LMFDB - Embedded newform 605.2.g.q.366.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.1
Character	$\chi$	$=$	605.366
Dual form			605.2.g.q.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12272 + 1.54225i) q^{2} +(0.414045 + 1.27430i) q^{3} +(1.50939 - 4.64542i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.84419 - 2.06642i) q^{6} +(-0.810808 + 2.49541i) q^{7} +(2.33876 + 7.19797i) q^{8} +(0.974647 - 0.708122i) q^{9} +O(q^{10})$	\(q+(-2.12272 + 1.54225i) q^{2} +(0.414045 + 1.27430i) q^{3} +(1.50939 - 4.64542i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.84419 - 2.06642i) q^{6} +(-0.810808 + 2.49541i) q^{7} +(2.33876 + 7.19797i) q^{8} +(0.974647 - 0.708122i) q^{9} +2.62383 q^{10} +6.54461 q^{12} +(5.44317 - 3.95469i) q^{13} +(-2.12742 - 6.54753i) q^{14} +(0.414045 - 1.27430i) q^{15} +(-8.16235 - 5.93029i) q^{16} +(-1.44293 - 1.04835i) q^{17} +(-0.976805 + 3.00630i) q^{18} +(-0.457488 - 1.40800i) q^{19} +(-3.95163 + 2.87103i) q^{20} -3.51561 q^{21} +5.20473 q^{23} +(-8.20401 + 5.96056i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-5.45522 + 16.7894i) q^{26} +(4.55786 + 3.31148i) q^{27} +(10.3684 + 7.53309i) q^{28} +(0.363827 - 1.11974i) q^{29} +(1.08638 + 3.34354i) q^{30} +(3.69255 - 2.68279i) q^{31} +11.3356 q^{32} +4.67975 q^{34} +(2.12272 - 1.54225i) q^{35} +(-1.81841 - 5.59648i) q^{36} +(-0.210055 + 0.646484i) q^{37} +(3.14261 + 2.28324i) q^{38} +(7.29317 + 5.29880i) q^{39} +(2.33876 - 7.19797i) q^{40} +(1.69936 + 5.23010i) q^{41} +(7.46266 - 5.42194i) q^{42} +3.80120 q^{43} -1.20473 q^{45} +(-11.0482 + 8.02699i) q^{46} +(2.05809 + 6.33415i) q^{47} +(4.17739 - 12.8567i) q^{48} +(0.0934546 + 0.0678988i) q^{49} +(-2.12272 - 1.54225i) q^{50} +(0.738473 - 2.27279i) q^{51} +(-10.1554 - 31.2550i) q^{52} +(-11.5640 + 8.40177i) q^{53} -14.7822 q^{54} -19.8582 q^{56} +(1.60480 - 1.16595i) q^{57} +(0.954620 + 2.93802i) q^{58} +(-1.20037 + 3.69436i) q^{59} +(-5.29470 - 3.84682i) q^{60} +(-2.59898 - 1.88827i) q^{61} +(-3.70072 + 11.3896i) q^{62} +(0.976805 + 3.00630i) q^{63} +(-7.73763 + 5.62172i) q^{64} -6.72812 q^{65} +4.66012 q^{67} +(-7.04796 + 5.12064i) q^{68} +(2.15499 + 6.63238i) q^{69} +(-2.12742 + 6.54753i) q^{70} +(-3.14261 - 2.28324i) q^{71} +(7.37651 + 5.35935i) q^{72} +(-1.10230 + 3.39253i) q^{73} +(-0.551150 - 1.69626i) q^{74} +(-1.08398 + 0.787560i) q^{75} -7.23130 q^{76} -23.6535 q^{78} +(12.2459 - 8.89718i) q^{79} +(3.11774 + 9.59541i) q^{80} +(-1.21581 + 3.74187i) q^{81} +(-11.6734 - 8.48121i) q^{82} +(-5.93358 - 4.31100i) q^{83} +(-5.30642 + 16.3315i) q^{84} +(0.551150 + 1.69626i) q^{85} +(-8.06889 + 5.86239i) q^{86} +1.57753 q^{87} +3.44872 q^{89} +(2.55731 - 1.85799i) q^{90} +(5.45522 + 16.7894i) q^{91} +(7.85596 - 24.1782i) q^{92} +(4.94756 + 3.59461i) q^{93} +(-14.1376 - 10.2716i) q^{94} +(-0.457488 + 1.40800i) q^{95} +(4.69344 + 14.4449i) q^{96} +(-1.19332 + 0.866997i) q^{97} -0.303095 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	$ 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) $ 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−2.12272	+	1.54225i	−1.50099	+	1.09053i	−0.531007	+	0.847367i	$0.678186\pi$
$2$	−2.12272	+	1.54225i	−1.50099	+	1.09053i	−0.969984	+	0.243167i	$0.921814\pi$
$3$	0.414045	+	1.27430i	0.239049	+	0.735717i	0.996558	+	0.0828927i	$0.0264159\pi$
$3$	0.414045	+	1.27430i	0.239049	+	0.735717i	−0.757510	+	0.652824i	$0.773584\pi$
$4$	1.50939	−	4.64542i	0.754694	−	2.32271i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−2.84419	−	2.06642i	−1.16113	−	0.843614i
$7$	−0.810808	+	2.49541i	−0.306457	+	0.943177i	0.672673	+	0.739940i	$0.265146\pi$
$7$	−0.810808	+	2.49541i	−0.306457	+	0.943177i	−0.979130	+	0.203237i	$0.934854\pi$
$8$	2.33876	+	7.19797i	0.826877	+	2.54487i
$9$	0.974647	−	0.708122i	0.324882	−	0.236041i
$10$	2.62383			0.829728
$11$		0			0
$11$		0			0
$12$	6.54461			1.88927
$13$	5.44317	−	3.95469i	1.50966	−	1.09683i	0.543336	−	0.839515i	$-0.317161\pi$
$13$	5.44317	−	3.95469i	1.50966	−	1.09683i	0.966327	−	0.257319i	$-0.0828390\pi$
$14$	−2.12742	−	6.54753i	−0.568578	−	1.74990i
$15$	0.414045	−	1.27430i	0.106906	−	0.329022i
$16$	−8.16235	−	5.93029i	−2.04059	−	1.48257i
$17$	−1.44293	−	1.04835i	−0.349962	−	0.254262i	0.398891	−	0.916998i	$-0.369395\pi$
$17$	−1.44293	−	1.04835i	−0.349962	−	0.254262i	−0.748853	+	0.662736i	$0.769395\pi$
$18$	−0.976805	+	3.00630i	−0.230235	+	0.708591i
$19$	−0.457488	−	1.40800i	−0.104955	−	0.323018i	0.884765	−	0.466038i	$-0.154319\pi$
$19$	−0.457488	−	1.40800i	−0.104955	−	0.323018i	−0.989720	+	0.143019i	$0.954319\pi$
$20$	−3.95163	+	2.87103i	−0.883611	+	0.641981i
$21$	−3.51561			−0.767169
$22$		0			0
$23$	5.20473			1.08526			0.542631	−	0.839971i	$-0.317428\pi$
$23$	5.20473			1.08526			0.542631	+	0.839971i	$0.317428\pi$
$24$	−8.20401	+	5.96056i	−1.67464	+	1.21670i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−5.45522	+	16.7894i	−1.06986	+	3.29268i
$27$	4.55786	+	3.31148i	0.877160	+	0.637294i
$28$	10.3684	+	7.53309i	1.95944	+	1.42362i
$29$	0.363827	−	1.11974i	0.0675609	−	0.207931i	−0.911576	−	0.411131i	$-0.865134\pi$
$29$	0.363827	−	1.11974i	0.0675609	−	0.207931i	0.979137	+	0.203199i	$0.0651340\pi$
$30$	1.08638	+	3.34354i	0.198345	+	0.610445i
$31$	3.69255	−	2.68279i	0.663201	−	0.481844i	−0.204542	−	0.978858i	$-0.565570\pi$
$31$	3.69255	−	2.68279i	0.663201	−	0.481844i	0.867742	+	0.497014i	$0.165570\pi$
$32$	11.3356			2.00387
$33$		0			0
$34$	4.67975			0.802571
$35$	2.12272	−	1.54225i	0.358806	−	0.260688i
$36$	−1.81841	−	5.59648i	−0.303068	−	0.932746i
$37$	−0.210055	+	0.646484i	−0.0345329	+	0.106281i	−0.966837	−	0.255394i	$-0.917795\pi$
$37$	−0.210055	+	0.646484i	−0.0345329	+	0.106281i	0.932304	+	0.361675i	$0.117795\pi$
$38$	3.14261	+	2.28324i	0.509799	+	0.370391i
$39$	7.29317	+	5.29880i	1.16784	+	0.848487i
$40$	2.33876	−	7.19797i	0.369791	−	1.13810i
$41$	1.69936	+	5.23010i	0.265396	+	0.816804i	0.991602	+	0.129327i	$0.0412817\pi$
$41$	1.69936	+	5.23010i	0.265396	+	0.816804i	−0.726206	+	0.687477i	$0.758718\pi$
$42$	7.46266	−	5.42194i	1.15151	−	0.836624i
$43$	3.80120			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$43$	3.80120			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$44$		0			0
$45$	−1.20473			−0.179591
$46$	−11.0482	+	8.02699i	−1.62897	+	1.18351i
$47$	2.05809	+	6.33415i	0.300203	+	0.923931i	0.981424	+	0.191853i	$0.0614496\pi$
$47$	2.05809	+	6.33415i	0.300203	+	0.923931i	−0.681220	+	0.732079i	$0.738550\pi$
$48$	4.17739	−	12.8567i	0.602954	−	1.85570i
$49$	0.0934546	+	0.0678988i	0.0133507	+	0.00969983i
$50$	−2.12272	−	1.54225i	−0.300198	−	0.218107i
$51$	0.738473	−	2.27279i	0.103407	−	0.318254i
$52$	−10.1554	−	31.2550i	−1.40829	−	4.33428i
$53$	−11.5640	+	8.40177i	−1.58844	+	1.15407i	−0.682324	+	0.731050i	$0.739031\pi$
$53$	−11.5640	+	8.40177i	−1.58844	+	1.15407i	−0.906119	+	0.423022i	$0.860969\pi$
$54$	−14.7822			−2.01160
$55$		0			0
$56$	−19.8582			−2.65366
$57$	1.60480	−	1.16595i	0.212561	−	0.154434i
$58$	0.954620	+	2.93802i	0.125348	+	0.385780i
$59$	−1.20037	+	3.69436i	−0.156275	+	0.480965i	−0.998288	−	0.0584924i	$-0.981371\pi$
$59$	−1.20037	+	3.69436i	−0.156275	+	0.480965i	0.842013	+	0.539458i	$0.181371\pi$
$60$	−5.29470	−	3.84682i	−0.683543	−	0.496623i
$61$	−2.59898	−	1.88827i	−0.332765	−	0.241768i	0.408838	−	0.912607i	$-0.365934\pi$
$61$	−2.59898	−	1.88827i	−0.332765	−	0.241768i	−0.741603	+	0.670839i	$0.765934\pi$
$62$	−3.70072	+	11.3896i	−0.469992	+	1.44649i
$63$	0.976805	+	3.00630i	0.123066	+	0.378758i
$64$	−7.73763	+	5.62172i	−0.967204	+	0.702715i
$65$	−6.72812			−0.834521
$66$		0			0
$67$	4.66012			0.569325			0.284662	−	0.958628i	$-0.408119\pi$
$67$	4.66012			0.569325			0.284662	+	0.958628i	$0.408119\pi$
$68$	−7.04796	+	5.12064i	−0.854691	+	0.620969i
$69$	2.15499	+	6.63238i	0.259430	+	0.798445i
$70$	−2.12742	+	6.54753i	−0.254276	+	0.782580i
$71$	−3.14261	−	2.28324i	−0.372960	−	0.270971i	0.385478	−	0.922717i	$-0.374037\pi$
$71$	−3.14261	−	2.28324i	−0.372960	−	0.270971i	−0.758437	+	0.651746i	$0.774037\pi$
$72$	7.37651	+	5.35935i	0.869330	+	0.631606i
$73$	−1.10230	+	3.39253i	−0.129014	+	0.397066i	−0.994611	−	0.103676i	$-0.966939\pi$
$73$	−1.10230	+	3.39253i	−0.129014	+	0.397066i	0.865597	+	0.500742i	$0.166939\pi$
$74$	−0.551150	−	1.69626i	−0.0640699	−	0.197187i
$75$	−1.08398	+	0.787560i	−0.125168	+	0.0909396i
$76$	−7.23130			−0.829487
$77$		0			0
$78$	−23.6535			−2.67823
$79$	12.2459	−	8.89718i	1.37777	−	1.00101i	0.380689	−	0.924703i	$-0.375687\pi$
$79$	12.2459	−	8.89718i	1.37777	−	1.00101i	0.997084	−	0.0763082i	$-0.0243133\pi$
