LMFDB - Embedded newform 380.2.n.a.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15432 - 0.817038i) q^{2} +(-1.05340 - 1.82454i) q^{3} +(0.664897 - 1.88624i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.70668 - 1.24543i) q^{6} -0.279006i q^{7} +(-0.773631 - 2.72057i) q^{8} +(-0.719298 + 1.24586i) q^{9} +O(q^{10})$	\(q+(1.15432 - 0.817038i) q^{2} +(-1.05340 - 1.82454i) q^{3} +(0.664897 - 1.88624i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.70668 - 1.24543i) q^{6} -0.279006i q^{7} +(-0.773631 - 2.72057i) q^{8} +(-0.719298 + 1.24586i) q^{9} +(1.28473 + 0.591149i) q^{10} -2.67897i q^{11} +(-4.14193 + 0.773835i) q^{12} +(-3.06953 - 1.77219i) q^{13} +(-0.227959 - 0.322061i) q^{14} +(1.05340 - 1.82454i) q^{15} +(-3.11582 - 2.50831i) q^{16} +(1.01431 + 1.75683i) q^{17} +(0.187618 + 2.02581i) q^{18} +(2.32453 + 3.68735i) q^{19} +(1.96598 - 0.367304i) q^{20} +(-0.509057 + 0.293904i) q^{21} +(-2.18882 - 3.09238i) q^{22} +(1.18271 + 0.682840i) q^{23} +(-4.14885 + 4.27736i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-4.99116 + 0.462250i) q^{26} -3.28956 q^{27} +(-0.526273 - 0.185510i) q^{28} +(1.05063 + 0.606582i) q^{29} +(-0.274763 - 2.96677i) q^{30} +3.76546 q^{31} +(-5.64604 - 0.349641i) q^{32} +(-4.88788 + 2.82202i) q^{33} +(2.60623 + 1.19921i) q^{34} +(0.241626 - 0.139503i) q^{35} +(1.87174 + 2.18514i) q^{36} +0.254205i q^{37} +(5.69596 + 2.35714i) q^{38} +7.46731i q^{39} +(1.96927 - 2.03027i) q^{40} +(6.19954 - 3.57931i) q^{41} +(-0.347483 + 0.755178i) q^{42} +(6.49988 - 3.75271i) q^{43} +(-5.05318 - 1.78124i) q^{44} -1.43860 q^{45} +(1.92313 - 0.178108i) q^{46} +(2.23985 + 1.29318i) q^{47} +(-1.29431 + 8.32720i) q^{48} +6.92216 q^{49} +(0.130417 + 1.40819i) q^{50} +(2.13694 - 3.70129i) q^{51} +(-5.38371 + 4.61156i) q^{52} +(-6.79826 - 3.92498i) q^{53} +(-3.79720 + 2.68770i) q^{54} +(2.32005 - 1.33948i) q^{55} +(-0.759055 + 0.215848i) q^{56} +(4.27905 - 8.12545i) q^{57} +(1.70836 - 0.158218i) q^{58} +(5.13577 + 8.89542i) q^{59} +(-2.74112 - 3.20010i) q^{60} +(1.28956 - 2.23358i) q^{61} +(4.34654 - 3.07653i) q^{62} +(0.347602 + 0.200688i) q^{63} +(-6.80299 + 4.20943i) q^{64} -3.54439i q^{65} +(-3.33647 + 7.25109i) q^{66} +(6.21206 - 10.7596i) q^{67} +(3.98822 - 0.745118i) q^{68} -2.87721i q^{69} +(0.164934 - 0.358449i) q^{70} +(-1.81765 - 3.14826i) q^{71} +(3.94592 + 0.993063i) q^{72} +(2.69470 + 4.66736i) q^{73} +(0.207695 + 0.293433i) q^{74} +2.10680 