i
$649$	−2.04452	−	14.2199i	−0.0802543	−	0.558181i
$650$		0			0
$651$	1.03383	−	2.26377i	0.0405189	−	0.0887241i
$652$	−3.81330	+	4.40078i	−0.149340	+	0.172348i
$653$	1.27345	−	8.85705i	0.0498340	−	0.346603i	−0.949615	−	0.313418i	$-0.898526\pi$
$653$	1.27345	−	8.85705i	0.0498340	−	0.346603i	0.999449	−	0.0331850i	$-0.0105650\pi$
$654$	−11.5219	−	25.2295i	−0.450542	−	0.986550i
$655$		0			0
$656$	6.14668	+	1.80483i	0.239988	+	0.0704667i
$657$	−1.05307	−	2.30589i	−0.0410840	−	0.0899614i
$658$	0.761039	−	5.29314i	0.0296684	−	0.206348i
$659$	−10.3891	+	11.9896i	−0.404700	+	0.467049i	−0.921115	−	0.389289i	$-0.872721\pi$
$659$	−10.3891	+	11.9896i	−0.404700	+	0.467049i	0.516415	+	0.856338i	$0.327266\pi$
$660$		0			0
$661$	11.6197	+	7.46752i	0.451954	+	0.290453i	0.746747	−	0.665108i	$-0.231615\pi$
$661$	11.6197	+	7.46752i	0.451954	+	0.290453i	−0.294794	+	0.955561i	$0.595251\pi$
$662$	−4.26186	−	29.6419i	−0.165642	−	1.15206i
$663$	−12.1315	+	7.79646i	−0.471150	+	0.302790i
$664$	9.18743	+	10.6029i	0.356541	+	0.411471i
$665$		0			0
$666$	2.09442			0.0811573
$667$	0.655346	+	12.7689i	0.0253751	+	0.494415i
$668$	17.1467			0.663424
$669$	8.82842	−	2.59226i	0.341326	−	0.100222i
$670$		0			0
$671$	8.64456	−	5.55552i	0.333720	−	0.214469i
$672$	1.36726	+	9.50948i	0.0527431	+	0.366836i
$673$	−6.84303	−	4.39775i	−0.263779	−	0.169521i	0.402065	−	0.915611i	$-0.368292\pi$
$673$	−6.84303	−	4.39775i	−0.263779	−	0.169521i	−0.665845	+	0.746090i	$0.731929\pi$
$674$	−2.34969	+	5.14510i	−0.0905066	+	0.198182i
$675$		0			0
$676$	2.21171	−	15.3828i	0.0850659	−	0.591646i
$677$	10.7664	+	23.5751i	0.413785	+	0.906063i	0.995685	+	0.0928023i	$0.0295825\pi$
$677$	10.7664	+	23.5751i	0.413785	+	0.906063i	−0.581899	+	0.813261i	$0.697690\pi$
$678$	2.16562	+	0.635884i	0.0831702	+	0.0244210i
$679$	20.7380	+	6.08922i	0.795851	+	0.233683i
$680$		0			0
$681$	−0.0741999	+	0.516072i	−0.00284335	+	0.0197759i
$682$	3.03625	−	3.50401i	0.116264	−	0.134176i
$683$	−16.8250	+	36.8417i	−0.643792	+	1.40971i	0.253091	+	0.967442i	$0.418553\pi$
$683$	−16.8250	+	36.8417i	−0.643792	+	1.40971i	−0.896884	+	0.442266i	$0.854175\pi$
$684$	−1.22495	−	0.787225i	−0.0468370	−	0.0301003i
$685$		0			0
$686$	−17.2210	+	11.0672i	−0.657500	+	0.422550i
$687$	12.8269	+	14.8030i	0.489377	+	0.564771i
$688$	−18.9484	+	5.56376i	−0.722402	+	0.212116i
$689$	12.4521			0.474387
$690$		0			0
$691$	25.6167			0.974504			0.487252	−	0.873261i	$-0.337999\pi$
$691$	25.6167			0.974504			0.487252	+	0.873261i	$0.337999\pi$
$692$	7.24256	−	2.12661i	0.275321	−	0.0808414i
$693$	1.21518	+	1.40239i	0.0461609	+	0.0532725i
$694$	−12.6265	+	8.11456i	−0.479296	+	0.308025i
$695$		0			0
$696$	−11.3722	−	7.30845i	−0.431061	−	0.277026i
$697$	−1.87169	+	4.09844i	−0.0708954	+	0.155239i
$698$	−1.36909	+	1.58001i	−0.0518208	+	0.0598044i
$699$	6.68820	−	46.5175i	0.252971	−	1.75945i
$700$		0			0
