LMFDB - Embedded newform 605.2.g.q.81.1

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			81.1
Character	$\chi$	$=$	605.81
Dual form			605.2.g.q.366.1

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

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	−0.969984	−	0.243167i	$-0.921814\pi$
$2$	−2.12272	−	1.54225i	−1.50099	−	1.09053i	−0.531007	−	0.847367i	$-0.678186\pi$
$3$	0.414045	−	1.27430i	0.239049	−	0.735717i	−0.757510	−	0.652824i	$-0.773584\pi$
$3$	0.414045	−	1.27430i	0.239049	−	0.735717i	0.996558	−	0.0828927i	$-0.0264159\pi$
$4$	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	−0.979130	−	0.203237i	$-0.934854\pi$
$7$	−0.810808	−	2.49541i	−0.306457	−	0.943177i	0.672673	−	0.739940i	$-0.265146\pi$
$8$	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	0.966327	+	0.257319i	$0.0828390\pi$
$13$	5.44317	+	3.95469i	1.50966	+	1.09683i	0.543336	+	0.839515i	$0.317161\pi$
$14$	−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	−0.748853	−	0.662736i	$-0.769395\pi$
$17$	−1.44293	+	1.04835i	−0.349962	+	0.254262i	0.398891	+	0.916998i	$0.369395\pi$
$18$	−0.976805	−	3.00630i	−0.230235	−	0.708591i
$19$	−0.457488	+	1.40800i	−0.104955	+	0.323018i	−0.989720	−	0.143019i	$-0.954319\pi$
$19$	−0.457488	+	1.40800i	−0.104955	+	0.323018i	0.884765	+	0.466038i	$0.154319\pi$
$20$	−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	0.979137	−	0.203199i	$-0.0651340\pi$
$29$	0.363827	+	1.11974i	0.0675609	+	0.207931i	−0.911576	+	0.411131i	$0.865134\pi$
$30$	1.08638	−	3.34354i	0.198345	−	0.610445i
$31$	3.69255	+	2.68279i	0.663201	+	0.481844i	0.867742	−	0.497014i	$-0.165570\pi$
$31$	3.69255	+	2.68279i	0.663201	+	0.481844i	−0.204542	+	0.978858i	$0.565570\pi$
$32$	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	0.932304	−	0.361675i	$-0.117795\pi$
$37$	−0.210055	−	0.646484i	−0.0345329	−	0.106281i	−0.966837	+	0.255394i	$0.917795\pi$
$38$	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	−0.726206	−	0.687477i	$-0.758718\pi$
$41$	1.69936	−	5.23010i	0.265396	−	0.816804i	0.991602	−	0.129327i	$-0.0412817\pi$
$42$	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	−0.681220	−	0.732079i	$-0.738550\pi$
$47$	2.05809	−	6.33415i	0.300203	−	0.923931i	0.981424	−	0.191853i	$-0.0614496\pi$
$48$	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	−0.906119	−	0.423022i	$-0.860969\pi$
$53$	−11.5640	−	8.40177i	−1.58844	−	1.15407i	−0.682324	−	0.731050i	$-0.739031\pi$
$54$	−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	0.842013	−	0.539458i	$-0.181371\pi$
$59$	−1.20037	−	3.69436i	−0.156275	−	0.480965i	−0.998288	+	0.0584924i	$0.981371\pi$
$60$	−5.29470	+	3.84682i	−0.683543	+	0.496623i
$61$	−2.59898	+	1.88827i	−0.332765	+	0.241768i	−0.741603	−	0.670839i	$-0.765934\pi$
$61$	−2.59898	+	1.88827i	−0.332765	+	0.241768i	0.408838	+	0.912607i	$0.365934\pi$
$62$	−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	−0.758437	−	0.651746i	$-0.774037\pi$
$71$	−3.14261	+	2.28324i	−0.372960	+	0.270971i	0.385478	+	0.922717i	$0.374037\pi$
$72$	7.37651	−	5.35935i	0.869330	−	0.631606i
$73$	−1.10230	−	3.39253i	−0.129014	−	0.397066i	0.865597	−	0.500742i	$-0.166939\pi$
$73$	−1.10230	−	3.39253i	−0.129014	−	0.397066i	−0.994611	+	0.103676i	$0.966939\pi$
$74$	−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	0.997084	+	0.0763082i	$0.0243133\pi$