$80$	3.11774	+	9.59541i	0.348574	+	1.07280i
$81$	−1.21581	+	3.74187i	−0.135090	+	0.415763i
$82$	−11.6734	−	8.48121i	−1.28911	−	0.936593i
$83$	−5.93358	−	4.31100i	−0.651295	−	0.473194i	0.212417	−	0.977179i	$-0.431867\pi$
$83$	−5.93358	−	4.31100i	−0.651295	−	0.473194i	−0.863712	+	0.503985i	$0.831867\pi$
$84$	−5.30642	+	16.3315i	−0.578978	+	1.78191i
$85$	0.551150	+	1.69626i	0.0597806	+	0.183986i
$86$	−8.06889	+	5.86239i	−0.870091	+	0.632158i
$87$	1.57753			0.169129
$88$		0			0
$89$	3.44872			0.365564			0.182782	−	0.983153i	$-0.441490\pi$
$89$	3.44872			0.365564			0.182782	+	0.983153i	$0.441490\pi$
$90$	2.55731	−	1.85799i	0.269564	−	0.195850i
$91$	5.45522	+	16.7894i	0.571862	+	1.76001i
$92$	7.85596	−	24.1782i	0.819040	−	2.52075i
$93$	4.94756	+	3.59461i	0.513038	+	0.372744i
$94$	−14.1376	−	10.2716i	−1.45818	−	1.05943i
$95$	−0.457488	+	1.40800i	−0.0469373	+	0.144458i
$96$	4.69344	+	14.4449i	0.479022	+	1.47428i
$97$	−1.19332	+	0.866997i	−0.121163	+	0.0880302i	−0.646717	−	0.762730i	$-0.723858\pi$
$97$	−1.19332	+	0.866997i	−0.121163	+	0.0880302i	0.525553	+	0.850761i	$0.323858\pi$
$98$	−0.303095			−0.0306172
$99$		0			0
$100$	4.88448			0.488448
$101$	2.76085	−	2.00587i	0.274715	−	0.199592i	−0.441894	−	0.897067i	$-0.645693\pi$
$101$	2.76085	−	2.00587i	0.274715	−	0.199592i	0.716609	+	0.697475i	$0.245693\pi$
$102$	1.93763	+	5.96340i	0.191854	+	0.590465i
$103$	−1.53696	+	4.73027i	−0.151441	+	0.466087i	−0.997783	−	0.0665527i	$-0.978800\pi$
$103$	−1.53696	+	4.73027i	−0.151441	+	0.466087i	0.846342	+	0.532640i	$0.178800\pi$
$104$	41.1960	+	29.9307i	4.03960	+	2.93494i
$105$	2.84419	+	2.06642i	0.277564	+	0.201662i
$106$	11.5896	−	35.6693i	1.12569	−	3.46450i
$107$	2.18327	+	6.71942i	0.211065	+	0.649591i	0.999410	+	0.0343573i	$0.0109384\pi$
$107$	2.18327	+	6.71942i	0.211065	+	0.649591i	−0.788345	+	0.615234i	$0.789062\pi$
$108$	22.2628	−	16.1749i	2.14224	−	1.55643i
$109$	−10.6439			−1.01950			−0.509750	−	0.860323i	$-0.670262\pi$
$109$	−10.6439			−1.01950			−0.509750	+	0.860323i	$0.670262\pi$
$110$		0			0
$111$	−0.910786			−0.0864480
$112$	21.4166	−	15.5601i	2.02368	−	1.47029i
$113$	−4.25484	−	13.0951i	−0.400262	−	1.23188i	−0.924787	−	0.380485i	$-0.875757\pi$
$113$	−4.25484	−	13.0951i	−0.400262	−	1.23188i	0.524525	−	0.851395i	$-0.324243\pi$
$114$	−1.60835	+	4.94999i	−0.150636	+	0.463609i
$115$	−4.21071	−	3.05926i	−0.392651	−	0.285278i
$116$	−4.65252	−	3.38026i	−0.431976	−	0.313849i
$117$	2.50476	−	7.70886i	0.231565	−	0.712684i
$118$	−3.14957	−	9.69338i	−0.289941	−	0.892348i
$119$	3.78600	−	2.75069i	0.347062	−	0.252155i
$120$	10.1407			0.925717
$121$		0			0
$122$	8.42909			0.763134
$123$	−5.96109	+	4.33099i	−0.537494	+	0.390512i
$124$	−6.88921	−	21.2028i	−0.618669	−	1.90407i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−6.70994	−	4.87506i	−0.597769	−	0.434305i
$127$	9.96133	+	7.23733i	0.883925	+	0.642209i	0.934287	−	0.356522i	$-0.116037\pi$
$127$	9.96133	+	7.23733i	0.883925	+	0.642209i	−0.0503620	+	0.998731i	$0.516037\pi$
$128$	0.748980	−	2.30512i	0.0662011	−	0.203746i
$129$	1.57387	+	4.84386i	0.138571	+	0.426478i
$130$	14.2819	−	10.3764i	1.25261	−	0.910074i
$131$	19.5102			1.70461			0.852306	−	0.523043i	$-0.175203\pi$
$131$	19.5102			1.70461			0.852306	+	0.523043i	$0.175203\pi$
$132$		0			0
$133$	3.88448			0.336827
$134$	−9.89215	+	7.18707i	−0.854552	+	0.620868i
$135$	−1.74095	−	5.35808i	−0.149837	−	0.461150i
$136$	4.17132	−	12.8380i	0.357688	−	1.10085i
$137$	6.92861	+	5.03393i	0.591951	+	0.430078i	0.843013	−	0.537893i	$-0.180780\pi$
$137$	6.92861	+	5.03393i	0.591951	+	0.430078i	−0.251062	+	0.967971i	$0.580780\pi$
$138$	−14.8032	−	10.7552i	−1.26013	−	0.915541i
$139$	0.612978	−	1.88655i	0.0519921	−	0.160015i	−0.921689	−	0.387929i	$-0.873190\pi$
$139$	0.612978	−	1.88655i	0.0519921	−	0.160015i	0.973681	+	0.227914i	$0.0731905\pi$
$140$	−3.96038	−	12.1888i	−0.334713	−	1.03014i
$141$	−7.21946	+	5.24525i	−0.607988	+	0.441729i
$142$	10.1922			0.855313
$143$		0			0
$144$	−12.1548			−1.01290
$145$	−0.952511	+	0.692040i	−0.0791017	+	0.0574708i
$146$	−2.89225	−	8.90142i	−0.239364	−	0.736687i
$147$	−0.0478289	+	0.147202i	−0.00394486	+	0.0121410i
$148$	2.68614	+	1.95159i	0.220799	+	0.160420i
$149$	14.8449	+	10.7855i	1.21614	+	0.883578i	0.995774	−	0.0918384i	$-0.0292743\pi$
$149$	14.8449	+	10.7855i	1.21614	+	0.883578i	0.220368	+	0.975417i	$0.429274\pi$
$150$	1.08638	−	3.34354i	0.0887028	−	0.272999i
$151$	5.32234	+	16.3805i	0.433126	+	1.33302i	0.894995	+	0.446076i	$0.147179\pi$
$151$	5.32234	+	16.3805i	0.433126	+	1.33302i	−0.461870	+	0.886948i	$0.652821\pi$
$152$	9.06482	−	6.58598i	0.735254	−	0.534193i
$153$	−2.14871			−0.173713
$154$		0			0
$155$	−4.56424			−0.366608
$156$	35.6234	−	25.8819i	2.85215	−	2.07221i
$157$	−6.45766	−	19.8746i	−0.515378	−	1.58617i	−0.782594	−	0.622533i	$-0.786104\pi$
$157$	−6.45766	−	19.8746i	−0.515378	−	1.58617i	0.267216	−	0.963637i	$-0.413896\pi$
$158$	−12.2730	+	37.7725i	−0.976390	+	3.00502i
$159$	−15.4944	−	11.2573i	−1.22879	−	0.892765i
$160$	−9.17069	−	6.66289i	−0.725006	−	0.526748i
$161$	−4.22004	+	12.9879i	−0.332586	+	1.02359i
$162$	−3.19007	−	9.81803i	−0.250636	−	0.771378i
$163$	−7.64957	+	5.55774i	−0.599161	+	0.435316i	−0.845581	−	0.533847i	$-0.820746\pi$
$163$	−7.64957	+	5.55774i	−0.599161	+	0.435316i	0.246420	+	0.969163i	$0.420746\pi$
$164$	26.8610			2.09749
$165$		0			0
$166$	19.2440			1.49362
$167$	7.64442	−	5.55399i	0.591543	−	0.429781i	−0.251324	−	0.967903i	$-0.580866\pi$
$167$	7.64442	−	5.55399i	0.591543	−	0.429781i	0.842867	+	0.538122i	$0.180866\pi$
$168$	−8.22218	−	25.3053i	−0.634355	−	1.95234i
$169$	9.97125	−	30.6884i	0.767019	−	2.36064i
$170$	−3.78600	−	2.75069i	−0.290373	−	0.210968i
$171$	−1.44293	−	1.04835i	−0.110344	−	0.0801693i
$172$	5.73748	−	17.6582i	0.437479	−	1.34642i
$173$	−2.80676	−	8.63831i	−0.213394	−	0.656759i	−0.999264	−	0.0383668i	$-0.987784\pi$
$173$	−2.80676	−	8.63831i	−0.213394	−	0.656759i	0.785870	−	0.618392i	$-0.212216\pi$
$174$	−3.34866	+	2.43294i	−0.253861	+	0.184441i
$175$	−2.62383			−0.198343
$176$		0			0
$177$	−5.20473			−0.391211
$178$	−7.32068	+	5.31879i	−0.548708	+	0.398660i
$179$	−4.25484	−	13.0951i	−0.318022	−	0.978771i	−0.974493	−	0.224420i	$-0.927951\pi$
$179$	−4.25484	−	13.0951i	−0.318022	−	0.978771i	0.656471	−	0.754352i	$-0.272049\pi$
$180$	−1.81841	+	5.59648i	−0.135536	+	0.417137i
$181$	19.3017	+	14.0235i	1.43468	+	1.04236i	0.989121	+	0.147106i	$0.0469959\pi$
$181$	19.3017	+	14.0235i	1.43468	+	1.04236i	0.445561	+	0.895251i	$0.353004\pi$
$182$	−37.4734	−	27.2260i	−2.77771	−	2.01813i
$183$	1.33012	−	4.09370i	0.0983256	−	0.302615i
$184$	12.1726	+	37.4635i	0.897378	+	2.76185i
$185$	0.549932	−	0.399549i	0.0404318	−	0.0293754i
$186$	−16.0461			−1.17656
$187$		0			0
$188$	32.5313			2.37259
$189$	−11.9590	+	8.68875i	−0.869892	+	0.632014i
$190$	−1.20037	−	3.69436i	−0.0870841	−	0.268017i
$191$	4.96371	−	15.2767i	0.359162	−	1.10539i	−0.594395	−	0.804173i	$-0.702609\pi$
$191$	4.96371	−	15.2767i	0.359162	−	1.10539i	0.953557	−	0.301213i	$-0.0973915\pi$
$192$	−10.3675	−	7.53241i	−0.748208	−	0.543605i
$193$	−17.3605	−	12.6132i	−1.24964	−	0.907916i	−0.251438	−	0.967873i	$-0.580903\pi$
$193$	−17.3605	−	12.6132i	−1.24964	−	0.907916i	−0.998201	+	0.0599578i	$0.980903\pi$
$194$	1.19596	−	3.68079i	0.0858650	−	0.264265i
$195$	−2.78574	−	8.57364i	−0.199491	−	0.613971i
$196$	0.456478	−	0.331650i	0.0326056	−	0.0236893i
$197$	9.21494			0.656537			0.328269	−	0.944584i	$-0.393535\pi$
$197$	9.21494			0.656537			0.328269	+	0.944584i	$0.393535\pi$
$198$		0			0
$199$	−16.4880			−1.16880			−0.584401	−	0.811465i	$-0.698670\pi$
$199$	−16.4880			−1.16880			−0.584401	+	0.811465i	$0.698670\pi$
$200$	−6.12296	+	4.44859i	−0.432959	+	0.314563i
$201$	1.92950	+	5.93839i	0.136096	+	0.418862i
$202$	−2.76696	+	8.51582i	−0.194683	+	0.599171i
$203$	2.49923	+	1.81579i	0.175411	+	0.127444i
$204$	−9.44340	−	6.86103i	−0.661170	−	0.480368i
$205$	1.69936	−	5.23010i	0.118689	−	0.365286i
$206$	−4.03271	−	12.4114i	−0.280972	−	0.864744i
$207$	5.07277	−	3.68559i	0.352582	−	0.256166i
$208$	−67.8815			−4.70673
$209$		0			0
$210$	−9.22436			−0.636541
$211$	−12.0007	+	8.71903i	−0.826163	+	0.600243i	−0.918471	−	0.395488i	$-0.870576\pi$
$211$	−12.0007	+	8.71903i	−0.826163	+	0.600243i	0.0923082	+	0.995730i	$0.470576\pi$
$212$	21.5751	+	66.4014i	1.48178	+	4.56046i
$213$	1.60835	−	4.94999i	0.110202	−	0.339168i
$214$	−14.9975	−	10.8963i	−1.02521	−	0.744857i
$215$	−3.07523	−	2.23429i	−0.209729	−	0.152377i
$216$	−13.1762	+	40.5521i	−0.896525	+	2.75922i