q^{75} +(8.50081 - 1.93293i) q^{76} -0.747447 q^{77} +(6.10108 + 8.61965i) q^{78} +(5.63590 + 9.76166i) q^{79} +(0.614351 - 3.95254i) q^{80} +(5.62311 + 9.73952i) q^{81} +(4.23181 - 9.19692i) q^{82} +3.31499i q^{83} +(0.215905 + 1.15562i) q^{84} +(-1.01431 + 1.75683i) q^{85} +(4.43682 - 9.64247i) q^{86} -2.55589i q^{87} +(-7.28831 + 2.07253i) q^{88} +(0.830483 + 0.479480i) q^{89} +(-1.66060 + 1.17539i) q^{90} +(-0.494453 + 0.856417i) q^{91} +(2.07438 - 1.77687i) q^{92} +(-3.96653 - 6.87023i) q^{93} +(3.64207 - 0.337305i) q^{94} +(-2.03107 + 3.85678i) q^{95} +(5.30960 + 10.6697i) q^{96} +(1.76691 - 1.02013i) q^{97} +(7.99036 - 5.65567i) q^{98} +(3.33762 + 1.92697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.15432	−	0.817038i	0.816226	−	0.577733i
$2$	1.15432	−	0.817038i	0.816226	−	0.577733i
$3$	−1.05340	−	1.82454i	−0.608180	−	1.05340i	−0.991540	−	0.129800i	$-0.958567\pi$
$3$	−1.05340	−	1.82454i	−0.608180	−	1.05340i	0.383360	−	0.923599i	$-0.374767\pi$
$4$	0.664897	−	1.88624i	0.332448	−	0.943121i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.70668	−	1.24543i	−1.10500	−	0.508445i
$7$		−	0.279006i		−	0.105454i	−0.998609	−	0.0527272i	$-0.983209\pi$
$7$		−	0.279006i		−	0.105454i	0.998609	−	0.0527272i	$-0.0167914\pi$
$8$	−0.773631	−	2.72057i	−0.273520	−	0.961866i
$9$	−0.719298	+	1.24586i	−0.239766	+	0.415287i
$10$	1.28473	+	0.591149i	0.406269	+	0.186938i
$11$		−	2.67897i		−	0.807738i	−0.914817	−	0.403869i	$-0.867665\pi$
$11$		−	2.67897i		−	0.807738i	0.914817	−	0.403869i	$-0.132335\pi$
$12$	−4.14193	+	0.773835i	−1.19567	+	0.223387i
$13$	−3.06953	−	1.77219i	−0.851335	−	0.491518i	0.00976619	−	0.999952i	$-0.496891\pi$
$13$	−3.06953	−	1.77219i	−0.851335	−	0.491518i	−0.861101	+	0.508434i	$0.830225\pi$
$14$	−0.227959	−	0.322061i	−0.0609245	−	0.0860745i
$15$	1.05340	−	1.82454i	0.271986	−	0.471094i
$16$	−3.11582	−	2.50831i	−0.778956	−	0.627078i
$17$	1.01431	+	1.75683i	0.246005	+	0.426094i	0.962414	−	0.271587i	$-0.0875486\pi$
$17$	1.01431	+	1.75683i	0.246005	+	0.426094i	−0.716408	+	0.697681i	$0.754215\pi$
$18$	0.187618	+	2.02581i	0.0442219	+	0.477488i
$19$	2.32453	+	3.68735i	0.533285	+	0.845936i
$19$	2.32453	+	3.68735i	0.533285	+	0.845936i
$20$	1.96598	−	0.367304i	0.439607	−	0.0821317i
$21$	−0.509057	+	0.293904i	−0.111085	+	0.0641352i
$22$	−2.18882	−	3.09238i	−0.466657	−	0.659297i
$23$	1.18271	+	0.682840i	0.246613	+	0.142382i	0.618212	−	0.786011i	$-0.287857\pi$