$79$	12.2459	+	8.89718i	1.37777	+	1.00101i	0.380689	+	0.924703i	$0.375687\pi$
$80$	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	−0.863712	−	0.503985i	$-0.831867\pi$
$83$	−5.93358	+	4.31100i	−0.651295	+	0.473194i	0.212417	+	0.977179i	$0.431867\pi$
$84$	−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	0.525553	−	0.850761i	$-0.323858\pi$
$97$	−1.19332	−	0.866997i	−0.121163	−	0.0880302i	−0.646717	+	0.762730i	$0.723858\pi$
$98$	−0.303095			−0.0306172
$99$		0			0
$100$	4.88448			0.488448
$101$	2.76085	+	2.00587i	0.274715	+	0.199592i	0.716609	−	0.697475i	$-0.245693\pi$
$101$	2.76085	+	2.00587i	0.274715	+	0.199592i	−0.441894	+	0.897067i	$0.645693\pi$
$102$	1.93763	−	5.96340i	0.191854	−	0.590465i
$103$	−1.53696	−	4.73027i	−0.151441	−	0.466087i	0.846342	−	0.532640i	$-0.178800\pi$
$103$	−1.53696	−	4.73027i	−0.151441	−	0.466087i	−0.997783	+	0.0665527i	$0.978800\pi$
$104$	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	−0.788345	−	0.615234i	$-0.789062\pi$
$107$	2.18327	−	6.71942i	0.211065	−	0.649591i	0.999410	−	0.0343573i	$-0.0109384\pi$
$108$	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	0.524525	+	0.851395i	$0.324243\pi$
$113$	−4.25484	+	13.0951i	−0.400262	+	1.23188i	−0.924787	+	0.380485i	$0.875757\pi$
$114$	−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	−0.0503620	−	0.998731i	$-0.516037\pi$
$127$	9.96133	−	7.23733i	0.883925	−	0.642209i	0.934287	+	0.356522i	$0.116037\pi$
$128$	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	−0.251062	−	0.967971i	$-0.580780\pi$
$137$	6.92861	−	5.03393i	0.591951	−	0.430078i	0.843013	+	0.537893i	$0.180780\pi$
$138$	−14.8032	+	10.7552i	−1.26013	+	0.915541i
$139$	0.612978	+	1.88655i	0.0519921	+	0.160015i	0.973681	−	0.227914i	$-0.0731905\pi$
$139$	0.612978	+	1.88655i	0.0519921	+	0.160015i	−0.921689	+	0.387929i	$0.873190\pi$
$140$	−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	0.220368	−	0.975417i	$-0.429274\pi$
$149$	14.8449	−	10.7855i	1.21614	−	0.883578i	0.995774	+	0.0918384i	$0.0292743\pi$
$150$	1.08638	+	3.34354i	0.0887028	+	0.272999i
$151$	5.32234	−	16.3805i	0.433126	−	1.33302i	−0.461870	−	0.886948i	$-0.652821\pi$
$151$	5.32234	−	16.3805i	0.433126	−	1.33302i	0.894995	−	0.446076i	$-0.147179\pi$
$152$	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	0.267216	+	0.963637i	$0.413896\pi$
$157$	−6.45766	+	19.8746i	−0.515378	+	1.58617i	−0.782594	+	0.622533i	$0.786104\pi$
$158$	−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	0.246420	−	0.969163i	$-0.420746\pi$
$163$	−7.64957	−	5.55774i	−0.599161	−	0.435316i	−0.845581	+	0.533847i	$0.820746\pi$
$164$	26.8610			2.09749
$165$		0			0
$166$	19.2440			1.49362
$167$	7.64442	+	5.55399i	0.591543	+	0.429781i	0.842867	−	0.538122i	$-0.180866\pi$
$167$	7.64442	+	5.55399i	0.591543	+	0.429781i	−0.251324	+	0.967903i	$0.580866\pi$
$168$	−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	0.785870	+	0.618392i	$0.212216\pi$
$173$	−2.80676	+	8.63831i	−0.213394	+	0.656759i	−0.999264	+	0.0383668i	$0.987784\pi$
$174$	−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	0.656471	+	0.754352i	$0.272049\pi$
$179$	−4.25484	+	13.0951i	−0.318022	+	0.978771i	−0.974493	+	0.224420i	$0.927951\pi$
$180$	−1.81841	−	5.59648i	−0.135536	−	0.417137i
$181$	19.3017	−	14.0235i	1.43468	−	1.04236i	0.445561	−	0.895251i	$-0.353004\pi$
$181$	19.3017	−	14.0235i	1.43468	−	1.04236i	0.989121	−	0.147106i	$-0.0469959\pi$