$701$	−17.6347	−	5.17801i	−0.666053	−	0.195571i	−0.0688083	−	0.997630i	$-0.521920\pi$
$701$	−17.6347	−	5.17801i	−0.666053	−	0.195571i	−0.597245	+	0.802059i	$0.703738\pi$
$702$	35.0602	+	10.2946i	1.32326	+	0.388545i
$703$	19.2368	+	42.1227i	0.725529	+	1.58869i
$704$	−5.04346	+	35.0780i	−0.190082	+	1.32205i
$705$		0			0
$706$	15.1125	−	33.0918i	0.568767	−	1.24543i
$707$	−19.6727	−	12.6429i	−0.739869	−	0.475485i
$708$	−0.566867	−	3.94265i	−0.0213042	−	0.148174i
$709$	−28.3837	+	18.2411i	−1.06597	+	0.685058i	−0.951275	−	0.308342i	$-0.900226\pi$
$709$	−28.3837	+	18.2411i	−1.06597	+	0.685058i	−0.114696	+	0.993401i	$0.536589\pi$
$710$		0			0
$711$	−1.67628	+	0.492200i	−0.0628654	+	0.0184589i
$712$	−26.9736			−1.01088
$713$	−4.65663	−	0.427374i	−0.174392	−	0.0160053i
$714$	4.29493			0.160734
$715$		0			0
$716$	−4.22692	−	4.87813i	−0.157967	−	0.182304i
$717$	25.7943	−	16.5770i	0.963306	−	0.619079i
$718$	−3.53904	−	24.6146i	−0.132076	−	0.918608i
$719$	11.6164	+	7.46538i	0.433217	+	0.278412i	0.739020	−	0.673683i	$-0.235289\pi$
$719$	11.6164	+	7.46538i	0.433217	+	0.278412i	−0.305803	+	0.952095i	$0.598925\pi$
$720$		0			0
$721$	−10.5205	+	12.1413i	−0.391804	+	0.452166i
$722$	−5.37793	+	37.4043i	−0.200146	+	1.39205i
$723$	−18.4114	−	40.3153i	−0.684726	−	1.49934i
$724$	−12.9795	−	3.81113i	−0.482380	−	0.141639i
$725$		0			0
$726$	−5.01105	−	10.9727i	−0.185977	−	0.407234i
$727$	0.0793427	−	0.551840i	0.00294266	−	0.0204666i	−0.988297	−	0.152541i	$-0.951255\pi$
$727$	0.0793427	−	0.551840i	0.00294266	−	0.0204666i	0.991240	+	0.132074i	$0.0421636\pi$
$728$	−18.5102	+	21.3619i	−0.686032	+	0.791723i
$729$	12.0738	−	26.4378i	0.447176	−	0.979179i
$730$		0			0
$731$	−1.97667	−	13.7481i	−0.0731099	−	0.508490i
$732$	2.39681	−	1.54034i	0.0885886	−	0.0569325i
$733$	−17.2480	−	19.9053i	−0.637070	−	0.735218i	0.341784	−	0.939779i	$-0.388969\pi$
$733$	−17.2480	−	19.9053i	−0.637070	−	0.735218i	−0.978854	+	0.204560i	$0.934424\pi$
$734$	5.12735	−	1.50552i	0.189254	−	0.0555699i
$735$		0			0
$736$	16.0148	−	8.33091i	0.590313	−	0.307081i
$737$	−14.9582			−0.550991
$738$	0.955973	−	0.280699i	0.0351899	−	0.0103327i
$739$	17.1655	+	19.8101i	0.631444	+	0.728725i	0.977838	−	0.209364i	$-0.0671394\pi$
$739$	17.1655	+	19.8101i	0.631444	+	0.728725i	−0.346394	+	0.938089i	$0.612594\pi$
$740$		0			0
$741$	10.0340	+	69.7883i	0.368610	+	2.56374i
$742$	−3.11987	−	2.00502i	−0.114534	−	0.0736066i
$743$	17.0201	−	37.2688i	0.624407	−	1.36726i	−0.287863	−	0.957672i	$-0.592945\pi$
$743$	17.0201	−	37.2688i	0.624407	−	1.36726i	0.912270	−	0.409589i	$-0.134328\pi$
$744$	3.23768	−	3.73648i	0.118699	−	0.136986i
$745$		0			0
$746$	−3.42719	−	7.50450i	−0.125478	−	0.274759i
$747$	1.25434	+	0.368308i	0.0458939	+	0.0134757i
$748$	−4.15905	−	1.22121i	−0.152070	−	0.0446518i
$749$	−8.22223	−	18.0042i	−0.300434	−	0.657858i
$750$		0			0
$751$	−7.01809	+	8.09931i	−0.256094	+	0.295548i	−0.869208	−	0.494446i	$-0.835371\pi$