$23$	1.18271	+	0.682840i	0.246613	+	0.142382i	−0.371599	+	0.928393i	$0.621191\pi$
$24$	−4.14885	+	4.27736i	−0.846879	+	0.873113i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.99116	+	0.462250i	−0.978848	+	0.0906546i
$27$	−3.28956			−0.633077
$28$	−0.526273	−	0.185510i	−0.0994562	−	0.0350581i
$29$	1.05063	+	0.606582i	0.195097	+	0.112639i	0.594367	−	0.804194i	$-0.297403\pi$
$29$	1.05063	+	0.606582i	0.195097	+	0.112639i	−0.399269	+	0.916834i	$0.630736\pi$
$30$	−0.274763	−	2.96677i	−0.0501646	−	0.541655i
$31$	3.76546			0.676297			0.338148	−	0.941093i	$-0.390199\pi$
$31$	3.76546			0.676297			0.338148	+	0.941093i	$0.390199\pi$
$32$	−5.64604	−	0.349641i	−0.998088	−	0.0618084i
$33$	−4.88788	+	2.82202i	−0.850871	+	0.491250i
$34$	2.60623	+	1.19921i	0.446965	+	0.205663i
$35$	0.241626	−	0.139503i	0.0408423	−	0.0235803i
$36$	1.87174	+	2.18514i	0.311956	+	0.364190i
$37$			0.254205i			0.0417910i	0.999782	+	0.0208955i	$0.00665173\pi$
$37$			0.254205i			0.0417910i	−0.999782	+	0.0208955i	$0.993348\pi$
$38$	5.69596	+	2.35714i	0.924006	+	0.382378i
$39$			7.46731i			1.19573i
$40$	1.96927	−	2.03027i	0.311368	−	0.321014i
$41$	6.19954	−	3.57931i	0.968206	−	0.558994i	0.0695172	−	0.997581i	$-0.477854\pi$
$41$	6.19954	−	3.57931i	0.968206	−	0.558994i	0.898689	+	0.438587i	$0.144521\pi$
$42$	−0.347483	+	0.755178i	−0.0536177	+	0.116527i
$43$	6.49988	−	3.75271i	0.991223	−	0.572283i	0.0855832	−	0.996331i	$-0.472725\pi$
$43$	6.49988	−	3.75271i	0.991223	−	0.572283i	0.905640	+	0.424048i	$0.139391\pi$
$44$	−5.05318	−	1.78124i	−0.761795	−	0.268531i
$45$	−1.43860			−0.214453
$46$	1.92313	−	0.178108i	0.283551	−	0.0262606i
$47$	2.23985	+	1.29318i	0.326715	+	0.188629i	0.654382	−	0.756164i	$-0.272929\pi$
$47$	2.23985	+	1.29318i	0.326715	+	0.188629i	−0.327667	+	0.944793i	$0.606262\pi$
$48$	−1.29431	+	8.32720i	−0.186818	+	1.20193i
$49$	6.92216			0.988879
$50$	0.130417	+	1.40819i	0.0184438	+	0.199148i
$51$	2.13694	−	3.70129i	0.299231	−	0.518284i
$52$	−5.38371	+	4.61156i	−0.746586	+	0.639508i
$53$	−6.79826	−	3.92498i	−0.933813	−	0.539137i	−0.0457977	−	0.998951i	$-0.514583\pi$
$53$	−6.79826	−	3.92498i	−0.933813	−	0.539137i	−0.888016	+	0.459813i	$0.847916\pi$
$54$	−3.79720	+	2.68770i	−0.516733	+	0.365750i
$55$	2.32005	−	1.33948i	0.312836	−	0.180616i
$56$	−0.759055	+	0.215848i	−0.101433	+	0.0288439i
$57$	4.27905	−	8.12545i	0.566774	−	1.07624i
$58$	1.70836	−	0.158218i	0.224319	−	0.0207750i