$182$	−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	0.953557	+	0.301213i	$0.0973915\pi$
$191$	4.96371	+	15.2767i	0.359162	+	1.10539i	−0.594395	+	0.804173i	$0.702609\pi$
$192$	−10.3675	+	7.53241i	−0.748208	+	0.543605i
$193$	−17.3605	+	12.6132i	−1.24964	+	0.907916i	−0.998201	−	0.0599578i	$-0.980903\pi$
$193$	−17.3605	+	12.6132i	−1.24964	+	0.907916i	−0.251438	+	0.967873i	$0.580903\pi$
$194$	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	0.0923082	−	0.995730i	$-0.470576\pi$
$211$	−12.0007	−	8.71903i	−0.826163	−	0.600243i	−0.918471	+	0.395488i	$0.870576\pi$
$212$	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	−0.348738	−	0.937220i	$-0.613390\pi$
$223$	7.23186	−	22.2574i	0.484281	−	1.49046i	0.833019	−	0.553244i	$-0.186610\pi$
$224$	−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	0.920537	−	0.390656i	$-0.127752\pi$
$227$	−0.810808	−	2.49541i	−0.0538152	−	0.165626i	−0.974352	+	0.225030i	$0.927752\pi$
$228$	−2.99408	+	9.21483i	−0.198288	+	0.610267i
$229$	17.8280	+	12.9528i	1.17811	+	0.855945i	0.991957	−	0.126577i	$-0.0403990\pi$
$229$	17.8280	+	12.9528i	1.17811	+	0.855945i	0.186150	+	0.982521i	$0.440399\pi$
$230$	13.6563			0.900471
$231$		0			0
$232$	8.91079			0.585022
$233$	−4.32397	−	3.14155i	−0.283273	−	0.205810i	0.437071	−	0.899427i	$-0.356016\pi$
$233$	−4.32397	−	3.14155i	−0.283273	−	0.205810i	−0.720344	+	0.693617i	$0.756016\pi$
$234$	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	0.743003	+	0.669288i	$0.233401\pi$
$239$	−3.88804	+	11.9662i	−0.251497	+	0.774027i	−0.994500	+	0.104739i	$0.966599\pi$
$240$	−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	0.300426	−	0.953805i	$-0.402871\pi$
$251$	−8.14107	−	5.91483i	−0.513860	−	0.373341i	−0.814286	+	0.580464i	$0.802871\pi$
$252$	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	0.915901	−	0.401403i	$-0.131477\pi$
$257$	−0.978184	−	3.01054i	−0.0610174	−	0.187792i	−0.976919	+	0.213611i	$0.931477\pi$
$258$	−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	−0.907348	−	0.420380i	$-0.861897\pi$
$269$	−12.9230	+	9.38910i	−0.787929	+	0.572464i	0.119419	+	0.992844i	$0.461897\pi$
$270$	11.9590	−	8.68875i	0.727804	−	0.528781i
$271$	−4.83301	−	14.8745i	−0.293585	−	0.903561i	−0.983693	−	0.179855i	$-0.942437\pi$
$271$	−4.83301	−	14.8745i	−0.293585	−	0.903561i	0.690108	−	0.723706i	$-0.257563\pi$
$272$	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	−0.171060	−	0.985261i	$-0.554719\pi$
$277$	−19.3222	−	14.0384i	−1.16096	−	0.843486i	−0.989899	+	0.141775i	$0.954719\pi$
$278$	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	−0.842642	−	0.538475i	$-0.819001\pi$
$281$	−9.90550	+	7.19676i	−0.590912	+	0.429323i	0.251729	+	0.967798i	$0.419001\pi$
$282$	7.23544	+	22.2684i	0.430864	+	1.32606i
$283$	−6.44412	+	19.8330i	−0.383063	+	1.17895i	0.554812	+	0.831976i	$0.312790\pi$
$283$	−6.44412	+	19.8330i	−0.383063	+	1.17895i	−0.937875	+	0.346972i	$0.887210\pi$
$284$	−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	0.993076	+	0.117471i	$0.0374787\pi$
$293$	4.42837	+	13.6291i	0.258708	+	0.796222i	−0.734368	+	0.678752i	$0.762521\pi$
$294$	−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	0.630829	+	0.775922i	$0.282715\pi$
$311$	−5.91833	+	18.2148i	−0.335598	+	1.03286i	−0.966427	+	0.256942i	$0.917285\pi$
$312$	−21.0836	−	64.8887i	−1.19362	−	3.67360i