$751$	−7.01809	+	8.09931i	−0.256094	+	0.295548i	0.613115	+	0.789994i	$0.289916\pi$
$752$	2.64412	−	5.78982i	0.0964212	−	0.211133i
$753$	16.7235	+	10.7476i	0.609439	+	0.391663i
$754$	−2.56075	−	17.8104i	−0.0932572	−	0.648618i
$755$		0			0
$756$	3.86068	+	4.45546i	0.140412	+	0.162044i
$757$	28.7797	−	8.45047i	1.04601	−	0.307138i	0.286808	−	0.957988i	$-0.407406\pi$
$757$	28.7797	−	8.45047i	1.04601	−	0.307138i	0.759206	+	0.650850i	$0.225587\pi$
$758$	18.5475			0.673675
$759$	−16.3847	+	28.6218i	−0.594727	+	1.03890i
$760$		0			0
$761$	5.62283	−	1.65101i	0.203827	−	0.0598491i	−0.178225	−	0.983990i	$-0.557036\pi$
$761$	5.62283	−	1.65101i	0.203827	−	0.0598491i	0.382052	+	0.924141i	$0.375217\pi$
$762$	4.23919	+	4.89229i	0.153570	+	0.177229i
$763$	19.2716	−	12.3851i	0.697680	−	0.448372i
$764$	−0.125148	−	0.870423i	−0.00452770	−	0.0314908i
$765$		0			0
$766$	−12.5726	+	27.5302i	−0.454268	+	0.994707i
$767$	13.3533	−	15.4105i	0.482158	−	0.556440i
$768$	−3.40834	+	23.7056i	−0.122988	+	0.855401i
$769$	5.99078	+	13.1180i	0.216033	+	0.473047i	0.986360	−	0.164603i	$-0.0526342\pi$
$769$	5.99078	+	13.1180i	0.216033	+	0.473047i	−0.770327	+	0.637649i	$0.779907\pi$
$770$		0			0
$771$	10.6457	+	3.12584i	0.383394	+	0.112575i
$772$	4.10815	+	8.99558i	0.147855	+	0.323758i
$773$	3.72952	−	25.9394i	0.134142	−	0.932976i	−0.805933	−	0.592007i	$-0.798336\pi$
$773$	3.72952	−	25.9394i	0.134142	−	0.932976i	0.940075	−	0.340969i	$-0.110755\pi$
$774$	−2.01134	+	2.32121i	−0.0722960	+	0.0834341i
$775$		0			0
$776$	36.1218	+	23.2141i	1.29670	+	0.833338i
$777$	−2.32859	−	16.1957i	−0.0835376	−	0.581017i
$778$	15.4628	−	9.93736i	0.554370	−	0.356272i
$779$	14.4258	+	16.6482i	0.516856	+	0.596484i
$780$		0			0
$781$	27.4871			0.983566
$782$	−2.66754	−	7.61657i	−0.0953909	−	0.272368i
$783$	−14.4337			−0.515819
$784$	−9.26949	+	2.72177i	−0.331053	+	0.0972060i
$785$		0			0
$786$	16.9478	−	10.8917i	0.604506	−	0.388493i
$787$	−3.55646	−	24.7357i	−0.126774	−	0.881734i	−0.949605	−	0.313448i	$-0.898516\pi$
$787$	−3.55646	−	24.7357i	−0.126774	−	0.881734i	0.822831	−	0.568286i	$-0.192393\pi$
$788$	13.3208	+	8.56073i	0.474532	+	0.304963i
$789$	−11.6663	+	25.5456i	−0.415331	+	0.909448i
$790$		0			0
$791$	−0.265302	+	1.84522i	−0.00943306	+	0.0656084i
$792$	1.53141	+	3.35333i	0.0544164	+	0.119155i
$793$	13.9944	+	4.10914i	0.496957	+	0.145920i
$794$	8.86862	+	2.60406i	0.314736	+	0.0924147i
$795$		0			0
$796$	−0.148519	+	1.03297i	−0.00526412	+	0.0366128i
$797$	−17.5579	+	20.2629i	−0.621932	+	0.717747i	−0.976073	−	0.217445i	$-0.930228\pi$
$797$	−17.5579	+	20.2629i	−0.621932	+	0.717747i	0.354141	+	0.935192i	$0.384773\pi$
$798$	8.72320	−	19.1011i	0.308798	−	0.676173i
$799$	3.76599	+	2.42026i	0.133231	+	0.0856226i
$800$		0			0
$801$	−2.11443	+	1.35886i	−0.0747099	+	0.0480131i
$802$	−20.0088	−	23.0914i	−0.706535	−	0.815385i
$803$	−35.4009	+	10.3946i	−1.24927	+	0.366819i
$804$	−4.14733			−0.146265