$217$	3.70072	+	11.3896i	0.251221	+	0.773180i
$218$	22.5940	−	16.4155i	1.53026	−	1.11180i
$219$	−4.77950			−0.322968
$220$		0			0
$221$	−12.0000			−0.807207
$222$	1.93335	−	1.40466i	0.129758	−	0.0942745i
$223$	7.23186	+	22.2574i	0.484281	+	1.49046i	0.833019	+	0.553244i	$0.186610\pi$
$223$	7.23186	+	22.2574i	0.484281	+	1.49046i	−0.348738	+	0.937220i	$0.613390\pi$
$224$	−9.19099	+	28.2870i	−0.614099	+	1.89000i
$225$	0.974647	+	0.708122i	0.0649765	+	0.0472082i
$226$	29.2277	+	21.2352i	1.94420	+	1.41254i
$227$	−0.810808	+	2.49541i	−0.0538152	+	0.165626i	−0.974352	−	0.225030i	$-0.927752\pi$
$227$	−0.810808	+	2.49541i	−0.0538152	+	0.165626i	0.920537	+	0.390656i	$0.127752\pi$
$228$	−2.99408	−	9.21483i	−0.198288	−	0.610267i
$229$	17.8280	−	12.9528i	1.17811	−	0.855945i	0.186150	−	0.982521i	$-0.440399\pi$
$229$	17.8280	−	12.9528i	1.17811	−	0.855945i	0.991957	+	0.126577i	$0.0403990\pi$
$230$	13.6563			0.900471
$231$		0			0
$232$	8.91079			0.585022
$233$	−4.32397	+	3.14155i	−0.283273	+	0.205810i	−0.720344	−	0.693617i	$-0.756016\pi$
$233$	−4.32397	+	3.14155i	−0.283273	+	0.205810i	0.437071	+	0.899427i	$0.356016\pi$
$234$	6.57206	+	20.2267i	0.429629	+	1.32226i
$235$	2.05809	−	6.33415i	0.134255	−	0.413195i
$236$	15.3500	+	11.1525i	0.999203	+	0.725963i
$237$	16.4080	+	11.9211i	1.06582	+	0.774360i
$238$	−3.79438	+	11.6779i	−0.245953	+	0.756966i
$239$	−3.88804	−	11.9662i	−0.251497	−	0.774027i	−0.994500	−	0.104739i	$-0.966599\pi$
$239$	−3.88804	−	11.9662i	−0.251497	−	0.774027i	0.743003	−	0.669288i	$-0.233401\pi$
$240$	−10.9365	+	7.94586i	−0.705950	+	0.512903i
$241$	−4.28687			−0.276141			−0.138071	−	0.990422i	$-0.544090\pi$
$241$	−4.28687			−0.276141			−0.138071	+	0.990422i	$0.544090\pi$
$242$		0			0
$243$	11.6298			0.746052
$244$	−12.6947	+	9.22322i	−0.812693	+	0.590456i
$245$	−0.0356965	−	0.109863i	−0.00228057	−	0.00701886i
$246$	5.97429	−	18.3870i	0.380907	−	1.17231i
$247$	−8.05841	−	5.85478i	−0.512744	−	0.372530i
$248$	27.9466	+	20.3044i	1.77461	+	1.28933i
$249$	3.03673	−	9.34611i	0.192445	−	0.592285i
$250$	0.810808	+	2.49541i	0.0512800	+	0.157824i
$251$	−8.14107	+	5.91483i	−0.513860	+	0.373341i	−0.814286	−	0.580464i	$-0.802871\pi$
$251$	−8.14107	+	5.91483i	−0.513860	+	0.373341i	0.300426	+	0.953805i	$0.402871\pi$
$252$	15.4399			0.972621
$253$		0			0
$254$	−32.3069			−2.02712
$255$	−1.93335	+	1.40466i	−0.121071	+	0.0879632i
$256$	−3.94583	−	12.1440i	−0.246614	−	0.759001i
$257$	−0.978184	+	3.01054i	−0.0610174	+	0.187792i	−0.976919	−	0.213611i	$-0.931477\pi$
$257$	−0.978184	+	3.01054i	−0.0610174	+	0.187792i	0.915901	+	0.401403i	$0.131477\pi$
$258$	−10.8113	−	7.85488i	−0.673083	−	0.489024i
$259$	−1.44293	−	1.04835i	−0.0896592	−	0.0651413i
$260$	−10.1554	+	31.2550i	−0.629808	+	1.93835i
$261$	−0.438313	−	1.34899i	−0.0271309	−	0.0835003i
$262$	−41.4147	+	30.0895i	−2.55861	+	1.85894i
$263$	22.3681			1.37928			0.689638	−	0.724155i	$-0.257770\pi$
$263$	22.3681			1.37928			0.689638	+	0.724155i	$0.257770\pi$
$264$		0			0
$265$	14.2939			0.878070
$266$	−8.24568	+	5.99084i	−0.505575	+	0.367322i
$267$	1.42792	+	4.39470i	0.0873876	+	0.268951i
$268$	7.03394	−	21.6482i	0.429666	−	1.32238i
$269$	−12.9230	−	9.38910i	−0.787929	−	0.572464i	0.119419	−	0.992844i	$-0.461897\pi$
$269$	−12.9230	−	9.38910i	−0.787929	−	0.572464i	−0.907348	+	0.420380i	$0.861897\pi$
$270$	11.9590	+	8.68875i	0.727804	+	0.528781i
$271$	−4.83301	+	14.8745i	−0.293585	+	0.903561i	0.690108	+	0.723706i	$0.257563\pi$
$271$	−4.83301	+	14.8745i	−0.293585	+	0.903561i	−0.983693	+	0.179855i	$0.942437\pi$
$272$	5.56067	+	17.1140i	0.337165	+	1.03769i
$273$	−19.1360	+	13.9031i	−1.15817	+	0.841457i
$274$	−22.4711			−1.35753
$275$		0			0
$276$	34.0629			2.05035
$277$	−19.3222	+	14.0384i	−1.16096	+	0.843486i	−0.989899	−	0.141775i	$-0.954719\pi$
$277$	−19.3222	+	14.0384i	−1.16096	+	0.843486i	−0.171060	+	0.985261i	$0.554719\pi$
$278$	1.60835	+	4.94999i	0.0964624	+	0.296881i
$279$	1.69918	−	5.22955i	0.101727	−	0.313085i
$280$	16.0656	+	11.6723i	0.960104	+	0.697556i
$281$	−9.90550	−	7.19676i	−0.590912	−	0.429323i	0.251729	−	0.967798i	$-0.419001\pi$
$281$	−9.90550	−	7.19676i	−0.590912	−	0.429323i	−0.842642	+	0.538475i	$0.819001\pi$
$282$	7.23544	−	22.2684i	0.430864	−	1.32606i
$283$	−6.44412	−	19.8330i	−0.383063	−	1.17895i	−0.937875	−	0.346972i	$-0.887210\pi$
$283$	−6.44412	−	19.8330i	−0.383063	−	1.17895i	0.554812	−	0.831976i	$-0.312790\pi$
$284$	−15.3500	+	11.1525i	−0.910858	+	0.661777i
$285$	−1.98364			−0.117501
$286$		0			0
$287$	−14.4291			−0.851722
$288$	11.0482	−	8.02699i	0.651021	−	0.472995i
$289$	−4.27028	−	13.1426i	−0.251193	−	0.773093i
$290$	0.954620	−	2.93802i	0.0560572	−	0.172526i
$291$	−1.59890	−	1.16167i	−0.0937292	−	0.0680983i
$292$	14.0959	+	10.2413i	0.824902	+	0.599326i
$293$	4.42837	−	13.6291i	0.258708	−	0.796222i	−0.734368	−	0.678752i	$-0.762521\pi$
$293$	4.42837	−	13.6291i	0.258708	−	0.796222i	0.993076	−	0.117471i	$-0.0374787\pi$
$294$	−0.125495	−	0.386234i	−0.00731901	−	0.0225256i
$295$	3.14261	−	2.28324i	0.182970	−	0.132936i
$296$	−5.14464			−0.299026
$297$		0			0
$298$	−48.1455			−2.78899
$299$	28.3302	−	20.5831i	1.63838	−	1.19035i
$300$	2.02239	+	6.22429i	0.116763	+	0.359360i
$301$	−3.08204	+	9.48555i	−0.177646	+	0.546738i
$302$	−36.5606	−	26.5628i	−2.10383	−	1.52852i
$303$	3.69919	+	2.68762i	0.212513	+	0.154400i
$304$	−4.61570	+	14.2057i	−0.264728	+	0.814750i
$305$	0.992721	+	3.05528i	0.0568431	+	0.174945i
$306$	4.56111	−	3.31384i	0.260741	−	0.189440i
$307$	10.2952			0.587580			0.293790	−	0.955870i	$-0.405083\pi$
$307$	10.2952			0.587580			0.293790	+	0.955870i	$0.405083\pi$
$308$		0			0
$309$	−6.66414			−0.379110
$310$	9.68861	−	7.03919i	0.550276	−	0.399799i
$311$	−5.91833	−	18.2148i	−0.335598	−	1.03286i	−0.966427	−	0.256942i	$-0.917285\pi$
$311$	−5.91833	−	18.2148i	−0.335598	−	1.03286i	0.630829	−	0.775922i	$-0.282715\pi$
$312$	−21.0836	+	64.8887i	−1.19362	+	3.67360i
$313$	12.1140	+	8.80132i	0.684722	+	0.497480i	0.874921	−	0.484266i	$-0.160913\pi$
$313$	12.1140	+	8.80132i	0.684722	+	0.497480i	−0.190199	+	0.981746i	$0.560913\pi$
$314$	44.3595	+	32.2291i	2.50335	+	1.81879i
$315$	0.976805	−	3.00630i	0.0550367	−	0.169386i
$316$	−22.8473	−	70.3167i	−1.28526	−	3.95563i
$317$	−9.85255	+	7.15830i	−0.553375	+	0.402050i	−0.829028	−	0.559207i	$-0.811106\pi$
$317$	−9.85255	+	7.15830i	−0.553375	+	0.402050i	0.275654	+	0.961257i	$0.411106\pi$
$318$	50.2519			2.81799
$319$		0			0
$320$	9.56424			0.534657
$321$	−7.65858	+	5.56428i	−0.427460	+	0.310568i
$322$	−11.0727	−	34.0781i	−0.617055	−	1.89910i
$323$	−0.815957	+	2.51126i	−0.0454011	+	0.139730i
$324$	15.5474	+	11.2959i	0.863746	+	0.627549i
$325$	5.44317	+	3.95469i	0.301933	+	0.219367i
$326$	7.66651	−	23.5951i	0.424609	−	1.30681i
$327$	−4.40705	−	13.5635i	−0.243710	−	0.750063i
$328$	−33.6717	+	24.4639i	−1.85921	+	1.35079i
$329$	−17.4750			−0.963430
$330$		0			0
$331$	−15.8319			−0.870199			−0.435099	−	0.900382i	$-0.643287\pi$
$331$	−15.8319			−0.870199			−0.435099	+	0.900382i	$0.643287\pi$
$332$	−28.9825	+	21.0570i	−1.59062	+	1.15565i
$333$	0.253060	+	0.778839i	0.0138676	+	0.0426801i
$334$	−7.66134	+	23.5792i	−0.419210	+	1.29020i
$335$	−3.77012	−	2.73915i	−0.205984	−	0.149656i
$336$	28.6956	+	20.8486i	1.56547	+	1.13738i
$337$	2.07910	−	6.39883i	0.113256	−	0.348566i	−0.878323	−	0.478067i	$-0.841338\pi$
$337$	2.07910	−	6.39883i	0.113256	−	0.348566i	0.991579	+	0.129501i	$0.0413375\pi$
$338$	26.1629	+	80.5210i	1.42307	+	4.37977i
$339$	14.9253	−	10.8439i	0.810633	−	0.588959i
$340$	8.71176			0.472462
$341$		0			0
$342$	4.67975			0.253052
$343$	−15.1043	+	10.9739i	−0.815554	+	0.592535i
$344$	8.89010	+	27.3609i	0.479322	+	1.47520i
$345$	2.15499	−	6.63238i	0.116021	−	0.357075i
$346$	19.2804	+	14.0080i	1.03652	+	0.753076i
$347$	−27.1050	−	19.6929i	−1.45507	−	1.05717i	−0.984613	−	0.174749i	$-0.944088\pi$
$347$	−27.1050	−	19.6929i	−1.45507	−	1.05717i	−0.470459	−	0.882422i	$-0.655912\pi$
$348$	2.38110	−	7.32828i	0.127641	−	0.392837i
$349$	7.03761	+	21.6595i	0.376715	+	1.15941i	0.942314	+	0.334729i	$0.108645\pi$
$349$	7.03761	+	21.6595i	0.376715	+	1.15941i	−0.565600	+	0.824680i	$0.691355\pi$
$350$	5.56966	−	4.04660i	0.297711	−	0.216300i
$351$	37.9050			2.02322
$352$		0			0
$353$	−15.4617			−0.822942			−0.411471	−	0.911423i	$-0.634985\pi$
$353$	−15.4617			−0.822942			−0.411471	+	0.911423i	$0.634985\pi$
$354$	11.0482	−	8.02699i	0.587205	−	0.426630i
$355$	1.20037	+	3.69436i	0.0637091	+	0.196076i
$356$	5.20546	−	16.0208i	0.275889	−	0.849099i
$357$	5.07277	+	3.68559i	0.268480	+	0.195062i