$313$	12.1140	−	8.80132i	0.684722	−	0.497480i	−0.190199	−	0.981746i	$-0.560913\pi$
$313$	12.1140	−	8.80132i	0.684722	−	0.497480i	0.874921	+	0.484266i	$0.160913\pi$
$314$	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	0.275654	−	0.961257i	$-0.411106\pi$
$317$	−9.85255	−	7.15830i	−0.553375	−	0.402050i	−0.829028	+	0.559207i	$0.811106\pi$
$318$	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	0.991579	−	0.129501i	$-0.0413375\pi$
$337$	2.07910	+	6.39883i	0.113256	+	0.348566i	−0.878323	+	0.478067i	$0.841338\pi$
$338$	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	−0.470459	+	0.882422i	$0.655912\pi$
$347$	−27.1050	+	19.6929i	−1.45507	+	1.05717i	−0.984613	+	0.174749i	$0.944088\pi$
$348$	2.38110	+	7.32828i	0.127641	+	0.392837i
$349$	7.03761	−	21.6595i	0.376715	−	1.15941i	−0.565600	−	0.824680i	$-0.691355\pi$
$349$	7.03761	−	21.6595i	0.376715	−	1.15941i	0.942314	−	0.334729i	$-0.108645\pi$
$350$	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	0.998294	−	0.0583815i	$-0.0185940\pi$
$359$	2.96225	+	9.11686i	0.156341	+	0.481169i	−0.841953	+	0.539551i	$0.818594\pi$
$360$	−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	0.824794	−	0.565433i	$-0.191291\pi$
$367$	−3.34930	−	10.3081i	−0.174832	−	0.538077i	−0.999626	+	0.0273564i	$0.991291\pi$
$368$	−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	−0.671466	−	0.741035i	$-0.734335\pi$
$379$	−3.39121	+	2.46386i	−0.174195	+	0.126560i	0.497272	+	0.867595i	$0.334335\pi$
$380$	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	0.114073	−	0.993472i	$-0.463610\pi$
$383$	−15.5687	−	11.3113i	−0.795524	−	0.577982i	−0.909598	+	0.415490i	$0.863610\pi$
$384$	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	−0.882137	−	0.470994i	$-0.843895\pi$
$389$	−8.78301	−	27.0313i	−0.445316	−	1.37054i	0.436820	−	0.899549i	$-0.356105\pi$
$390$	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	−0.936366	−	0.351026i	$-0.885833\pi$
$401$	−17.8598	+	12.9759i	−0.891874	+	0.647984i	0.0444923	+	0.999010i	$0.485833\pi$
$402$	−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	−0.0276868	−	0.999617i	$-0.508814\pi$
$409$	−19.9595	−	14.5014i	−0.986934	−	0.717050i	−0.959248	+	0.282567i	$0.908814\pi$
$410$	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	−0.938916	−	0.344146i	$-0.888168\pi$
$421$	0.471244	−	1.45034i	0.0229670	−	0.0706852i	0.961883	+	0.273461i	$0.0881684\pi$
$422$	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	0.864191	−	0.503163i	$-0.167831\pi$
$431$	13.5505	+	9.84501i	0.652704	+	0.474217i	−0.211487	+	0.977381i	$0.567831\pi$
$432$	−17.5648	+	54.0588i	−0.845086	+	2.60091i
$433$	2.30991	+	7.10917i	0.111007	+	0.341645i	0.991093	−	0.133169i	$-0.0425153\pi$
$433$	2.30991	+	7.10917i	0.111007	+	0.341645i	−0.880086	+	0.474814i	$0.842515\pi$
$434$	−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	0.783527	+	0.621358i	$0.213419\pi$
$443$	−4.53754	+	13.9651i	−0.215585	+	0.663502i	−0.999112	+	0.0421438i	$0.986581\pi$
$444$	−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	0.612462	−	0.790500i	$-0.290179\pi$
$449$	1.05762	+	0.768404i	0.0499121	+	0.0362632i	−0.562549	+	0.826764i	$0.690179\pi$
$450$	−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	−0.763698	−	0.645574i	$-0.776618\pi$
$457$	−8.24568	+	5.99084i	−0.385717	+	0.280240i	0.377981	+	0.925813i	$0.376618\pi$