$805$		0			0
$806$	6.58091			0.231803
$807$	21.3099	−	6.25714i	0.750143	−	0.220262i
$808$	−30.4232	−	35.1102i	−1.07028	−	1.23517i
$809$	6.24527	−	4.01359i	0.219572	−	0.141110i	−0.426231	−	0.904614i	$-0.640159\pi$
$809$	6.24527	−	4.01359i	0.219572	−	0.141110i	0.645803	+	0.763504i	$0.276523\pi$
$810$		0			0
$811$	−0.537875	−	0.345671i	−0.0188874	−	0.0121382i	0.531163	−	0.847270i	$-0.321755\pi$
$811$	−0.537875	−	0.345671i	−0.0188874	−	0.0121382i	−0.550050	+	0.835131i	$0.685392\pi$
$812$	1.20599	−	2.64074i	0.0423218	−	0.0926719i
$813$	19.8170	−	22.8701i	0.695013	−	0.802088i
$814$	4.33825	−	30.1732i	0.152055	−	1.05757i
$815$		0			0
$816$	4.90502	+	1.44024i	0.171710	+	0.0504186i
$817$	−65.1574	−	19.1319i	−2.27957	−	0.669342i
$818$	18.3045	+	40.0812i	0.640000	+	1.40141i
$819$	−0.374835	+	2.60703i	−0.0130978	+	0.0910971i
$820$		0			0
$821$	−9.25485	+	20.2653i	−0.322997	+	0.707264i	−0.999576	−	0.0291056i	$-0.990734\pi$
$821$	−9.25485	+	20.2653i	−0.322997	+	0.707264i	0.676580	+	0.736369i	$0.263461\pi$
$822$	10.3955	+	6.68078i	0.362585	+	0.233019i
$823$	−7.15529	−	49.7661i	−0.249418	−	1.73474i	−0.601593	−	0.798803i	$-0.705467\pi$
$823$	−7.15529	−	49.7661i	−0.249418	−	1.73474i	0.352175	−	0.935934i	$-0.385442\pi$
$824$	−26.8493	+	17.2550i	−0.935340	+	0.601106i
$825$		0			0
$826$	−5.82704	+	1.71097i	−0.202749	+	0.0595323i
$827$	−4.49737			−0.156389			−0.0781944	−	0.996938i	$-0.524915\pi$
$827$	−4.49737			−0.156389			−0.0781944	+	0.996938i	$0.524915\pi$
$828$	0.480287	−	0.838994i	0.0166911	−	0.0291571i
$829$	30.5110			1.05969			0.529845	−	0.848094i	$-0.322250\pi$
$829$	30.5110			1.05969			0.529845	+	0.848094i	$0.322250\pi$
$830$		0			0
$831$	23.7893	+	27.4544i	0.825243	+	0.952381i
$832$	−42.3158	+	27.1947i	−1.46704	+	0.942808i
$833$	−0.966980	−	6.72550i	−0.0335039	−	0.233025i
$834$	−4.73050	−	3.04011i	−0.163804	−	0.105270i
$835$		0			0
$836$	−13.8784	+	16.0165i	−0.479994	+	0.553942i
$837$	0.751270	−	5.22520i	0.0259677	−	0.180609i
$838$	0.0331054	+	0.0724907i	0.00114361	+	0.00250415i
$839$	−38.0401	−	11.1696i	−1.31329	−	0.385616i	−0.451222	−	0.892412i	$-0.649012\pi$
$839$	−38.0401	−	11.1696i	−1.31329	−	0.385616i	−0.862066	+	0.506795i	$0.830830\pi$
$840$		0			0
$841$	−9.09443	−	19.9140i	−0.313601	−	0.686691i
$842$	4.13811	−	28.7812i	0.142609	−	0.991865i
$843$	−3.61893	+	4.17647i	−0.124643	+	0.143845i
$844$	−3.61380	+	7.91313i	−0.124392	+	0.272381i
$845$		0			0
$846$	−0.140882	−	0.979853i	−0.00484361	−	0.0336880i
$847$	8.38152	−	5.38648i	0.287993	−	0.185082i
$848$	−2.89069	−	3.33603i	−0.0992667	−	0.114560i
$849$	14.8215	−	4.35199i	0.508674	−	0.149360i
$850$		0			0
$851$	−27.2749	+	14.1884i	−0.934973	+	0.486374i
$852$	7.62113			0.261096
$853$	46.2530	−	13.5811i	1.58367	−	0.465008i	0.632729	−	0.774373i	$-0.281935\pi$
$853$	46.2530	−	13.5811i	1.58367	−	0.465008i	0.950943	+	0.309365i	$0.100117\pi$
$854$	−2.84466	−	3.28291i	−0.0973423	−	0.112339i