$358$	29.2277	+	21.2352i	1.54473	+	1.12231i
$359$	2.96225	−	9.11686i	0.156341	−	0.481169i	−0.841953	−	0.539551i	$-0.818594\pi$
$359$	2.96225	−	9.11686i	0.156341	−	0.481169i	0.998294	+	0.0583815i	$0.0185940\pi$
$360$	−2.81758	−	8.67161i	−0.148499	−	0.457034i
$361$	13.5981	−	9.87963i	0.715692	−	0.519980i
$362$	−62.5998			−3.29017
$363$		0			0
$364$	86.2280			4.51957
$365$	2.88586	−	2.09670i	0.151053	−	0.109746i
$366$	3.49002	+	10.7412i	0.182426	+	0.561450i
$367$	−3.34930	+	10.3081i	−0.174832	+	0.538077i	−0.999626	−	0.0273564i	$-0.991291\pi$
$367$	−3.34930	+	10.3081i	−0.174832	+	0.538077i	0.824794	+	0.565433i	$0.191291\pi$
$368$	−42.4828	−	30.8656i	−2.21457	−	1.60898i
$369$	5.35983	+	3.89414i	0.279021	+	0.202721i
$370$	−0.551150	+	1.69626i	−0.0286529	+	0.0881846i
$371$	−11.5896	−	35.6693i	−0.601704	−	1.85186i
$372$	24.1663	−	17.5578i	1.25296	−	0.910330i
$373$	−10.0212			−0.518878			−0.259439	−	0.965759i	$-0.583538\pi$
$373$	−10.0212			−0.518878			−0.259439	+	0.965759i	$0.583538\pi$
$374$		0			0
$375$	1.33988			0.0691909
$376$	−40.7797	+	29.6282i	−2.10305	+	1.52796i
$377$	−2.44787	−	7.53377i	−0.126072	−	0.388009i
$378$	11.9855	−	36.8876i	0.616468	−	1.89729i
$379$	−3.39121	−	2.46386i	−0.174195	−	0.126560i	0.497272	−	0.867595i	$-0.334335\pi$
$379$	−3.39121	−	2.46386i	−0.174195	−	0.126560i	−0.671466	+	0.741035i	$0.734335\pi$
$380$	5.85024	+	4.25045i	0.300111	+	0.218044i
$381$	−5.09808	+	15.6903i	−0.261183	+	0.803838i
$382$	13.0239	+	40.0836i	0.666363	+	2.05085i
$383$	−15.5687	+	11.3113i	−0.795524	+	0.577982i	−0.909598	−	0.415490i	$-0.863610\pi$
$383$	−15.5687	+	11.3113i	−0.795524	+	0.577982i	0.114073	+	0.993472i	$0.463610\pi$
$384$	3.24753			0.165725
$385$		0			0
$386$	56.3042			2.86581
$387$	3.70483	−	2.69171i	0.188327	−	0.136828i
$388$	2.22638	+	6.85211i	0.113028	+	0.347863i
$389$	−8.78301	+	27.0313i	−0.445316	+	1.37054i	0.436820	+	0.899549i	$0.356105\pi$
$389$	−8.78301	+	27.0313i	−0.445316	+	1.37054i	−0.882137	+	0.470994i	$0.843895\pi$
$390$	19.1360	+	13.9031i	0.968991	+	0.704013i
$391$	−7.51006	−	5.45637i	−0.379800	−	0.275941i
$392$	−0.270165	+	0.831483i	−0.0136454	+	0.0419962i
$393$	8.07809	+	24.8618i	0.407486	+	1.25411i
$394$	−19.5608	+	14.2117i	−0.985457	+	0.715976i
$395$	−15.1368			−0.761615
$396$		0			0
$397$	−22.1784			−1.11310			−0.556552	−	0.830813i	$-0.687876\pi$
$397$	−22.1784			−1.11310			−0.556552	+	0.830813i	$0.687876\pi$
$398$	34.9994	−	25.4286i	1.75436	−	1.27462i
$399$	1.60835	+	4.94999i	0.0805182	+	0.247810i
$400$	3.11774	−	9.59541i	0.155887	−	0.479771i
$401$	−17.8598	−	12.9759i	−0.891874	−	0.647984i	0.0444923	−	0.999010i	$-0.485833\pi$
$401$	−17.8598	−	12.9759i	−0.891874	−	0.647984i	−0.936366	+	0.351026i	$0.885833\pi$
$402$	−13.2543	−	9.62979i	−0.661063	−	0.480290i
$403$	9.48953	−	29.2058i	0.472707	−	1.45484i
$404$	−5.15093	−	15.8529i	−0.256268	−	0.788713i
$405$	3.18303	−	2.31260i	0.158166	−	0.114914i
$406$	−8.10557			−0.402273
$407$		0			0
$408$	18.0866			0.895418
$409$	−19.9595	+	14.5014i	−0.986934	+	0.717050i	−0.959248	−	0.282567i	$-0.908814\pi$
$409$	−19.9595	+	14.5014i	−0.986934	+	0.717050i	−0.0276868	+	0.999617i	$0.508814\pi$
$410$	4.45883	+	13.7229i	0.220206	+	0.677725i
$411$	−3.54598	+	10.9134i	−0.174910	+	0.538318i
$412$	19.6542	+	14.2796i	0.968294	+	0.703506i
$413$	−8.24568	−	5.99084i	−0.405744	−	0.294790i
$414$	−5.08400	+	15.6470i	−0.249865	+	0.769006i
$415$	2.26643	+	6.97535i	0.111255	+	0.342406i
$416$	61.7015	−	44.8288i	3.02517	−	2.19791i
$417$	2.65783			0.130155
$418$		0			0
$419$	17.6535			0.862428			0.431214	−	0.902250i	$-0.358085\pi$
$419$	17.6535			0.862428			0.431214	+	0.902250i	$0.358085\pi$
$420$	13.8924	−	10.0934i	0.677879	−	0.492508i
$421$	0.471244	+	1.45034i	0.0229670	+	0.0706852i	0.961883	−	0.273461i	$-0.0881684\pi$
$421$	0.471244	+	1.45034i	0.0229670	+	0.0706852i	−0.938916	+	0.344146i	$0.888168\pi$
$422$	12.0273	−	37.0162i	0.585479	−	1.80192i
$423$	6.49127	+	4.71618i	0.315616	+	0.229309i
$424$	−87.5212	−	63.5879i	−4.25041	−	3.08810i
$425$	0.551150	−	1.69626i	0.0267347	−	0.0822809i
$426$	4.22004	+	12.9879i	0.204461	+	0.629268i
$427$	6.81928	−	4.95450i	0.330008	−	0.239765i
$428$	34.5099			1.66810
$429$		0			0
$430$	9.97370			0.480974
$431$	13.5505	−	9.84501i	0.652704	−	0.474217i	−0.211487	−	0.977381i	$-0.567831\pi$
$431$	13.5505	−	9.84501i	0.652704	−	0.474217i	0.864191	+	0.503163i	$0.167831\pi$
$432$	−17.5648	−	54.0588i	−0.845086	−	2.60091i
$433$	2.30991	−	7.10917i	0.111007	−	0.341645i	−0.880086	−	0.474814i	$-0.842515\pi$
$433$	2.30991	−	7.10917i	0.111007	−	0.341645i	0.991093	+	0.133169i	$0.0425153\pi$
$434$	−25.4213	−	18.4696i	−1.22026	−	0.886571i
$435$	−1.27625	−	0.927248i	−0.0611914	−	0.0444581i
$436$	−16.0658	+	49.4454i	−0.769411	+	2.36800i
$437$	−2.38110	−	7.32828i	−0.113904	−	0.350559i
$438$	10.1455	−	7.37117i	0.484773	−	0.352208i
$439$	17.4585			0.833250			0.416625	−	0.909078i	$-0.363213\pi$
$439$	17.4585			0.833250			0.416625	+	0.909078i	$0.363213\pi$
$440$		0			0
$441$	0.139166			0.00662695
$442$	25.4727	−	18.5070i	1.21161	−	0.880287i
$443$	−4.53754	−	13.9651i	−0.215585	−	0.663502i	−0.999112	−	0.0421438i	$-0.986581\pi$
$443$	−4.53754	−	13.9651i	−0.215585	−	0.663502i	0.783527	−	0.621358i	$-0.213419\pi$
$444$	−1.37473	+	4.23099i	−0.0652418	+	0.200794i
$445$	−2.79007	−	2.02711i	−0.132262	−	0.0960941i
$446$	−49.6776	−	36.0929i	−2.35230	−	1.70905i
$447$	−7.59743	+	23.3825i	−0.359346	+	1.10595i
$448$	−7.75476	−	23.8667i	−0.366378	−	1.12760i
$449$	1.05762	−	0.768404i	0.0499121	−	0.0362632i	−0.562549	−	0.826764i	$-0.690179\pi$
$449$	1.05762	−	0.768404i	0.0499121	−	0.0362632i	0.612462	+	0.790500i	$0.290179\pi$
$450$	−3.16101			−0.149011
$451$		0			0
$452$	−67.2543			−3.16338
$453$	−18.6699	+	13.5645i	−0.877189	+	0.637315i
$454$	−2.12742	−	6.54753i	−0.0998449	−	0.307291i
$455$	5.45522	−	16.7894i	0.255744	−	0.787101i
$456$	12.1457	+	8.82440i	0.568776	+	0.413240i
$457$	−8.24568	−	5.99084i	−0.385717	−	0.280240i	0.377981	−	0.925813i	$-0.376618\pi$
$457$	−8.24568	−	5.99084i	−0.385717	−	0.280240i	−0.763698	+	0.645574i	$0.776618\pi$
$458$	−17.8675	+	54.9904i	−0.834892	+	2.56953i
$459$	−3.10508	−	9.55645i	−0.144933	−	0.446057i
$460$	−20.5672	+	14.9429i	−0.958949	+	0.696717i
$461$	−4.12180			−0.191971			−0.0959857	−	0.995383i	$-0.530600\pi$
$461$	−4.12180			−0.191971			−0.0959857	+	0.995383i	$0.530600\pi$
$462$		0			0
$463$	32.7623			1.52259			0.761296	−	0.648404i	$-0.224563\pi$
$463$	32.7623			1.52259			0.761296	+	0.648404i	$0.224563\pi$
$464$	−9.61008	+	6.98214i	−0.446137	+	0.324137i
$465$	−1.88980	−	5.81620i	−0.0876373	−	0.269720i
$466$	4.33355	−	13.3373i	0.200748	−	0.617838i
$467$	−30.6734	−	22.2855i	−1.41940	−	1.03125i	−0.991871	−	0.127248i	$-0.959386\pi$
$467$	−30.6734	−	22.2855i	−1.41940	−	1.03125i	−0.427525	−	0.904003i	$-0.640614\pi$
$468$	−32.0302	−	23.2713i	−1.48060	−	1.07572i
$469$	−3.77847	+	11.6289i	−0.174473	+	0.536974i
$470$	5.40008	+	16.6197i	0.249087	+	0.766612i
$471$	22.6525	−	16.4580i	1.04377	−	0.758344i
$472$	−29.3993			−1.35321
$473$		0			0
$474$	−53.2150			−2.44425
$475$	1.19772	−	0.870194i	0.0549552	−	0.0399273i
$476$	−7.06357	−	21.7394i	−0.323758	−	0.996425i
$477$	−5.32138	+	16.3775i	−0.243649	+	0.749875i
$478$	26.7080	+	19.4045i	1.22160	+	0.887543i
$479$	5.22628	+	3.79712i	0.238795	+	0.173495i	0.700746	−	0.713411i	$-0.252851\pi$
$479$	5.22628	+	3.79712i	0.238795	+	0.173495i	−0.461951	+	0.886905i	$0.652851\pi$
$480$	4.69344	−	14.4449i	0.214225	−	0.659318i
$481$	1.41328	+	4.34963i	0.0644400	+	0.198326i
$482$	9.09983	−	6.61141i	0.414486	−	0.301142i
$483$	−18.2978			−0.832579
$484$		0			0
$485$	1.47502			0.0669774
$486$	−24.6868	+	17.9360i	−1.11982	+	0.813596i
$487$	13.4304	+	41.3345i	0.608589	+	1.87305i	0.469925	+	0.882706i	$0.344281\pi$
$487$	13.4304	+	41.3345i	0.608589	+	1.87305i	0.138664	+	0.990339i	$0.455719\pi$
$488$	7.51331	−	23.1236i	0.340111	−	1.04676i
$489$	−10.2495	−	7.44669i	−0.463498	−	0.336751i
$490$	0.245209	+	0.178155i	0.0110774	+	0.00804822i
$491$	−1.68528	+	5.18677i	−0.0760558	+	0.234076i	−0.981856	−	0.189630i	$-0.939271\pi$
$491$	−1.68528	+	5.18677i	−0.0760558	+	0.234076i	0.905800	+	0.423706i	$0.139271\pi$
$492$	11.1216	+	34.2289i	0.501403	+	1.54316i
$493$	−1.69886	+	1.23429i	−0.0765127	+	0.0555898i
$494$	26.1353			1.17588
$495$		0			0
$496$	−46.0496			−2.06769
$497$	8.24568	−	5.99084i	0.369869	−	0.268726i
$498$	7.96787	+	24.5226i	0.357049	+	1.09888i
$499$	3.85900	−	11.8768i	0.172753	−	0.531678i	−0.826771	−	0.562538i	$-0.809825\pi$