$458$	−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	−0.427525	+	0.904003i	$0.640614\pi$
$467$	−30.6734	+	22.2855i	−1.41940	+	1.03125i	−0.991871	+	0.127248i	$0.959386\pi$
$468$	−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	−0.461951	−	0.886905i	$-0.652851\pi$
$479$	5.22628	−	3.79712i	0.238795	−	0.173495i	0.700746	+	0.713411i	$0.252851\pi$
$480$	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	0.138664	−	0.990339i	$-0.455719\pi$
$487$	13.4304	−	41.3345i	0.608589	−	1.87305i	0.469925	−	0.882706i	$-0.344281\pi$
$488$	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	0.905800	−	0.423706i	$-0.139271\pi$
$491$	−1.68528	−	5.18677i	−0.0760558	−	0.234076i	−0.981856	+	0.189630i	$0.939271\pi$
$492$	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	0.999524	−	0.0308608i	$-0.00982486\pi$
$499$	3.85900	+	11.8768i	0.172753	+	0.531678i	−0.826771	+	0.562538i	$0.809825\pi$
$500$	−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	0.698362	+	0.715745i	$0.253913\pi$
$503$	−6.44412	+	19.8330i	−0.287329	+	0.884309i	−0.985691	+	0.168563i	$0.946087\pi$
$504$	−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	0.586562	+	0.809904i	$0.300481\pi$
$509$	−8.21281	+	25.2764i	−0.364026	+	1.12036i	−0.950589	+	0.310453i	$0.899519\pi$
$510$	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	−0.977007	−	0.213208i	$-0.931609\pi$
$521$	−7.11952	−	21.9116i	−0.311912	−	0.959966i	0.665095	−	0.746759i	$-0.268391\pi$
$522$	3.01089	−	2.18754i	0.131783	−	0.0957461i
$523$	0.957324	−	0.695537i	0.0418609	−	0.0304137i	−0.566658	−	0.823953i	$-0.691764\pi$
$523$	0.957324	−	0.695537i	0.0418609	−	0.0304137i	0.608519	+	0.793539i	$0.291764\pi$
$524$	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	0.980948	−	0.194273i	$-0.0622347\pi$
$541$	25.5694	+	18.5772i	1.09931	+	0.798697i	0.118365	+	0.992970i	$0.462235\pi$
$542$	−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	−0.978549	−	0.206016i	$-0.933950\pi$
$547$	−1.53877	+	4.73586i	−0.0657932	+	0.202491i	0.912755	+	0.408506i	$0.133950\pi$
$548$	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	−0.969591	−	0.244732i	$-0.921300\pi$
$557$	−7.76527	−	23.8990i	−0.329025	−	1.01263i	0.640566	−	0.767903i	$-0.278700\pi$
$558$	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	0.764019	−	0.645194i	$-0.223223\pi$
$563$	9.17069	+	6.66289i	0.386498	+	0.280807i	−0.377521	+	0.926001i	$0.623223\pi$
$564$	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	−0.998154	−	0.0607395i	$-0.980654\pi$
$569$	−3.69562	+	11.3740i	−0.154929	+	0.476821i	0.843225	+	0.537561i	$0.180654\pi$
$570$	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	−0.231232	−	0.972899i	$-0.574276\pi$
$577$	14.9553	−	10.8656i	0.622596	−	0.452342i	0.853827	+	0.520557i	$0.174276\pi$
$578$	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	0.932482	−	0.361217i	$-0.117639\pi$
$587$	−0.829331	−	2.55242i	−0.0342302	−	0.105350i	−0.966712	+	0.255868i	$0.917639\pi$
$588$	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	0.144187	−	0.989551i	$-0.453943\pi$
$599$	27.6528	−	20.0909i	1.12986	−	0.820892i	0.985675	+	0.168658i	$0.0539434\pi$
$600$	−8.20401	+	5.96056i	−0.334927	+	0.243339i
$601$	−10.0299	−	30.8687i	−0.409126	−	1.25916i	−0.917400	−	0.397966i	$-0.869716\pi$
$601$	−10.0299	−	30.8687i	−0.409126	−	1.25916i	0.508274	−	0.861196i	$-0.330284\pi$