$855$		0			0
$856$	−5.59598	−	38.9209i	−0.191266	−	1.33029i
$857$	4.19686	+	2.69716i	0.143362	+	0.0921332i	0.610356	−	0.792128i	$-0.291027\pi$
$857$	4.19686	+	2.69716i	0.143362	+	0.0921332i	−0.466994	+	0.884261i	$0.654663\pi$
$858$	19.2807	−	42.2187i	0.658231	−	1.44132i
$859$	−17.9322	+	20.6949i	−0.611840	+	0.706101i	−0.974136	−	0.225962i	$-0.927447\pi$
$859$	−17.9322	+	20.6949i	−0.611840	+	0.706101i	0.362296	+	0.932063i	$0.381993\pi$
$860$		0			0
$861$	−3.23343	−	7.08023i	−0.110195	−	0.241294i
$862$	1.95720	+	0.574686i	0.0666625	+	0.0195739i
$863$	−20.6616	−	6.06681i	−0.703331	−	0.206516i	−0.0895375	−	0.995983i	$-0.528539\pi$
$863$	−20.6616	−	6.06681i	−0.703331	−	0.206516i	−0.613793	+	0.789467i	$0.710357\pi$
$864$	8.46568	+	18.5373i	0.288008	+	0.630650i
$865$		0			0
$866$	−11.1931	+	12.9175i	−0.380356	+	0.438954i
$867$	10.1388	−	22.2008i	0.344331	−	0.753979i
$868$	0.893213	+	0.574033i	0.0303176	+	0.0194840i
$869$	3.61871	+	25.1687i	0.122756	+	0.853790i
$870$		0			0
$871$	−13.9035	−	16.0455i	−0.471103	−	0.543682i
$872$	43.6669	−	12.8218i	1.47875	−	0.434199i
$873$	4.00103			0.135414
$874$	−39.2916	−	3.60608i	−1.32906	−	0.121978i
$875$		0			0
$876$	−9.81533	+	2.88204i	−0.331629	+	0.0973751i
$877$	2.10792	+	2.43267i	0.0711794	+	0.0821454i	0.790222	−	0.612820i	$-0.209965\pi$
$877$	2.10792	+	2.43267i	0.0711794	+	0.0821454i	−0.719043	+	0.694966i	$0.755420\pi$
$878$	0.281040	−	0.180613i	0.00948463	−	0.00609540i
$879$	−0.953572	−	6.63224i	−0.0321632	−	0.223700i
$880$		0			0
$881$	19.5428	−	42.7927i	0.658413	−	1.44172i	−0.225581	−	0.974224i	$-0.572428\pi$
$881$	19.5428	−	42.7927i	0.658413	−	1.44172i	0.883994	−	0.467499i	$-0.154845\pi$
$882$	−0.983938	+	1.13552i	−0.0331309	+	0.0382351i
$883$	1.00519	−	6.99127i	0.0338274	−	0.235275i	−0.965892	−	0.258944i	$-0.916626\pi$
$883$	1.00519	−	6.99127i	0.0338274	−	0.235275i	0.999720	+	0.0236687i	$0.00753468\pi$
$884$	−2.55584	−	5.59650i	−0.0859620	−	0.188231i
$885$		0			0
$886$	−19.0029	−	5.57975i	−0.638415	−	0.187456i
$887$	−1.96380	−	4.30012i	−0.0659379	−	0.144384i	0.873794	−	0.486297i	$-0.161653\pi$
$887$	−1.96380	−	4.30012i	−0.0659379	−	0.144384i	−0.939732	+	0.341913i	$0.888925\pi$
$888$	4.62606	−	32.1749i	0.155240	−	1.07972i
$889$	−3.50133	+	4.04075i	−0.117431	+	0.135522i
$890$		0			0
$891$	−28.2980	−	18.1860i	−0.948020	−	0.609256i
$892$	0.558667	+	3.88562i	0.0187056	+	0.130100i
$893$	18.4127	−	11.8331i	0.616157	−	0.395980i
$894$	5.61251	+	6.47718i	0.187710	+	0.216629i
$895$		0			0
$896$	3.31589			0.110776
$897$	−45.9319	+	9.02801i	−1.53362	+	0.301437i
$898$	−29.6897			−0.990757
$899$	−2.49421	+	0.732366i	−0.0831866	+	0.0244258i
$900$		0			0
$901$	2.61176	−	1.67847i	0.0870102	−	0.0559181i
$902$	−2.06373	−	14.3536i	−0.0687148	−	0.477922i
$903$	20.1856	+	12.9725i	0.671733	+	0.431697i
$904$	−1.53848	+	3.36880i	−0.0511690	+	0.112044i
$905$		0			0
$906$	2.90822	−	20.2271i	0.0966191	−	0.672001i