$499$	3.85900	−	11.8768i	0.172753	−	0.531678i	0.999524	+	0.0308608i	$0.00982486\pi$
$500$	−3.95163	−	2.87103i	−0.176722	−	0.128396i
$501$	10.2426	+	7.44167i	0.457605	+	0.332469i
$502$	8.15909	−	25.1111i	0.364158	−	1.12076i
$503$	−6.44412	−	19.8330i	−0.287329	−	0.884309i	−0.985691	−	0.168563i	$-0.946087\pi$
$503$	−6.44412	−	19.8330i	−0.287329	−	0.884309i	0.698362	−	0.715745i	$-0.253913\pi$
$504$	−19.3547	+	14.0620i	−0.862128	+	0.626372i
$505$	−3.41259			−0.151858
$506$		0			0
$507$	43.2347			1.92012
$508$	48.6559	−	35.3506i	2.15876	−	1.56843i
$509$	−8.21281	−	25.2764i	−0.364026	−	1.12036i	−0.950589	−	0.310453i	$-0.899519\pi$
$509$	−8.21281	−	25.2764i	−0.364026	−	1.12036i	0.586562	−	0.809904i	$-0.300481\pi$
$510$	1.93763	−	5.96340i	0.0857996	−	0.264064i
$511$	−7.57200	−	5.50138i	−0.334966	−	0.243367i
$512$	31.0267	+	22.5422i	1.37120	+	0.996234i
$513$	2.57741	−	7.93244i	0.113795	−	0.350226i
$514$	−2.56659	−	7.89914i	−0.113207	−	0.348416i
$515$	4.02381	−	2.92347i	0.177310	−	0.128823i
$516$	24.8773			1.09516
$517$		0			0
$518$	4.67975			0.205617
$519$	9.84567	−	7.15330i	0.432177	−	0.313995i
$520$	−15.7355	−	48.4288i	−0.690047	−	2.12374i
$521$	−7.11952	+	21.9116i	−0.311912	+	0.959966i	0.665095	+	0.746759i	$0.268391\pi$
$521$	−7.11952	+	21.9116i	−0.311912	+	0.959966i	−0.977007	+	0.213208i	$0.931609\pi$
$522$	3.01089	+	2.18754i	0.131783	+	0.0957461i
$523$	0.957324	+	0.695537i	0.0418609	+	0.0304137i	0.608519	−	0.793539i	$-0.291764\pi$
$523$	0.957324	+	0.695537i	0.0418609	+	0.0304137i	−0.566658	+	0.823953i	$0.691764\pi$
$524$	29.4484	−	90.6330i	1.28646	−	3.95932i
$525$	−1.08638	−	3.34354i	−0.0474136	−	0.145924i
$526$	−47.4813	+	34.4972i	−2.07028	+	1.50415i
$527$	−8.14058			−0.354609
$528$		0			0
$529$	4.08921			0.177792
$530$	−30.3421	+	22.0448i	−1.31798	+	0.957566i
$531$	1.44612	+	4.45071i	0.0627564	+	0.193144i
$532$	5.86319	−	18.0451i	0.254202	−	0.782353i
$533$	29.9333	+	21.7478i	1.29656	+	0.942003i
$534$	−9.80881	−	7.12652i	−0.424469	−	0.308395i
$535$	2.18327	−	6.71942i	0.0943911	−	0.290506i
$536$	10.8989	+	33.5434i	0.470762	+	1.44886i
$537$	14.9253	−	10.8439i	0.644075	−	0.467948i
$538$	41.9123			1.80697
$539$		0			0
$540$	−27.5183			−1.18420
$541$	25.5694	−	18.5772i	1.09931	−	0.798697i	0.118365	−	0.992970i	$-0.462235\pi$
$541$	25.5694	−	18.5772i	1.09931	−	0.798697i	0.980948	+	0.194273i	$0.0622347\pi$
$542$	−12.6810	−	39.0281i	−0.544696	−	1.67640i
$543$	−9.87835	+	30.4024i	−0.423921	+	1.30469i
$544$	−16.3565	−	11.8837i	−0.701277	−	0.509508i
$545$	8.61109	+	6.25632i	0.368859	+	0.267991i
$546$	19.1784	−	59.0251i	0.820760	−	2.52604i
$547$	−1.53877	−	4.73586i	−0.0657932	−	0.202491i	0.912755	−	0.408506i	$-0.133950\pi$
$547$	−1.53877	−	4.73586i	−0.0657932	−	0.202491i	−0.978549	+	0.206016i	$0.933950\pi$
$548$	33.8427	−	24.5882i	1.44569	−	1.05035i
$549$	−3.87021			−0.165177
$550$		0			0
$551$	−1.74305			−0.0742564
$552$	−42.6997	+	31.0231i	−1.81742	+	1.32043i
$553$	12.2730	+	37.7725i	0.521902	+	1.60625i
$554$	19.3650	−	59.5993i	0.822739	−	2.53213i
$555$	0.736842	+	0.535347i	0.0312772	+	0.0227242i
$556$	−7.83861	−	5.69508i	−0.332431	−	0.241525i
$557$	−7.76527	+	23.8990i	−0.329025	+	1.01263i	0.640566	+	0.767903i	$0.278700\pi$
$557$	−7.76527	+	23.8990i	−0.329025	+	1.01263i	−0.969591	+	0.244732i	$0.921300\pi$
$558$	4.45837	+	13.7214i	0.188738	+	0.580875i
$559$	20.6906	−	15.0326i	0.875117	−	0.635810i
$560$	−26.4724			−1.11866
$561$		0			0
$562$	32.1258			1.35515
$563$	9.17069	−	6.66289i	0.386498	−	0.280807i	−0.377521	−	0.926001i	$-0.623223\pi$
$563$	9.17069	−	6.66289i	0.386498	−	0.280807i	0.764019	+	0.645194i	$0.223223\pi$
$564$	13.4694	+	41.4545i	0.567164	+	1.74555i
$565$	−4.25484	+	13.0951i	−0.179003	+	0.550914i
$566$	44.2665	+	32.1615i	1.86066	+	1.35185i
$567$	−8.35172	−	6.06788i	−0.350739	−	0.254827i
$568$	9.08489	−	27.9604i	0.381193	−	1.17319i
$569$	−3.69562	−	11.3740i	−0.154929	−	0.476821i	0.843225	−	0.537561i	$-0.180654\pi$
$569$	−3.69562	−	11.3740i	−0.154929	−	0.476821i	−0.998154	+	0.0607395i	$0.980654\pi$
$570$	4.21071	−	3.05926i	0.176367	−	0.128138i
$571$	−29.8054			−1.24732			−0.623659	−	0.781697i	$-0.714355\pi$
$571$	−29.8054			−1.24732			−0.623659	+	0.781697i	$0.714355\pi$
$572$		0			0
$573$	21.5223			0.899108
$574$	30.6290	−	22.2532i	1.27843	−	0.928832i
$575$	1.60835	+	4.94999i	0.0670728	+	0.206429i
$576$	−3.56059	+	10.9584i	−0.148358	+	0.456599i
$577$	14.9553	+	10.8656i	0.622596	+	0.452342i	0.853827	−	0.520557i	$-0.174276\pi$
$577$	14.9553	+	10.8656i	0.622596	+	0.452342i	−0.231232	+	0.972899i	$0.574276\pi$
$578$	29.3337	+	21.3122i	1.22012	+	0.886471i
$579$	8.88490	−	27.3449i	0.369244	−	1.13642i
$580$	1.77711	+	5.46937i	0.0737903	+	0.227103i
$581$	15.5687	−	11.3113i	0.645899	−	0.469273i
$582$	5.18561			0.214950
$583$		0			0
$584$	−26.9973			−1.11716
$585$	−6.55754	+	4.76434i	−0.271121	+	0.196981i
$586$	11.6193	+	35.7605i	0.479989	+	1.47725i
$587$	−0.829331	+	2.55242i	−0.0342302	+	0.105350i	−0.966712	−	0.255868i	$-0.917639\pi$
$587$	−0.829331	+	2.55242i	−0.0342302	+	0.105350i	0.932482	+	0.361217i	$0.117639\pi$
$588$	0.611624	+	0.444371i	0.0252229	+	0.0183255i
$589$	−5.46668	−	3.97177i	−0.225251	−	0.163654i
$590$	−3.14957	+	9.69338i	−0.129666	+	0.399070i
$591$	3.81540	+	11.7426i	0.156944	+	0.483025i
$592$	5.54839	−	4.03114i	0.228037	−	0.165679i
$593$	−28.7251			−1.17960			−0.589800	−	0.807550i	$-0.700793\pi$
$593$	−28.7251			−1.17960			−0.589800	+	0.807550i	$0.700793\pi$
$594$		0			0
$595$	−4.67975			−0.191851
$596$	72.5097	−	52.6814i	2.97011	−	2.15791i
$597$	−6.82676	−	21.0106i	−0.279401	−	0.859907i
$598$	−28.3929	+	87.3844i	−1.16107	+	3.57342i
$599$	27.6528	+	20.0909i	1.12986	+	0.820892i	0.985675	−	0.168658i	$-0.0539434\pi$
$599$	27.6528	+	20.0909i	1.12986	+	0.820892i	0.144187	+	0.989551i	$0.453943\pi$
$600$	−8.20401	−	5.96056i	−0.334927	−	0.243339i
$601$	−10.0299	+	30.8687i	−0.409126	+	1.25916i	0.508274	+	0.861196i	$0.330284\pi$
$601$	−10.0299	+	30.8687i	−0.409126	+	1.25916i	−0.917400	+	0.397966i	$0.869716\pi$
$602$	−8.08675	−	24.8885i	−0.329591	−	1.01438i
$603$	4.54197	−	3.29994i	0.184964	−	0.134384i
$604$	84.1276			3.42310
$605$		0			0
$606$	−11.9973			−0.487359
$607$	−4.32397	+	3.14155i	−0.175505	+	0.127512i	−0.672070	−	0.740488i	$-0.734594\pi$
$607$	−4.32397	+	3.14155i	−0.175505	+	0.127512i	0.496565	+	0.868000i	$0.334594\pi$
$608$	−5.18590	−	15.9606i	−0.210316	−	0.647286i
$609$	−1.27907	+	3.93658i	−0.0518306	+	0.159518i
$610$	−6.81928	−	4.95450i	−0.276104	−	0.200602i
$611$	36.2522	+	26.3387i	1.46661	+	1.06555i
$612$	−3.24323	+	9.98164i	−0.131100	+	0.403484i
$613$	−9.33404	−	28.7272i	−0.376998	−	1.16028i	−0.942121	−	0.335274i	$-0.891171\pi$
$613$	−9.33404	−	28.7272i	−0.376998	−	1.16028i	0.565122	−	0.825007i	$-0.308829\pi$
$614$	−21.8539	+	15.8778i	−0.881953	+	0.640777i
$615$	7.36831			0.297119
$616$		0			0
$617$	0.973697			0.0391996			0.0195998	−	0.999808i	$-0.493761\pi$
$617$	0.973697			0.0391996			0.0195998	+	0.999808i	$0.493761\pi$
$618$	14.1461	−	10.2778i	0.569041	−	0.413432i
$619$	0.562897	+	1.73242i	0.0226247	+	0.0696318i	0.961731	−	0.273994i	$-0.0883448\pi$
$619$	0.562897	+	1.73242i	0.0226247	+	0.0696318i	−0.939107	+	0.343626i	$0.888345\pi$
$620$	−6.88921	+	21.2028i	−0.276677	+	0.851525i
$621$	23.7224	+	17.2353i	0.951948	+	0.691630i
$622$	40.6547	+	29.5373i	1.63010	+	1.18434i
$623$	−2.79625	+	8.60598i	−0.112029	+	0.344791i
$624$	−28.1060	−	86.5013i	−1.12514	−	3.46282i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−39.2884			−1.57028
$627$		0			0
$628$	−102.073			−4.07316
$629$	0.980836	−	0.712619i	0.0391085	−	0.0284140i
$630$	2.56297	+	7.88801i	0.102111	+	0.314266i
$631$	−9.99882	+	30.7732i	−0.398047	+	1.22506i	0.528517	+	0.848923i	$0.322748\pi$
$631$	−9.99882	+	30.7732i	−0.398047	+	1.22506i	−0.926563	+	0.376139i	$0.877252\pi$
$632$	92.6820	+	67.3374i	3.68669	+	2.67854i
$633$	−16.0795	−	11.6824i	−0.639102	−	0.464335i
$634$	9.87437	−	30.3902i	0.392161	−	1.20695i
$635$	−3.80489	−	11.7102i	−0.150992	−	0.464707i
$636$	−75.6821	+	54.9863i	−3.00099	+	2.18035i
$637$	0.777208			0.0307941
$638$		0			0
$639$	−4.67975			−0.185128
$640$	−1.96085	+	1.42464i	−0.0775096	+	0.0563140i
$641$	−4.25484	−	13.0951i	−0.168056	−	0.517224i	0.831192	−	0.555985i	$-0.187659\pi$
$641$	−4.25484	−	13.0951i	−0.168056	−	0.517224i	−0.999249	+	0.0387611i	$0.987659\pi$
$642$	7.67553	−	23.6229i	0.302929	−	0.932320i
$643$	−26.0188	−	18.9038i	−1.02608	−	0.745493i	−0.0585622	−	0.998284i	$-0.518652\pi$
$643$	−26.0188	−	18.9038i	−1.02608	−	0.745493i	−0.967521	+	0.252791i	$0.918652\pi$