$59$	5.13577	+	8.89542i	0.668620	+	1.15808i	0.978290	+	0.207240i	$0.0664482\pi$
$59$	5.13577	+	8.89542i	0.668620	+	1.15808i	−0.309670	+	0.950844i	$0.600218\pi$
$60$	−2.74112	−	3.20010i	−0.353878	−	0.413131i
$61$	1.28956	−	2.23358i	0.165111	−	0.285980i	−0.771584	−	0.636128i	$-0.780535\pi$
$61$	1.28956	−	2.23358i	0.165111	−	0.285980i	0.936695	+	0.350147i	$0.113869\pi$
$62$	4.34654	−	3.07653i	0.552011	−	0.390719i
$63$	0.347602	+	0.200688i	0.0437938	+	0.0252843i
$64$	−6.80299	+	4.20943i	−0.850374	+	0.526179i
$65$		−	3.54439i		−	0.439627i
$66$	−3.33647	+	7.25109i	−0.410691	+	0.892547i
$67$	6.21206	−	10.7596i	0.758923	−	1.31449i	−0.184477	−	0.982837i	$-0.559059\pi$
$67$	6.21206	−	10.7596i	0.758923	−	1.31449i	0.943400	−	0.331657i	$-0.107608\pi$
$68$	3.98822	−	0.745118i	0.483642	−	0.0903588i
$69$		−	2.87721i		−	0.346376i
$70$	0.164934	−	0.358449i	0.0197134	−	0.0428428i
$71$	−1.81765	−	3.14826i	−0.215715	−	0.373629i	0.737778	−	0.675043i	$-0.235875\pi$
$71$	−1.81765	−	3.14826i	−0.215715	−	0.373629i	−0.953494	+	0.301413i	$0.902542\pi$
$72$	3.94592	+	0.993063i	0.465031	+	0.117034i
$73$	2.69470	+	4.66736i	0.315391	+	0.546273i	0.979521	−	0.201344i	$-0.0645310\pi$
$73$	2.69470	+	4.66736i	0.315391	+	0.546273i	−0.664129	+	0.747618i	$0.731198\pi$
$74$	0.207695	+	0.293433i	0.0241441	+	0.0341109i
$75$	2.10680			0.243272
$76$	8.50081	−	1.93293i	0.975110	−	0.221722i
$77$	−0.747447			−0.0851795
$78$	6.10108	+	8.61965i	0.690811	+	0.975983i
$79$	5.63590	+	9.76166i	0.634088	+	1.09827i	0.986708	+	0.162506i	$0.0519577\pi$
$79$	5.63590	+	9.76166i	0.634088	+	1.09827i	−0.352619	+	0.935767i	$0.614709\pi$
$80$	0.614351	−	3.95254i	0.0686865	−	0.441907i
$81$	5.62311	+	9.73952i	0.624791	+	1.08217i
$82$	4.23181	−	9.19692i	0.467325	−	1.01563i
$83$			3.31499i			0.363868i	0.983311	+	0.181934i	$0.0582356\pi$
$83$			3.31499i			0.363868i	−0.983311	+	0.181934i	$0.941764\pi$
$84$	0.215905	+	1.15562i	0.0235571	+	0.126089i
$85$	−1.01431	+	1.75683i	−0.110017	+	0.190555i
$86$	4.43682	−	9.64247i	0.478435	−	1.03977i
$87$		−	2.55589i		−	0.274020i
$88$	−7.28831	+	2.07253i	−0.776936	+	0.220932i
$89$	0.830483	+	0.479480i	0.0880310	+	0.0508247i	0.543369	−	0.839494i	$-0.317148\pi$
$89$	0.830483	+	0.479480i	0.0880310	+	0.0508247i	−0.455338	+	0.890319i	$0.650482\pi$
$90$	−1.66060	+	1.17539i	−0.175042	+	0.123897i
$91$	−0.494453	+	0.856417i	−0.0518327	+	0.0897769i
$92$	2.07438	−	1.77687i	0.216270	−	0.185251i
$93$	−3.96653	−	6.87023i	−0.411310	−	0.712410i