$907$	−8.07339	−	17.6783i	−0.268072	−	0.586997i	0.726945	−	0.686695i	$-0.240939\pi$
$907$	−8.07339	−	17.6783i	−0.268072	−	0.586997i	−0.995018	+	0.0996986i	$0.968212\pi$
$908$	−0.213431	−	0.0626689i	−0.00708294	−	0.00207974i
$909$	−4.15362	−	1.21961i	−0.137767	−	0.0404520i
$910$		0			0
$911$	−5.48351	+	38.1386i	−0.181677	+	1.26359i	0.671121	+	0.741348i	$0.265813\pi$
$911$	−5.48351	+	38.1386i	−0.181677	+	1.26359i	−0.852798	+	0.522241i	$0.825096\pi$
$912$	16.3676	−	18.8892i	0.541985	−	0.625484i
$913$	7.90416	−	17.3077i	0.261589	−	0.572801i
$914$	10.5777	+	6.79785i	0.349878	+	0.224853i
$915$		0			0
$916$	−7.03010	+	4.51797i	−0.232281	+	0.149278i
$917$	10.8964	+	12.5751i	0.359832	+	0.415268i
$918$	8.74134	−	2.56669i	0.288507	−	0.0847134i
$919$	41.5199			1.36961			0.684807	−	0.728725i	$-0.259887\pi$
$919$	41.5199			1.36961			0.684807	+	0.728725i	$0.259887\pi$
$920$		0			0
$921$	−28.5020			−0.939171
$922$	−9.82112	+	2.88374i	−0.323441	+	0.0949710i
$923$	25.5491	+	29.4852i	0.840959	+	0.970519i
$924$	6.29954	−	4.04847i	0.207240	−	0.133185i
$925$		0			0
$926$	−29.8116	−	19.1587i	−0.979669	−	0.629595i
$927$	−1.23543	+	2.70521i	−0.0405767	+	0.0888507i
$928$	6.57164	−	7.58407i	0.215725	−	0.248959i
$929$	−5.26352	+	36.6086i	−0.172690	+	1.20109i	0.700480	+	0.713672i	$0.252969\pi$
$929$	−5.26352	+	36.6086i	−0.172690	+	1.20109i	−0.873170	+	0.487415i	$0.837940\pi$
$930$		0			0
$931$	−31.8747	−	9.35926i	−1.04465	−	0.306737i
$932$	19.2381	+	5.64883i	0.630166	+	0.185033i
$933$	4.27794	+	9.36739i	0.140054	+	0.306674i
$934$	3.50221	−	24.3584i	0.114596	−	0.797032i
$935$		0			0
$936$	−2.17365	+	4.75964i	−0.0710481	+	0.155574i
$937$	−7.05782	−	4.53579i	−0.230569	−	0.148178i	0.420256	−	0.907406i	$-0.361940\pi$
$937$	−7.05782	−	4.53579i	−0.230569	−	0.148178i	−0.650825	+	0.759228i	$0.725577\pi$
$938$	0.899900	+	6.25894i	0.0293828	+	0.204362i
$939$	21.1256	−	13.5766i	0.689409	−	0.443057i
$940$		0			0
$941$	−2.33024	+	0.684221i	−0.0759638	+	0.0223050i	−0.319494	−	0.947588i	$-0.603513\pi$
$941$	−2.33024	+	0.684221i	−0.0759638	+	0.0223050i	0.243530	+	0.969893i	$0.421695\pi$
$942$	−21.1854			−0.690257
$943$	−10.5477	+	10.1316i	−0.343481	+	0.329930i
$944$	−7.22850			−0.235268
$945$		0			0
$946$	29.2742	+	33.7842i	0.951785	+	1.09842i
$947$	7.67410	−	4.93184i	0.249375	−	0.160263i	−0.409982	−	0.912094i	$-0.634465\pi$
$947$	7.67410	−	4.93184i	0.249375	−	0.160263i	0.659357	+	0.751830i	$0.270829\pi$
$948$	1.00333	+	6.97833i	0.0325867	+	0.226646i
$949$	−44.0552	−	28.3126i	−1.43009	−	0.919065i
$950$		0			0
$951$	18.8759	−	21.7839i	0.612093	−	0.706393i
$952$	−1.00294	+	6.97560i	−0.0325055	+	0.226080i
$953$	3.11281	+	6.81610i	0.100834	+	0.220795i	0.953325	−	0.301947i	$-0.0976365\pi$
$953$	3.11281	+	6.81610i	0.100834	+	0.220795i	−0.852491	+	0.522742i	$0.824909\pi$
$954$	−0.658717	−	0.193417i	−0.0213268	−	0.00626210i
$955$		0			0