$644$	53.9648	+	39.2077i	2.12651	+	1.54500i
$645$	1.57387	−	4.84386i	0.0619709	−	0.190727i
$646$	−2.14093	−	6.58911i	−0.0842339	−	0.259245i
$647$	−15.7607	+	11.4508i	−0.619617	+	0.450178i	−0.852788	−	0.522257i	$-0.825090\pi$
$647$	−15.7607	+	11.4508i	−0.619617	+	0.450178i	0.233170	+	0.972436i	$0.425090\pi$
$648$	−29.7774			−1.16977
$649$		0			0
$650$	−17.6535			−0.692425
$651$	−12.9815	+	9.43165i	−0.508787	+	0.369655i
$652$	14.2719	+	43.9243i	0.558929	+	1.72021i
$653$	0.240928	−	0.741499i	0.00942823	−	0.0290171i	−0.946232	−	0.323490i	$-0.895144\pi$
$653$	0.240928	−	0.741499i	0.00942823	−	0.0290171i	0.955660	+	0.294472i	$0.0951439\pi$
$654$	30.2732	+	21.9948i	1.18378	+	0.860064i
$655$	−15.7841	−	11.4678i	−0.616734	−	0.448084i
$656$	17.1452	−	52.7675i	0.669408	−	2.06023i
$657$	1.32797	+	4.08708i	0.0518092	+	0.159452i
$658$	37.0947	−	26.9508i	1.44610	−	1.05065i
$659$	−28.1929			−1.09824			−0.549119	−	0.835744i	$-0.685037\pi$
$659$	−28.1929			−1.09824			−0.549119	+	0.835744i	$0.685037\pi$
$660$		0			0
$661$	1.70340			0.0662547			0.0331274	−	0.999451i	$-0.489453\pi$
$661$	1.70340			0.0662547			0.0331274	+	0.999451i	$0.489453\pi$
$662$	33.6067	−	24.4167i	1.30616	−	0.948982i
$663$	−4.96854	−	15.2916i	−0.192962	−	0.593876i
$664$	17.1532	−	52.7922i	0.665674	−	2.04873i
$665$	−3.14261	−	2.28324i	−0.121865	−	0.0885403i
$666$	−1.73834	−	1.26298i	−0.0673593	−	0.0489394i
$667$	1.89362	−	5.82796i	0.0733213	−	0.225660i
$668$	−14.2622	−	43.8947i	−0.551823	−	1.69834i
$669$	−25.3682	+	18.4311i	−0.980792	+	0.712587i
$670$	12.2274			0.472385
$671$		0			0
$672$	−39.8515			−1.53731
$673$	−8.90278	+	6.46825i	−0.343177	+	0.249333i	−0.746001	−	0.665945i	$-0.768029\pi$
$673$	−8.90278	+	6.46825i	−0.343177	+	0.249333i	0.402824	+	0.915277i	$0.368029\pi$
$674$	5.45522	+	16.7894i	0.210127	+	0.646705i
$675$	−1.74095	+	5.35808i	−0.0670091	+	0.206233i
$676$	−127.510	−	92.6413i	−4.90422	−	3.56313i
$677$	17.3055	+	12.5732i	0.665105	+	0.483227i	0.868383	−	0.495894i	$-0.165160\pi$
$677$	17.3055	+	12.5732i	0.665105	+	0.483227i	−0.203278	+	0.979121i	$0.565160\pi$
$678$	−14.9584	+	46.0371i	−0.574473	+	1.76805i
$679$	−1.19596	−	3.68079i	−0.0458968	−	0.141256i
$680$	−10.9207	+	7.93432i	−0.418788	+	0.304267i
$681$	−3.51561			−0.134718
$682$		0			0
$683$	34.0959			1.30464			0.652321	−	0.757942i	$-0.273795\pi$
$683$	34.0959			1.30464			0.652321	+	0.757942i	$0.273795\pi$
$684$	−7.04796	+	5.12064i	−0.269486	+	0.195793i
$685$	−2.64649	−	8.14507i	−0.101117	−	0.311207i
$686$	15.1377	−	46.5891i	0.577960	−	1.77878i
$687$	23.8873	+	17.3551i	0.911358	+	0.662140i
$688$	−31.0267	−	22.5422i	−1.18288	−	0.859414i
$689$	−29.7186	+	91.4644i	−1.13219	+	3.48452i
$690$	5.65433	+	17.4022i	0.215257	+	0.662492i
$691$	−37.4736	+	27.2261i	−1.42556	+	1.03573i	−0.434739	+	0.900556i	$0.643160\pi$
$691$	−37.4736	+	27.2261i	−1.42556	+	1.03573i	−0.990822	+	0.135175i	$0.956840\pi$
$692$	−44.3651			−1.68651
$693$		0			0
$694$	87.9077			3.33693
$695$	−1.60480	+	1.16595i	−0.0608734	+	0.0442271i
$696$	3.68946	+	11.3550i	0.139849	+	0.430410i
$697$	3.03091	−	9.32818i	0.114804	−	0.353330i
$698$	−48.3433	−	35.1235i	−1.82982	−	1.32944i
$699$	−5.79359	−	4.20929i	−0.219134	−	0.159210i
$700$	−3.96038	+	12.1888i	−0.149688	+	0.460693i
$701$	13.4004	+	41.2423i	0.506127	+	1.55770i	0.798868	+	0.601507i	$0.205433\pi$
$701$	13.4004	+	41.2423i	0.506127	+	1.55770i	−0.292741	+	0.956192i	$0.594567\pi$
$702$	−80.4619	+	58.4590i	−3.03684	+	2.20639i
$703$	1.00635			0.0379552
$704$		0			0
$705$	8.92375			0.336088
$706$	32.8209	−	23.8458i	1.23523	−	0.897447i
$707$	2.76696	+	8.51582i	0.104062	+	0.320271i
$708$	−7.85596	+	24.1782i	−0.295245	+	0.908671i
$709$	−15.5157	−	11.2728i	−0.582703	−	0.423359i	0.256994	−	0.966413i	$-0.417268\pi$
$709$	−15.5157	−	11.2728i	−0.582703	−	0.423359i	−0.839698	+	0.543054i	$0.817268\pi$
$710$	−8.24568	−	5.99084i	−0.309455	−	0.224832i
$711$	5.63515	−	17.3432i	0.211335	−	0.650422i
$712$	8.06574	+	24.8238i	0.302276	+	0.930311i
$713$	19.2187	−	13.9632i	0.719746	−	0.522926i
$714$	−16.4522			−0.615708
$715$		0			0
$716$	−67.2543			−2.51341
$717$	13.6386	−	9.90906i	0.509345	−	0.370061i
$718$	7.77243	+	23.9211i	0.290065	+	0.892727i
$719$	−9.97938	+	30.7134i	−0.372168	+	1.14542i	0.573202	+	0.819414i	$0.305701\pi$
$719$	−9.97938	+	30.7134i	−0.372168	+	1.14542i	−0.945369	+	0.326001i	$0.894299\pi$
$720$	9.83342	+	7.14440i	0.366470	+	0.266256i
$721$	−10.5578	−	7.67068i	−0.393192	−	0.285671i
$722$	−13.6282	+	41.9434i	−0.507191	+	1.56097i
$723$	−1.77495	−	5.46275i	−0.0660113	−	0.203162i
$724$	94.2787	−	68.4975i	3.50384	−	2.54569i
$725$	1.17737			0.0437264
$726$		0			0
$727$	−40.8622			−1.51550			−0.757748	−	0.652548i	$-0.773700\pi$
$727$	−40.8622			−1.51550			−0.757748	+	0.652548i	$0.773700\pi$
$728$	−108.091	+	78.5330i	−4.00613	+	2.91063i
$729$	8.46268	+	26.0455i	0.313433	+	0.964646i
$730$	−2.89225	+	8.90142i	−0.107047	+	0.329456i
$731$	−5.48486	−	3.98498i	−0.202865	−	0.147390i
$732$	−17.0093	−	12.3580i	−0.628682	−	0.456764i
$733$	−3.06673	+	9.43842i	−0.113272	+	0.348616i	−0.991583	−	0.129475i	$-0.958671\pi$
$733$	−3.06673	+	9.43842i	−0.113272	+	0.348616i	0.878311	+	0.478091i	$0.158671\pi$
$734$	−8.78798	−	27.0466i	−0.324370	−	0.998309i
$735$	0.125218	−	0.0909760i	0.00461873	−	0.00335570i
$736$	58.9987			2.17472
$737$		0			0
$738$	−17.3832			−0.639883
$739$	−26.9989	+	19.6159i	−0.993172	+	0.721582i	−0.960614	−	0.277888i	$-0.910366\pi$
$739$	−26.9989	+	19.6159i	−0.993172	+	0.721582i	−0.0325588	+	0.999470i	$0.510366\pi$
$740$	−1.02601	−	3.15774i	−0.0377170	−	0.116081i
$741$	4.12419	−	12.6930i	0.151506	−	0.466287i
$742$	79.6125	+	57.8418i	2.92267	+	2.12344i
$743$	−3.08005	−	2.23779i	−0.112996	−	0.0820964i	0.529852	−	0.848090i	$-0.322247\pi$
$743$	−3.08005	−	2.23779i	−0.112996	−	0.0820964i	−0.642848	+	0.765994i	$0.722247\pi$
$744$	−14.3027	+	44.0193i	−0.524364	+	1.61383i
$745$	−5.67025	−	17.4512i	−0.207742	−	0.639363i
$746$	21.2722	−	15.4552i	0.778832	−	0.565855i
$747$	−8.83587			−0.323287
$748$		0			0
$749$	−18.5379			−0.677361
$750$	−2.84419	+	2.06642i	−0.103855	+	0.0754551i
$751$	6.95578	+	21.4077i	0.253820	+	0.781177i	0.994060	+	0.108835i	$0.0347119\pi$
$751$	6.95578	+	21.4077i	0.253820	+	0.781177i	−0.740240	+	0.672343i	$0.765288\pi$
$752$	20.7645	−	63.9066i	0.757204	−	2.33043i
$753$	−10.9080	−	7.92514i	−0.397511	−	0.288808i
$754$	16.8151	+	12.2169i	0.612370	+	0.444913i
$755$	5.32234	−	16.3805i	0.193700	−	0.596146i
$756$	22.3121	+	68.6695i	0.811482	+	2.49748i
$757$	27.2580	−	19.8041i	0.990708	−	0.719792i	0.0306320	−	0.999531i	$-0.490248\pi$
$757$	27.2580	−	19.8041i	0.990708	−	0.719792i	0.960076	+	0.279739i	$0.0902480\pi$
$758$	10.9985			0.399483
$759$		0			0
$760$	−11.2047			−0.406438
$761$	−15.1868	+	11.0339i	−0.550521	+	0.399977i	−0.827977	−	0.560761i	$-0.810509\pi$
$761$	−15.1868	+	11.0339i	−0.550521	+	0.399977i	0.277457	+	0.960738i	$0.410509\pi$
$762$	−13.3765	−	41.1686i	−0.484580	−	1.49138i
$763$	8.63015	−	26.5609i	0.312433	−	0.961568i
$764$	−63.4747	−	46.1171i	−2.29643	−	1.66846i
$765$	1.73834	+	1.26298i	0.0628498	+	0.0456631i
$766$	15.6032	−	48.0217i	0.563766	−	1.73509i
$767$	8.07625	+	24.8561i	0.291616	+	0.897503i
$768$	13.8413	−	10.0563i	0.499457	−	0.362876i
$769$	−21.5618			−0.777539			−0.388770	−	0.921335i	$-0.627100\pi$
$769$	−21.5618			−0.777539			−0.388770	+	0.921335i	$0.627100\pi$
$770$		0			0
$771$	−4.24134			−0.152748
$772$	−84.7973	+	61.6088i	−3.05192	+	2.21735i
$773$	−7.22579	−	22.2387i	−0.259894	−	0.799871i	−0.992826	−	0.119569i	$-0.961849\pi$
$773$	−7.22579	−	22.2387i	−0.259894	−	0.799871i	0.732932	−	0.680302i	$-0.238151\pi$
$774$	−3.71303	+	11.4275i	−0.133462	+	0.410754i
$775$	3.69255	+	2.68279i	0.132640	+	0.0963687i
$776$	−9.03151	−	6.56178i	−0.324212	−	0.235554i
$777$	0.738473	−	2.27279i	0.0264926	−	0.0815357i
$778$	−23.0451	−	70.9256i	−0.826208	−	2.54281i
$779$	6.58656	−	4.78541i	0.235988	−	0.171455i
$780$	−44.0329			−1.57663
$781$		0			0
$782$	24.3569			0.870999
$783$	5.36627	−	3.89883i	0.191775	−	0.139333i
$784$	−0.360150	−	1.10843i	−0.0128625	−	0.0395867i
$785$	−6.45766	+	19.8746i	−0.230484	+	0.709357i
$786$	−55.4906	−	40.3163i	−1.97928	−	1.43803i
$787$	−20.3022	−	14.7504i	−0.723696	−	0.525796i	0.163867	−	0.986482i	$-0.447603\pi$
$787$	−20.3022	−	14.7504i	−0.723696	−	0.525796i	−0.887563	+	0.460686i	$0.847603\pi$
$788$	13.9089	−	42.8073i	0.495485	−	1.52495i
$789$	9.26139	+	28.5036i	0.329714	+	1.01476i
$790$	32.1312	−	23.3447i	1.14318	−	0.830567i
$791$	36.1274			1.28454
$792$		0			0
$793$	−21.6142			−0.767542