$94$	3.64207	−	0.337305i	0.375651	−	0.0347904i
$95$	−2.03107	+	3.85678i	−0.208383	+	0.395697i
$96$	5.30960	+	10.6697i	0.541908	+	1.08898i
$97$	1.76691	−	1.02013i	0.179403	−	0.103578i	−0.407609	−	0.913156i	$-0.633637\pi$
$97$	1.76691	−	1.02013i	0.179403	−	0.103578i	0.587012	+	0.809578i	$0.300304\pi$
$98$	7.99036	−	5.65567i	0.807149	−	0.571309i
$99$	3.33762	+	1.92697i	0.335443	+	0.193668i
$100$	1.30109	+	1.51894i	0.130109	+	0.151894i
$101$	−1.14846	+	1.98919i	−0.114276	+	0.197932i	−0.917490	−	0.397759i	$-0.869788\pi$
$101$	−1.14846	+	1.98919i	−0.114276	+	0.197932i	0.803214	+	0.595690i	$0.203121\pi$
$102$	−0.557387	−	6.01842i	−0.0551896	−	0.595912i
$103$	−18.8137			−1.85377			−0.926883	−	0.375349i	$-0.877523\pi$
$103$	−18.8137			−1.85377			−0.926883	+	0.375349i	$0.877523\pi$
$104$	−2.44669	+	9.72190i	−0.239918	+	0.953310i
$105$	−0.509057	−	0.293904i	−0.0496789	−	0.0286821i
$106$	−11.0542	+	1.02377i	−1.07368	+	0.0994374i
$107$	−8.93472			−0.863752			−0.431876	−	0.901933i	$-0.642148\pi$
$107$	−8.93472			−0.863752			−0.431876	+	0.901933i	$0.642148\pi$
$108$	−2.18722	+	6.20492i	−0.210465	+	0.597068i
$109$	−14.2615	+	8.23391i	−1.36601	+	0.788665i	−0.990416	−	0.138120i	$-0.955894\pi$
$109$	−14.2615	+	8.23391i	−1.36601	+	0.788665i	−0.375593	+	0.926785i	$0.622561\pi$
$110$	1.58367	−	3.44176i	0.150997	−	0.328159i
$111$	0.463807	−	0.267779i	0.0440226	−	0.0254165i
$112$	−0.699834	+	0.869333i	−0.0661281	+	0.0821443i
$113$			12.9810i			1.22115i	0.791958	+	0.610575i	$0.209062\pi$
$113$			12.9810i			1.22115i	−0.791958	+	0.610575i	$0.790938\pi$
$114$	−1.69942	−	12.8755i	−0.159166	−	1.20590i
$115$			1.36568i			0.127350i
$116$	1.84272	−	1.57843i	0.171092	−	0.146554i
$117$	4.41581	−	2.54947i	0.408242	−	0.235699i
$118$	13.1962	+	6.07201i	1.21481	+	0.558974i
$119$	0.490166	−	0.282997i	0.0449334	−	0.0259423i
$120$	−5.77873	−	1.45432i	−0.527523	−	0.132761i
$121$	3.82315			0.347559
$122$	−0.336361	−	3.63187i	−0.0304527	−	0.328814i
$123$	−13.0612	−	7.54088i	−1.17769	−	0.679938i
$124$	2.50364	−	7.10257i	0.224834	−	0.637830i
$125$	−1.00000			−0.0894427
$126$	0.565213	−	0.0523465i	0.0503532	−	0.00466339i
$127$	8.87396	−	15.3702i	0.787437	−	1.36388i	−0.140095	−	0.990138i	$-0.544741\pi$
$127$	8.87396	−	15.3702i	0.787437	−	1.36388i	0.927532	−	0.373743i	$-0.121926\pi$
$128$	−4.41354	+	10.4173i	−0.390106	+	0.920770i
$129$	−13.6939	−	7.90620i	−1.20568	−	0.696102i
$130$	−2.89590	−	4.09135i	−0.253987	−	0.358835i