$602$	−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	0.496565	−	0.868000i	$-0.334594\pi$
$607$	−4.32397	−	3.14155i	−0.175505	−	0.127512i	−0.672070	+	0.740488i	$0.734594\pi$
$608$	−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	0.565122	+	0.825007i	$0.308829\pi$
$613$	−9.33404	+	28.7272i	−0.376998	+	1.16028i	−0.942121	+	0.335274i	$0.891171\pi$
$614$	−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	−0.939107	−	0.343626i	$-0.888345\pi$
$619$	0.562897	−	1.73242i	0.0226247	−	0.0696318i	0.961731	+	0.273994i	$0.0883448\pi$
$620$	−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	−0.926563	−	0.376139i	$-0.877252\pi$
$631$	−9.99882	−	30.7732i	−0.398047	−	1.22506i	0.528517	−	0.848923i	$-0.322748\pi$
$632$	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	−0.999249	−	0.0387611i	$-0.987659\pi$
$641$	−4.25484	+	13.0951i	−0.168056	+	0.517224i	0.831192	+	0.555985i	$0.187659\pi$
$642$	7.67553	+	23.6229i	0.302929	+	0.932320i
$643$	−26.0188	+	18.9038i	−1.02608	+	0.745493i	−0.967521	−	0.252791i	$-0.918652\pi$
$643$	−26.0188	+	18.9038i	−1.02608	+	0.745493i	−0.0585622	+	0.998284i	$0.518652\pi$
$644$	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	0.233170	−	0.972436i	$-0.425090\pi$
$647$	−15.7607	−	11.4508i	−0.619617	−	0.450178i	−0.852788	+	0.522257i	$0.825090\pi$
$648$	−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	0.955660	−	0.294472i	$-0.0951439\pi$
$653$	0.240928	+	0.741499i	0.00942823	+	0.0290171i	−0.946232	+	0.323490i	$0.895144\pi$
$654$	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	0.402824	−	0.915277i	$-0.368029\pi$
$673$	−8.90278	−	6.46825i	−0.343177	−	0.249333i	−0.746001	+	0.665945i	$0.768029\pi$
$674$	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	−0.203278	−	0.979121i	$-0.565160\pi$
$677$	17.3055	−	12.5732i	0.665105	−	0.483227i	0.868383	+	0.495894i	$0.165160\pi$
$678$	−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	−0.990822	−	0.135175i	$-0.956840\pi$
$691$	−37.4736	−	27.2261i	−1.42556	−	1.03573i	−0.434739	−	0.900556i	$-0.643160\pi$
$692$	−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	−0.292741	−	0.956192i	$-0.594567\pi$
$701$	13.4004	−	41.2423i	0.506127	−	1.55770i	0.798868	−	0.601507i	$-0.205433\pi$
$702$	−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	−0.839698	−	0.543054i	$-0.817268\pi$
$709$	−15.5157	+	11.2728i	−0.582703	+	0.423359i	0.256994	+	0.966413i	$0.417268\pi$
$710$	−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	−0.945369	−	0.326001i	$-0.894299\pi$
$719$	−9.97938	−	30.7134i	−0.372168	−	1.14542i	0.573202	−	0.819414i	$-0.305701\pi$
$720$	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	0.878311	−	0.478091i	$-0.158671\pi$
$733$	−3.06673	−	9.43842i	−0.113272	−	0.348616i	−0.991583	+	0.129475i	$0.958671\pi$
$734$	−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	−0.0325588	−	0.999470i	$-0.510366\pi$
$739$	−26.9989	−	19.6159i	−0.993172	−	0.721582i	−0.960614	+	0.277888i	$0.910366\pi$
$740$	−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	−0.642848	−	0.765994i	$-0.722247\pi$
$743$	−3.08005	+	2.23779i	−0.112996	+	0.0820964i	0.529852	+	0.848090i	$0.322247\pi$
$744$	−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	−0.740240	−	0.672343i	$-0.765288\pi$
$751$	6.95578	−	21.4077i	0.253820	−	0.781177i	0.994060	−	0.108835i	$-0.0347119\pi$