$794$	47.0787	−	34.2046i	1.67076	−	1.21388i
$795$	5.91833	+	18.2148i	0.209902	+	0.646011i
$796$	−24.8868	+	76.5936i	−0.882088	+	2.71479i
$797$	9.76990	+	7.09824i	0.346067	+	0.251433i	0.747217	−	0.664580i	$-0.231389\pi$
$797$	9.76990	+	7.09824i	0.346067	+	0.251433i	−0.401150	+	0.916012i	$0.631389\pi$
$798$	−11.0482	−	8.02699i	−0.391102	−	0.284152i
$799$	3.67073	−	11.2973i	0.129861	−	0.399671i
$800$	3.50289	+	10.7808i	0.123846	+	0.381158i
$801$	3.36129	−	2.44212i	0.118765	−	0.0862880i
$802$	57.9233			2.04534
$803$		0			0
$804$	30.4987			1.07561
$805$	11.0482	−	8.02699i	0.389398	−	0.282914i
$806$	24.8989	+	76.6309i	0.877026	+	2.69921i
$807$	6.61383	−	20.3553i	0.232818	−	0.716539i
$808$	20.8952	+	15.1812i	0.735090	+	0.534074i
$809$	−7.37170	−	5.35585i	−0.259175	−	0.188302i	0.450608	−	0.892722i	$-0.351207\pi$
$809$	−7.37170	−	5.35585i	−0.259175	−	0.188302i	−0.709783	+	0.704420i	$0.751207\pi$
$810$	−3.19007	+	9.81803i	−0.112088	+	0.344971i
$811$	0.923957	+	2.84365i	0.0324445	+	0.0998540i	0.965967	−	0.258664i	$-0.0832822\pi$
$811$	0.923957	+	2.84365i	0.0324445	+	0.0998540i	−0.933523	+	0.358518i	$0.883282\pi$
$812$	12.2074	−	8.86922i	0.428397	−	0.311249i
$813$	−20.9556			−0.734946
$814$		0			0
$815$	9.45539			0.331208
$816$	−19.5060	+	14.1719i	−0.682845	+	0.496116i
$817$	−1.73900	−	5.35210i	−0.0608400	−	0.187246i
$818$	20.0037	−	61.5651i	0.699413	−	2.15257i
$819$	17.2059	+	12.5008i	0.601222	+	0.436814i
$820$	−21.7310	−	15.7885i	−0.758879	−	0.551358i
$821$	10.8989	−	33.5434i	0.380375	−	1.17067i	−0.559405	−	0.828894i	$-0.688970\pi$
$821$	10.8989	−	33.5434i	0.380375	−	1.17067i	0.939780	−	0.341779i	$-0.111030\pi$
$822$	−9.30404	−	28.6349i	−0.324516	−	0.998757i
$823$	−12.5863	+	9.14451i	−0.438732	+	0.318757i	−0.785131	−	0.619330i	$-0.787404\pi$
$823$	−12.5863	+	9.14451i	−0.438732	+	0.318757i	0.346399	+	0.938087i	$0.387404\pi$
$824$	−37.6429			−1.31135
$825$		0			0
$826$	26.7427			0.930496
$827$	8.51840	−	6.18898i	0.296214	−	0.215212i	−0.429745	−	0.902950i	$-0.641396\pi$
$827$	8.51840	−	6.18898i	0.296214	−	0.215212i	0.725958	+	0.687739i	$0.241396\pi$
$828$	−9.46431	−	29.1281i	−0.328907	−	1.01227i
$829$	7.91852	−	24.3707i	0.275022	−	0.846430i	−0.714192	−	0.699950i	$-0.753206\pi$
$829$	7.91852	−	24.3707i	0.275022	−	0.846430i	0.989214	−	0.146480i	$-0.0467944\pi$
$830$	−15.5687	−	11.3113i	−0.540398	−	0.392622i
$831$	−25.8894	−	18.8097i	−0.898093	−	0.652503i
$832$	−19.8850	+	61.1999i	−0.689390	+	2.12172i
$833$	−0.0636668	−	0.195946i	−0.00220592	−	0.00678913i
$834$	−5.64184	+	4.09904i	−0.195361	+	0.141938i
$835$	−9.44902			−0.326997
$836$		0			0
$837$	25.7141			0.888809
$838$	−37.4734	+	27.2260i	−1.29450	+	0.940507i
$839$	8.07332	+	24.8471i	0.278722	+	0.857818i	0.988211	+	0.153101i	$0.0489261\pi$
$839$	8.07332	+	24.8471i	0.278722	+	0.857818i	−0.709488	+	0.704717i	$0.751074\pi$
$840$	−8.22218	+	25.3053i	−0.283692	+	0.873114i
$841$	22.3400	+	16.2310i	0.770346	+	0.559689i
$842$	−3.23710	−	2.35189i	−0.111558	−	0.0810516i
$843$	5.06951	−	15.6023i	0.174603	−	0.537373i
$844$	22.3898	+	68.9087i	0.770689	+	2.37194i
$845$	−26.1051	+	18.9664i	−0.898042	+	0.652465i
$846$	−21.0527			−0.723806
$847$		0			0
$848$	144.215			4.95235
$849$	22.6050	−	16.4235i	0.775801	−	0.563652i
$850$	1.44612	+	4.45071i	0.0496016	+	0.152658i
$851$	−1.09328	+	3.36478i	−0.0374772	+	0.115343i
$852$	−20.5672	−	14.9429i	−0.704620	−	0.511936i
$853$	−2.22876	−	1.61929i	−0.0763112	−	0.0554433i	0.548976	−	0.835838i	$-0.315018\pi$
$853$	−2.22876	−	1.61929i	−0.0763112	−	0.0554433i	−0.625287	+	0.780395i	$0.715018\pi$
$854$	−6.83437	+	21.0340i	−0.233867	+	0.719770i
$855$	0.551150	+	1.69626i	0.0188489	+	0.0580110i
$856$	−43.2601	+	31.4303i	−1.47860	+	1.07426i
$857$	20.3164			0.693997			0.346998	−	0.937866i	$-0.387201\pi$
$857$	20.3164			0.693997			0.346998	+	0.937866i	$0.387201\pi$
$858$		0			0
$859$	22.6249			0.771951			0.385975	−	0.922509i	$-0.373865\pi$
$859$	22.6249			0.771951			0.385975	+	0.922509i	$0.373865\pi$
$860$	−15.0209	+	10.9133i	−0.512209	+	0.372142i
$861$	−5.97429	−	18.3870i	−0.203603	−	0.626626i
$862$	−13.5805	+	41.7965i	−0.462553	+	1.42359i
$863$	−34.8758	−	25.3387i	−1.18719	−	0.862541i	−0.194222	−	0.980958i	$-0.562218\pi$
$863$	−34.8758	−	25.3387i	−1.18719	−	0.862541i	−0.992964	+	0.118417i	$0.962218\pi$
$864$	51.6660	+	37.5375i	1.75771	+	1.27705i
$865$	−2.80676	+	8.63831i	−0.0954326	+	0.293711i
$866$	6.06081	+	18.6533i	0.205955	+	0.633863i
$867$	14.9795	−	10.8832i	0.508730	−	0.369614i
$868$	58.4955			1.98547
$869$		0			0
$870$	4.13917			0.140331
$871$	25.3658	−	18.4293i	0.859488	−	0.624455i
$872$	−24.8935	−	76.6144i	−0.843002	−	2.59449i
$873$	−0.549125	+	1.69003i	−0.0185851	+	0.0571989i
$874$	16.3565	+	11.8837i	0.553265	+	0.401971i
$875$	2.12272	+	1.54225i	0.0717611	+	0.0521375i
$876$	−7.21412	+	22.2028i	−0.243742	+	0.750162i
$877$	−5.15603	−	15.8686i	−0.174107	−	0.535845i	0.825485	−	0.564424i	$-0.190902\pi$
$877$	−5.15603	−	15.8686i	−0.174107	−	0.535845i	−0.999592	+	0.0285790i	$0.990902\pi$
$878$	−37.0596	+	26.9254i	−1.25070	+	0.908688i
$879$	19.2011			0.647638
$880$		0			0
$881$	−43.5116			−1.46594			−0.732972	−	0.680259i	$-0.761867\pi$
$881$	−43.5116			−1.46594			−0.732972	+	0.680259i	$0.761867\pi$
$882$	−0.295411	+	0.214628i	−0.00994700	+	0.00722692i
$883$	−8.34334	−	25.6782i	−0.280776	−	0.864139i	−0.987633	−	0.156783i	$-0.949888\pi$
$883$	−8.34334	−	25.6782i	−0.280776	−	0.864139i	0.706857	−	0.707356i	$-0.250112\pi$
$884$	−18.1127	+	55.7450i	−0.609195	+	1.87491i
$885$	4.21071	+	3.05926i	0.141542	+	0.102836i
$886$	31.1696	+	22.6460i	1.04716	+	0.760808i
$887$	−7.08894	+	21.8175i	−0.238023	+	0.732560i	0.758683	+	0.651460i	$0.225843\pi$
$887$	−7.08894	+	21.8175i	−0.238023	+	0.732560i	−0.996706	+	0.0810998i	$0.974157\pi$
$888$	−2.13011	−	6.55581i	−0.0714819	−	0.219999i
$889$	−26.1368	+	18.9895i	−0.876601	+	0.636888i
$890$	9.04886			0.303318
$891$		0			0
$892$	114.311			3.82740
$893$	7.97696	−	5.79560i	0.266939	−	0.193942i
$894$	−19.9344	−	61.3517i	−0.666705	−	2.05191i
$895$	−4.25484	+	13.0951i	−0.142224	+	0.437720i
$896$	5.14495	+	3.73802i	0.171881	+	0.124879i
$897$	37.9590	+	27.5788i	1.26741	+	0.920830i
$898$	−1.05996	+	3.26222i	−0.0353713	+	0.108862i
$899$	−1.66059	−	5.11078i	−0.0553838	−	0.170454i
$900$	4.76065	−	3.45881i	0.158688	−	0.115294i
$901$	25.4941			0.849331
$902$		0			0
$903$	−13.3635			−0.444710
$904$	84.3068	−	61.2525i	2.80400	−	2.03723i
$905$	−7.37258	−	22.6905i	−0.245073	−	0.754257i
$906$	18.7113	−	57.5873i	0.621640	−	1.91321i
$907$	−33.7633	−	24.5305i	−1.12109	−	0.814521i	−0.136718	−	0.990610i	$-0.543655\pi$
$907$	−33.7633	−	24.5305i	−1.12109	−	0.814521i	−0.984374	+	0.176089i	$0.943655\pi$
$908$	10.3684	+	7.53309i	0.344088	+	0.249994i
$909$	1.27045	−	3.91004i	0.0421381	−	0.129688i
$910$	14.3136	+	44.0526i	0.474490	+	1.46033i
$911$	31.3308	−	22.7632i	1.03804	−	0.754178i	0.0681358	−	0.997676i	$-0.478295\pi$
$911$	31.3308	−	22.7632i	1.03804	−	0.754178i	0.969901	+	0.243498i	$0.0782949\pi$
$912$	−20.0134			−0.662708
$913$		0			0
$914$	26.7427			0.884569
$915$	−3.48231	+	2.53005i	−0.115122	+	0.0836408i
$916$	−33.2618	−	102.369i	−1.09900	−	3.38238i
$917$	−15.8190	+	48.6859i	−0.522390	+	1.60775i
$918$	21.3296	+	15.4969i	0.703983	+	0.511474i
$919$	2.30729	+	1.67634i	0.0761103	+	0.0552974i	0.625190	−	0.780473i	$-0.285022\pi$
$919$	2.30729	+	1.67634i	0.0761103	+	0.0552974i	−0.549079	+	0.835770i	$0.685022\pi$
$920$	12.1726	−	37.4635i	0.401320	−	1.23513i
$921$	4.26269	+	13.1192i	0.140460	+	0.432293i
$922$	8.74944	−	6.35684i	0.288147	−	0.209351i
$923$	−26.1353			−0.860253
$924$		0			0
$925$	−0.679754			−0.0223502
$926$	−69.5453	+	50.5276i	−2.28540	+	1.66044i
$927$	1.85162	+	5.69869i	0.0608151	+	0.187170i
$928$	4.12419	−	12.6930i	0.135383	−	0.416667i
$929$	10.7020	+	7.77545i	0.351121	+	0.255104i	0.749339	−	0.662187i	$-0.230371\pi$
$929$	10.7020	+	7.77545i	0.351121	+	0.255104i	−0.398218	+	0.917291i	$0.630371\pi$
$930$	12.9815	+	9.43165i	0.425682	+	0.309276i
$931$	0.0528474	−	0.162647i	0.00173200	−	0.00533055i
$932$	8.06727	+	24.8285i	0.264252	+	0.813284i
$933$	20.7606	−	15.0834i	0.679671	−	0.493810i
$934$	99.4810			3.25512
$935$		0			0
$936$	61.3462			2.00516
$937$	−1.35959	+	0.987799i	−0.0444158	+	0.0322700i	−0.609772	−	0.792577i	$-0.708739\pi$
$937$	−1.35959	+	0.987799i	−0.0444158	+	0.0322700i	0.565356	+	0.824847i	$0.308739\pi$
$938$	−9.91405	−	30.5123i	−0.323705	−	0.996262i
$939$	−6.19978	+	19.0810i	−0.202322	+	0.622684i
$940$	−26.3183	−	19.1214i	−0.858410	−	0.623671i