$956$	5.43427	+	11.8994i	0.175757	+	0.384854i
$957$	−2.60913	+	18.1469i	−0.0843411	+	0.586605i
$958$	−29.1105	+	33.5953i	−0.940518	+	1.08542i
$959$	−4.23985	+	9.28398i	−0.136912	+	0.299795i
$960$		0			0
$961$	4.27646	+	29.7434i	0.137950	+	0.959465i
$962$	36.3989	−	23.3922i	1.17355	−	0.754194i
$963$	−2.39940	−	2.76906i	−0.0773197	−	0.0892317i
$964$	18.1429	−	5.32724i	0.584344	−	0.171579i
$965$		0			0
$966$	12.9619	+	5.13393i	0.417043	+	0.165181i
$967$	−23.9003			−0.768580			−0.384290	−	0.923212i	$-0.625554\pi$
$967$	−23.9003			−0.768580			−0.384290	+	0.923212i	$0.625554\pi$
$968$	18.9914	−	5.57637i	0.610406	−	0.179231i
$969$	11.5117	+	13.2852i	0.369808	+	0.426781i
$970$		0			0
$971$	−6.15950	−	42.8403i	−0.197668	−	1.37481i	−0.811028	−	0.585007i	$-0.801092\pi$
$971$	−6.15950	−	42.8403i	−0.197668	−	1.37481i	0.613361	−	0.789803i	$-0.289817\pi$
$972$	1.75607	+	1.12856i	0.0563261	+	0.0361986i
$973$	1.92936	−	4.22470i	0.0618523	−	0.135438i
$974$	−15.2013	+	17.5432i	−0.487081	+	0.562122i
$975$		0			0
$976$	−2.14786	−	4.70316i	−0.0687514	−	0.150544i
$977$	41.8355	+	12.2840i	1.33844	+	0.393001i	0.871112	−	0.491085i	$-0.163399\pi$
$977$	41.8355	+	12.2840i	1.33844	+	0.393001i	0.467325	+	0.884085i	$0.345218\pi$
$978$	−14.9157	−	4.37965i	−0.476952	−	0.140046i
$979$	15.1967	+	33.2761i	0.485688	+	1.06351i
$980$		0			0
$981$	2.77708	−	3.20492i	0.0886653	−	0.102325i
$982$	−8.13378	+	17.8105i	−0.259559	+	0.568356i
$983$	−21.5942	−	13.8777i	−0.688747	−	0.442631i	0.148893	−	0.988853i	$-0.452429\pi$
$983$	−21.5942	−	13.8777i	−0.688747	−	0.442631i	−0.837640	+	0.546222i	$0.816065\pi$
$984$	−2.20065	−	15.3058i	−0.0701541	−	0.487932i
$985$		0			0
$986$	−2.93785	−	3.39046i	−0.0935603	−	0.107974i
$987$	−7.42034	+	2.17881i	−0.236192	+	0.0693522i
$988$	−30.0807			−0.956994
$989$	10.4682	−	43.8538i	0.332868	−	1.39447i
$990$		0			0
$991$	40.0096	−	11.7479i	1.27095	−	0.373184i	0.424390	−	0.905480i	$-0.360489\pi$
$991$	40.0096	−	11.7479i	1.27095	−	0.373184i	0.846559	+	0.532296i	$0.178670\pi$
$992$	2.40349	+	2.77377i	0.0763108	+	0.0880673i
$993$	−36.4335	+	23.4144i	−1.15618	+	0.743033i
$994$	−1.65365	−	11.5014i	−0.0524507	−	0.364803i
$995$		0			0
$996$	2.19152	−	4.79877i	0.0694411	−	0.152055i
$997$	13.7518	−	15.8704i	0.435524	−	0.502622i	−0.494979	−	0.868905i	$-0.664824\pi$
$997$	13.7518	−	15.8704i	0.435524	−	0.502622i	0.930504	+	0.366283i	$0.119370\pi$
$998$	1.59092	−	11.0651i	0.0503598	−	0.350260i
$999$	−14.4180	−	31.5710i	−0.456165	−	0.998861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.101.4		100
5.2	odd	4		115.2.j.a.9.4	✓	100
5.3	odd	4		115.2.j.a.9.7	yes	100
5.4	even	2	inner	575.2.k.g.101.7		100
23.18	even	11	inner	575.2.k.g.501.4		100
115.18	odd	44		115.2.j.a.64.4	yes	100
115.64	even	22	inner	575.2.k.g.501.7		100
115.87	odd	44		115.2.j.a.64.7	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.4	✓	100	5.2	odd	4
115.2.j.a.9.7	yes	100	5.3	odd	4