$752$	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	0.960076	−	0.279739i	$-0.0902480\pi$
$757$	27.2580	+	19.8041i	0.990708	+	0.719792i	0.0306320	+	0.999531i	$0.490248\pi$
$758$	10.9985			0.399483
$759$		0			0
$760$	−11.2047			−0.406438
$761$	−15.1868	−	11.0339i	−0.550521	−	0.399977i	0.277457	−	0.960738i	$-0.410509\pi$
$761$	−15.1868	−	11.0339i	−0.550521	−	0.399977i	−0.827977	+	0.560761i	$0.810509\pi$
$762$	−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	0.732932	+	0.680302i	$0.238151\pi$
$773$	−7.22579	+	22.2387i	−0.259894	+	0.799871i	−0.992826	+	0.119569i	$0.961849\pi$
$774$	−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	−0.887563	−	0.460686i	$-0.847603\pi$
$787$	−20.3022	+	14.7504i	−0.723696	+	0.525796i	0.163867	+	0.986482i	$0.447603\pi$
$788$	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	−0.401150	−	0.916012i	$-0.631389\pi$
$797$	9.76990	−	7.09824i	0.346067	−	0.251433i	0.747217	+	0.664580i	$0.231389\pi$
$798$	−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	−0.709783	−	0.704420i	$-0.751207\pi$
$809$	−7.37170	+	5.35585i	−0.259175	+	0.188302i	0.450608	+	0.892722i	$0.351207\pi$
$810$	−3.19007	−	9.81803i	−0.112088	−	0.344971i
$811$	0.923957	−	2.84365i	0.0324445	−	0.0998540i	−0.933523	−	0.358518i	$-0.883282\pi$
$811$	0.923957	−	2.84365i	0.0324445	−	0.0998540i	0.965967	+	0.258664i	$0.0832822\pi$
$812$	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	0.939780	+	0.341779i	$0.111030\pi$
$821$	10.8989	+	33.5434i	0.380375	+	1.17067i	−0.559405	+	0.828894i	$0.688970\pi$
$822$	−9.30404	+	28.6349i	−0.324516	+	0.998757i
$823$	−12.5863	−	9.14451i	−0.438732	−	0.318757i	0.346399	−	0.938087i	$-0.387404\pi$
$823$	−12.5863	−	9.14451i	−0.438732	−	0.318757i	−0.785131	+	0.619330i	$0.787404\pi$
$824$	−37.6429			−1.31135
$825$		0			0
$826$	26.7427			0.930496
$827$	8.51840	+	6.18898i	0.296214	+	0.215212i	0.725958	−	0.687739i	$-0.241396\pi$
$827$	8.51840	+	6.18898i	0.296214	+	0.215212i	−0.429745	+	0.902950i	$0.641396\pi$
$828$	−9.46431	+	29.1281i	−0.328907	+	1.01227i
$829$	7.91852	+	24.3707i	0.275022	+	0.846430i	0.989214	+	0.146480i	$0.0467944\pi$
$829$	7.91852	+	24.3707i	0.275022	+	0.846430i	−0.714192	+	0.699950i	$0.753206\pi$
$830$	−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	−0.709488	−	0.704717i	$-0.751074\pi$
$839$	8.07332	−	24.8471i	0.278722	−	0.857818i	0.988211	−	0.153101i	$-0.0489261\pi$
$840$	−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	−0.625287	−	0.780395i	$-0.715018\pi$
$853$	−2.22876	+	1.61929i	−0.0763112	+	0.0554433i	0.548976	+	0.835838i	$0.315018\pi$
$854$	−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	−0.992964	−	0.118417i	$-0.962218\pi$
$863$	−34.8758	+	25.3387i	−1.18719	+	0.862541i	−0.194222	+	0.980958i	$0.562218\pi$
$864$	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	−0.999592	−	0.0285790i	$-0.990902\pi$
$877$	−5.15603	+	15.8686i	−0.174107	+	0.535845i	0.825485	+	0.564424i	$0.190902\pi$
$878$	−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	0.706857	+	0.707356i	$0.250112\pi$
$883$	−8.34334	+	25.6782i	−0.280776	+	0.864139i	−0.987633	+	0.156783i	$0.949888\pi$
$884$	−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	−0.996706	−	0.0810998i	$-0.974157\pi$
$887$	−7.08894	−	21.8175i	−0.238023	−	0.732560i	0.758683	−	0.651460i	$-0.225843\pi$
$888$	−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	−0.984374	−	0.176089i	$-0.943655\pi$