$941$	11.8805	+	8.63170i	0.387294	+	0.281385i	0.764346	−	0.644807i	$-0.223062\pi$
$941$	11.8805	+	8.63170i	0.387294	+	0.281385i	−0.377052	+	0.926192i	$0.623062\pi$
$942$	−22.7026	+	69.8715i	−0.739692	+	2.27654i
$943$	8.84471	+	27.2212i	0.288024	+	0.886445i
$944$	31.7065	−	23.0361i	1.03196	−	0.749762i
$945$	14.7822			0.480865
$946$		0			0
$947$	17.6535			0.573660			0.286830	−	0.957981i	$-0.407399\pi$
$947$	17.6535			0.573660			0.286830	+	0.957981i	$0.407399\pi$
$948$	80.1447	−	58.2286i	2.60298	−	1.89118i
$949$	7.41641	+	22.8254i	0.240747	+	0.740942i
$950$	−1.20037	+	3.69436i	−0.0389452	+	0.119861i
$951$	−13.2012	−	9.59124i	−0.428079	−	0.311017i
$952$	28.6539	+	20.8183i	0.928680	+	0.674725i
$953$	6.72663	−	20.7025i	0.217897	−	0.670618i	−0.781038	−	0.624483i	$-0.785310\pi$
$953$	6.72663	−	20.7025i	0.217897	−	0.670618i	0.998935	−	0.0461349i	$-0.0146904\pi$
$954$	−13.9624	−	42.9718i	−0.452049	−	1.39126i
$955$	−12.9952	+	9.44154i	−0.420514	+	0.305521i
$956$	−61.4564			−1.98764
$957$		0			0
$958$	−16.9500			−0.547631
$959$	−18.1795	+	13.2082i	−0.587047	+	0.426514i
$960$	3.96002	+	12.1877i	0.127809	+	0.393356i
$961$	−3.14200	+	9.67009i	−0.101355	+	0.311938i
$962$	−9.70820	−	7.05342i	−0.313005	−	0.227411i
$963$	6.88609	+	5.00304i	0.221901	+	0.161221i
$964$	−6.47055	+	19.9143i	−0.208402	+	0.641396i
$965$	6.63113	+	20.4085i	0.213464	+	0.656974i
$966$	38.8412	−	28.2197i	1.24969	−	0.907956i
$967$	−14.0684			−0.452409			−0.226204	−	0.974080i	$-0.572632\pi$
$967$	−14.0684			−0.452409			−0.226204	+	0.974080i	$0.572632\pi$
$968$		0			0
$969$	−3.53793			−0.113655
$970$	−3.13107	+	2.27485i	−0.100533	+	0.0730411i
$971$	−4.55255	−	14.0113i	−0.146098	−	0.449644i	0.851052	−	0.525081i	$-0.175965\pi$
$971$	−4.55255	−	14.0113i	−0.146098	−	0.449644i	−0.997151	+	0.0754367i	$0.975965\pi$
$972$	17.5539	−	54.0253i	0.563041	−	1.73286i
$973$	4.21071	+	3.05926i	0.134989	+	0.0980755i
$974$	−92.2571	−	67.0287i	−2.95611	−	2.14774i
$975$	−2.78574	+	8.57364i	−0.0892152	+	0.274576i
$976$	10.0158	+	30.8254i	0.320597	+	0.986697i
$977$	−10.6320	+	7.72457i	−0.340146	+	0.247131i	−0.744724	−	0.667373i	$-0.767419\pi$
$977$	−10.6320	+	7.72457i	−0.340146	+	0.247131i	0.404577	+	0.914504i	$0.367419\pi$
$978$	33.2415			1.06294
$979$		0			0
$980$	−0.564237			−0.0180239
$981$	−10.3740	+	7.53718i	−0.331218	+	0.240644i
$982$	−4.42190	−	13.6092i	−0.141108	−	0.434287i
$983$	5.69078	−	17.5144i	0.181508	−	0.558623i	−0.818363	−	0.574702i	$-0.805118\pi$
$983$	5.69078	−	17.5144i	0.181508	−	0.558623i	0.999871	+	0.0160784i	$0.00511815\pi$
$984$	−45.1159	−	32.7786i	−1.43824	−	1.04494i
$985$	−7.45504	−	5.41640i	−0.237537	−	0.172581i
$986$	1.70262	−	5.24012i	0.0542225	−	0.166880i
$987$	−7.23544	−	22.2684i	−0.230307	−	0.708811i
$988$	−39.3612	+	28.5976i	−1.25225	+	0.909809i
$989$	19.7842			0.629101
$990$		0			0
$991$	44.3591			1.40911			0.704557	−	0.709647i	$-0.251146\pi$
$991$	44.3591			1.40911			0.704557	+	0.709647i	$0.251146\pi$
$992$	41.8572	−	30.4110i	1.32897	−	0.965551i
$993$	−6.55511	−	20.1745i	−0.208020	−	0.640220i
$994$	−8.26394	+	25.4338i	−0.262116	+	0.806711i
$995$	13.3391	+	9.69139i	0.422877	+	0.307238i
$996$	−38.8330	−	28.2138i	−1.23047	−	0.893989i
$997$	15.6032	−	48.0217i	0.494158	−	1.52086i	−0.324107	−	0.946020i	$-0.605064\pi$
$997$	15.6032	−	48.0217i	0.494158	−	1.52086i	0.818265	−	0.574841i	$-0.194936\pi$
$998$	10.1254	+	31.1626i	0.320513	+	0.986436i
$999$	−3.09822	+	2.25099i	−0.0980233	+	0.0712181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.q.366.1		24
11.2	odd	10		605.2.a.m.1.1	✓	6
11.3	even	5	inner	605.2.g.q.511.6		24
11.4	even	5	inner	605.2.g.q.81.1		24
11.5	even	5	inner	605.2.g.q.251.6		24
11.6	odd	10	inner	605.2.g.q.251.1		24
11.7	odd	10	inner	605.2.g.q.81.6		24
11.8	odd	10	inner	605.2.g.q.511.1		24
11.9	even	5		605.2.a.m.1.6	yes	6
11.10	odd	2	inner	605.2.g.q.366.6		24
33.2	even	10		5445.2.a.bx.1.6		6
33.20	odd	10		5445.2.a.bx.1.1		6
44.31	odd	10		9680.2.a.cw.1.4		6
44.35	even	10		9680.2.a.cw.1.3		6
55.9	even	10		3025.2.a.bg.1.1		6
55.24	odd	10		3025.2.a.bg.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.1	✓	6	11.2	odd	10
605.2.a.m.1.6	yes	6	11.9	even	5
605.2.g.q.81.1		24	11.4	even	5	inner
605.2.g.q.81.6		24	11.7	odd	10	inner
605.2.g.q.251.1		24	11.6	odd	10	inner
605.2.g.q.251.6		24	11.5	even	5	inner
605.2.g.q.366.1		24	1.1	even	1	trivial
605.2.g.q.366.6		24	11.10	odd	2	inner
605.2.g.q.511.1		24	11.8	odd	10	inner
605.2.g.q.511.6		24	11.3	even	5	inner
3025.2.a.bg.1.1		6	55.9	even	10
3025.2.a.bg.1.6		6	55.24	odd	10
5445.2.a.bx.1.1		6	33.20	odd	10
5445.2.a.bx.1.6		6	33.2	even	10
9680.2.a.cw.1.3		6	44.35	even	10
9680.2.a.cw.1.4		6	44.31	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.12272 + 1.54225i) q^{2} +(0.414045 + 1.27430i) q^{3} +(1.50939 - 4.64542i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.84419 - 2.06642i) q^{6} +(-0.810808 + 2.49541i) q^{7} +(2.33876 + 7.19797i) q^{8} +(0.974647 - 0.708122i) q^{9} +O(q^{10})\)	\(q+(-2.12272 + 1.54225i) q^{2} +(0.414045 + 1.27430i) q^{3} +(1.50939 - 4.64542i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-2.84419 - 2.06642i) q^{6} +(-0.810808 + 2.49541i) q^{7} +(2.33876 + 7.19797i) q^{8} +(0.974647 - 0.708122i) q^{9} +2.62383 q^{10} +6.54461 q^{12} +(5.44317 - 3.95469i) q^{13} +(-2.12742 - 6.54753i) q^{14} +(0.414045 - 1.27430i) q^{15} +(-8.16235 - 5.93029i) q^{16} +(-1.44293 - 1.04835i) q^{17} +(-0.976805 + 3.00630i) q^{18} +(-0.457488 - 1.40800i) q^{19} +(-3.95163 + 2.87103i) q^{20} -3.51561 q^{21} +5.20473 q^{23} +(-8.20401 + 5.96056i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-5.45522 + 16.7894i) q^{26} +(4.55786 + 3.31148i) q^{27} +(10.3684 + 7.53309i) q^{28} +(0.363827 - 1.11974i) q^{29} +(1.08638 + 3.34354i) q^{30} +(3.69255 - 2.68279i) q^{31} +11.3356 q^{32} +4.67975 q^{34} +(2.12272 - 1.54225i) q^{35} +(-1.81841 - 5.59648i) q^{36} +(-0.210055 + 0.646484i) q^{37} +(3.14261 + 2.28324i) q^{38} +(7.29317 + 5.29880i) q^{39} +(2.33876 - 7.19797i) q^{40} +(1.69936 + 5.23010i) q^{41} +(7.46266 - 5.42194i) q^{42} +3.80120 q^{43} -1.20473 q^{45} +(-11.0482 + 8.02699i) q^{46} +(2.05809 + 6.33415i) q^{47} +(4.17739 - 12.8567i) q^{48} +(0.0934546 + 0.0678988i) q^{49} +(-2.12272 - 1.54225i) q^{50} +(0.738473 - 2.27279i) q^{51} +(-10.1554 - 31.2550i) q^{52} +(-11.5640 + 8.40177i) q^{53} -14.7822 q^{54} -19.8582 q^{56} +(1.60480 - 1.16595i) q^{57} +(0.954620 + 2.93802i) q^{58} +(-1.20037 + 3.69436i) q^{59} +(-5.29470 - 3.84682i) q^{60} +(-2.59898 - 1.88827i) q^{61} +(-3.70072 + 11.3896i) q^{62} +(0.976805 + 3.00630i) q^{63} +(-7.73763 + 5.62172i) q^{64} -6.72812 q^{65} +4.66012 q^{67} +(-7.04796 + 5.12064i) q^{68} +(2.15499 + 6.63238i) q^{69} +(-2.12742 + 6.54753i) q^{70} +(-3.14261 - 2.28324i) q^{71} +(7.37651 + 5.35935i) q^{72} +(-1.10230 + 3.39253i) q^{73} +(-0.551150 - 1.69626i) q^{74} +(-1.08398 + 0.787560i) q^{75} -7.23130 q^{76} -23.6535 q^{78} +(12.2459 - 8.89718i) q^{79} +(3.11774 + 9.59541i) q^{80} +(-1.21581 + 3.74187i) q^{81} +(-11.6734 - 8.48121i) q^{82} +(-5.93358 - 4.31100i) q^{83} +(-5.30642 + 16.3315i) q^{84} +(0.551150 + 1.69626i) q^{85} +(-8.06889 + 5.86239i) q^{86} +1.57753 q^{87} +3.44872 q^{89} +(2.55731 - 1.85799i) q^{90} +(5.45522 + 16.7894i) q^{91} +(7.85596 - 24.1782i) q^{92} +(4.94756 + 3.59461i) q^{93} +(-14.1376 - 10.2716i) q^{94} +(-0.457488 + 1.40800i) q^{95} +(4.69344 + 14.4449i) q^{96} +(-1.19332 + 0.866997i) q^{97} -0.303095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9	\( 24 q - 6 q^{3} - 6 q^{4} - 6 q^{5} - 12 q^{9} + 72 q^{12} + 18 q^{14} - 6 q^{15} - 18 q^{16} - 6 q^{20} + 48 q^{23} - 6 q^{25} + 36 q^{26} - 30 q^{27} + 96 q^{34} + 12 q^{36} + 30 q^{42} + 48 q^{45} - 42 q^{47} + 6 q^{48} + 24 q^{49} - 24 q^{53} - 120 q^{56} + 24 q^{58} - 18 q^{60} - 30 q^{64} + 120 q^{67} + 24 q^{69} + 18 q^{70} - 6 q^{75} - 288 q^{78} - 18 q^{80} - 30 q^{81} - 42 q^{82} + 6 q^{86} - 120 q^{89} - 36 q^{91} - 36 q^{92} + 60 q^{93} - 24 q^{97}+O(q^{100}) \) 24 * q - 6 * q^3 - 6 * q^4 - 6 * q^5 - 12 * q^9 + 72 * q^12 + 18 * q^14 - 6 * q^15 - 18 * q^16 - 6 * q^20 + 48 * q^23 - 6 * q^25 + 36 * q^26 - 30 * q^27 + 96 * q^34 + 12 * q^36 + 30 * q^42 + 48 * q^45 - 42 * q^47 + 6 * q^48 + 24 * q^49 - 24 * q^53 - 120 * q^56 + 24 * q^58 - 18 * q^60 - 30 * q^64 + 120 * q^67 + 24 * q^69 + 18 * q^70 - 6 * q^75 - 288 * q^78 - 18 * q^80 - 30 * q^81 - 42 * q^82 + 6 * q^86 - 120 * q^89 - 36 * q^91 - 36 * q^92 + 60 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

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