115.2.j.a.64.4	yes	100	115.18	odd	44
115.2.j.a.64.7	yes	100	115.87	odd	44
575.2.k.g.101.4		100	1.1	even	1	trivial
575.2.k.g.101.7		100	5.4	even	2	inner
575.2.k.g.501.4		100	23.18	even	11	inner
575.2.k.g.501.7		100	115.64	even	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09283 + 0.320885i) q^{2} +(1.07866 + 1.24484i) q^{3} +(-0.591189 + 0.379934i) q^{4} +(-1.57825 - 1.01428i) q^{6} +(0.643697 - 1.40950i) q^{7} +(2.01589 - 2.32646i) q^{8} +(0.0408222 - 0.283925i) q^{9} +O(q^{10})\)	\(q+(-1.09283 + 0.320885i) q^{2} +(1.07866 + 1.24484i) q^{3} +(-0.591189 + 0.379934i) q^{4} +(-1.57825 - 1.01428i) q^{6} +(0.643697 - 1.40950i) q^{7} +(2.01589 - 2.32646i) q^{8} +(0.0408222 - 0.283925i) q^{9} +(-4.00579 - 1.17621i) q^{11} +(-1.11065 - 0.326117i) q^{12} +(-2.46165 - 5.39026i) q^{13} +(-0.251167 + 1.74690i) q^{14} +(-0.872642 + 1.91082i) q^{16} +(-1.24289 - 0.798760i) q^{17} +(0.0464953 + 0.323382i) q^{18} +(-6.07675 + 3.90529i) q^{19} +(2.44894 - 0.719074i) q^{21} +4.75509 q^{22} +(-2.79621 - 3.89631i) q^{23} +5.07055 q^{24} +(4.41983 + 5.10075i) q^{26} +(4.55453 - 2.92702i) q^{27} +(0.154970 + 1.07784i) q^{28} +(-2.24279 - 1.44135i) q^{29} +(0.638526 - 0.736898i) q^{31} +(-0.535690 + 3.72580i) q^{32} +(-2.85671 - 6.25531i) q^{33} +(1.61459 + 0.474086i) q^{34} +(0.0837390 + 0.183363i) q^{36} +(0.912338 - 6.34545i) q^{37} +(5.38773 - 6.21777i) q^{38} +(4.05474 - 8.87865i) q^{39} +(-0.434006 - 3.01857i) q^{41} +(-2.44555 + 1.57166i) q^{42} +(6.15639 + 7.10485i) q^{43} +(2.81506 - 0.826575i) q^{44} +(4.30606 + 3.36076i) q^{46} -3.03002 q^{47} +(-3.31996 + 0.974829i) q^{48} +(3.01168 + 3.47566i) q^{49} +(-0.346334 - 2.40881i) q^{51} +(3.50324 + 2.25140i) q^{52} +(-0.872932 + 1.91146i) q^{53} +(-4.03811 + 4.66022i) q^{54} +(-1.98152 - 4.33893i) q^{56} +(-11.4163 - 3.35212i) q^{57} +(2.91350 + 0.855482i) q^{58} +(1.42947 + 3.13011i) q^{59} +(-1.61183 + 1.86015i) q^{61} +(-0.461343 + 1.01020i) q^{62} +(-0.373915 - 0.240301i) q^{63} +(-1.20804 - 8.40212i) q^{64} +(5.12914 + 5.91934i) q^{66} +(3.43775 - 1.00941i) q^{67} +1.03826 q^{68} +(1.83413 - 7.68365i) q^{69} +(-6.31720 + 1.85490i) q^{71} +(-0.578247 - 0.667332i) q^{72} +(7.43453 - 4.77788i) q^{73} +(1.03913 + 7.22728i) q^{74} +(2.10875 - 4.61753i) q^{76} +(-4.23637 + 4.88904i) q^{77} +(-1.58214 + 11.0040i) q^{78} +(-2.53011 - 5.54018i) q^{79} +(7.73081 + 2.26997i) q^{81} +(1.44291 + 3.15953i) q^{82} +(-0.648601 + 4.51112i) q^{83} +(-1.17459 + 1.35554i) q^{84} +(-9.00775 - 5.78893i) q^{86} +(-0.624955 - 4.34666i) q^{87} +(-10.8116 + 6.94820i) q^{88} +(-5.73812 - 6.62215i) q^{89} -9.18213 q^{91} +(3.13343 + 1.24108i) q^{92} +1.60608 q^{93} +(3.31131 - 0.972287i) q^{94} +(-5.21588 + 3.35204i) q^{96} +(1.98507 + 13.8065i) q^{97} +(-4.40655 - 2.83192i) q^{98} +(-0.497479 + 1.08933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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