$907$	−33.7633	+	24.5305i	−1.12109	+	0.814521i	−0.136718	+	0.990610i	$0.543655\pi$
$908$	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	0.969901	−	0.243498i	$-0.0782949\pi$
$911$	31.3308	+	22.7632i	1.03804	+	0.754178i	0.0681358	+	0.997676i	$0.478295\pi$
$912$	−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	−0.549079	−	0.835770i	$-0.685022\pi$
$919$	2.30729	−	1.67634i	0.0761103	−	0.0552974i	0.625190	+	0.780473i	$0.285022\pi$
$920$	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	−0.398218	−	0.917291i	$-0.630371\pi$
$929$	10.7020	−	7.77545i	0.351121	−	0.255104i	0.749339	+	0.662187i	$0.230371\pi$
$930$	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	0.565356	−	0.824847i	$-0.308739\pi$
$937$	−1.35959	−	0.987799i	−0.0444158	−	0.0322700i	−0.609772	+	0.792577i	$0.708739\pi$
$938$	−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	−0.377052	−	0.926192i	$-0.623062\pi$
$941$	11.8805	−	8.63170i	0.387294	−	0.281385i	0.764346	+	0.644807i	$0.223062\pi$
$942$	−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	0.998935	+	0.0461349i	$0.0146904\pi$
$953$	6.72663	+	20.7025i	0.217897	+	0.670618i	−0.781038	+	0.624483i	$0.785310\pi$
$954$	−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	−0.997151	−	0.0754367i	$-0.975965\pi$
$971$	−4.55255	+	14.0113i	−0.146098	+	0.449644i	0.851052	+	0.525081i	$0.175965\pi$
$972$	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	0.404577	−	0.914504i	$-0.367419\pi$
$977$	−10.6320	−	7.72457i	−0.340146	−	0.247131i	−0.744724	+	0.667373i	$0.767419\pi$
$978$	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	0.999871	−	0.0160784i	$-0.00511815\pi$
$983$	5.69078	+	17.5144i	0.181508	+	0.558623i	−0.818363	+	0.574702i	$0.805118\pi$
$984$	−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	0.818265	+	0.574841i	$0.194936\pi$
$997$	15.6032	+	48.0217i	0.494158	+	1.52086i	−0.324107	+	0.946020i	$0.605064\pi$
$998$	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.81.1		24
11.2	odd	10	inner	605.2.g.q.511.1		24
11.3	even	5	inner	605.2.g.q.366.1		24
11.4	even	5	inner	605.2.g.q.251.6		24
11.5	even	5		605.2.a.m.1.6	yes	6
11.6	odd	10		605.2.a.m.1.1	✓	6
11.7	odd	10	inner	605.2.g.q.251.1		24
11.8	odd	10	inner	605.2.g.q.366.6		24
11.9	even	5	inner	605.2.g.q.511.6		24
11.10	odd	2	inner	605.2.g.q.81.6		24
33.5	odd	10		5445.2.a.bx.1.1		6
33.17	even	10		5445.2.a.bx.1.6		6
44.27	odd	10		9680.2.a.cw.1.4		6
44.39	even	10		9680.2.a.cw.1.3		6
55.39	odd	10		3025.2.a.bg.1.6		6
55.49	even	10		3025.2.a.bg.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.1	✓	6	11.6	odd	10
605.2.a.m.1.6	yes	6	11.5	even	5
605.2.g.q.81.1		24	1.1	even	1	trivial
605.2.g.q.81.6		24	11.10	odd	2	inner
605.2.g.q.251.1		24	11.7	odd	10	inner
605.2.g.q.251.6		24	11.4	even	5	inner
605.2.g.q.366.1		24	11.3	even	5	inner
605.2.g.q.366.6		24	11.8	odd	10	inner
605.2.g.q.511.1		24	11.2	odd	10	inner
605.2.g.q.511.6		24	11.9	even	5	inner
3025.2.a.bg.1.1		6	55.49	even	10
3025.2.a.bg.1.6		6	55.39	odd	10
5445.2.a.bx.1.1		6	33.5	odd	10
5445.2.a.bx.1.6		6	33.17	even	10
9680.2.a.cw.1.3		6	44.39	even	10
9680.2.a.cw.1.4		6	44.27	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

Varieties

Fields

Representations

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Database

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