$131$	−0.358926	+	0.207226i	−0.0313595	+	0.0181054i	−0.515598	−	0.856831i	$-0.672430\pi$
$131$	−0.358926	+	0.207226i	−0.0313595	+	0.0181054i	0.484238	+	0.874936i	$0.339097\pi$
$132$	2.07308	+	11.0961i	0.180438	+	0.965790i
$133$	1.02879	−	0.648559i	0.0892076	−	0.0562372i
$134$	−1.62032	−	17.4955i	−0.139974	−	1.51138i
$135$	−1.64478	−	2.84885i	−0.141560	−	0.245190i
$136$	3.99488	−	4.11863i	0.342558	−	0.353170i
$137$	−10.8706	+	18.8284i	−0.928738	+	1.60862i	−0.143302	+	0.989679i	$0.545772\pi$
$137$	−10.8706	+	18.8284i	−0.928738	+	1.60862i	−0.785436	+	0.618943i	$0.787561\pi$
$138$	−2.35079	−	3.32122i	−0.200113	−	0.282721i
$139$	5.15253	+	2.97481i	0.437032	+	0.252320i	0.702338	−	0.711844i	$-0.252140\pi$
$139$	5.15253	+	2.97481i	0.437032	+	0.252320i	−0.265306	+	0.964164i	$0.585473\pi$
$140$	−0.102480	−	0.548521i	−0.00866114	−	0.0463585i
$141$		−	5.44892i		−	0.458882i
$142$	−4.67039	−	2.14900i	−0.391930	−	0.180340i
$143$	−4.74765	+	8.22317i	−0.397018	+	0.687656i
$144$	5.36621	−	2.07766i	0.447184	−	0.173138i
$145$			1.21316i			0.100748i
$146$	6.92396	+	3.18594i	0.573031	+	0.263670i
$147$	−7.29179	−	12.6298i	−0.601417	−	1.04168i
$148$	0.479492	+	0.169020i	0.0394140	+	0.0138934i
$149$	−0.0492800	−	0.0853554i	−0.00403717	−	0.00699259i	0.864000	−	0.503492i	$-0.167952\pi$
$149$	−0.0492800	−	0.0853554i	−0.00403717	−	0.00699259i	−0.868037	+	0.496500i	$0.834618\pi$
$150$	2.43191	−	1.72133i	0.198565	−	0.140546i
$151$	−14.3041			−1.16405			−0.582026	−	0.813170i	$-0.697740\pi$
$151$	−14.3041			−1.16405			−0.582026	+	0.813170i	$0.697740\pi$
$152$	8.23335	−	9.17670i	0.667813	−	0.744329i
$153$	−2.91835			−0.235935
$154$	−0.862791	+	0.610693i	−0.0695257	+	0.0492110i
$155$	1.88273	+	3.26098i	0.151225	+	0.261929i
$156$	14.0852	+	4.96499i	1.12772	+	0.397517i
$157$	9.43635	+	16.3442i	0.753102	+	1.30441i	0.946312	+	0.323254i	$0.104777\pi$
$157$	9.43635	+	16.3442i	0.753102	+	1.30441i	−0.193210	+	0.981157i	$0.561890\pi$
$158$	14.4813	+	6.66331i	1.15207	+	0.530105i
$159$			16.5383i			1.31157i
$160$	−2.52022	−	5.06443i	−0.199241	−	0.400379i
$161$	0.190516	−	0.329984i	0.0150148	−	0.0260064i
$162$	14.4484	+	6.64820i	1.13518	+	0.522332i
$163$		−	20.6686i		−	1.61889i	−0.587198	−	0.809443i	$-0.699769\pi$
$163$		−	20.6686i		−	1.61889i	0.587198	−	0.809443i	$-0.300231\pi$
$164$	−2.62939	−	14.0737i	−0.205321	−	1.09897i
$165$	−4.88788	−	2.82202i	−0.380521	−	0.219694i
$166$	2.70847	+	3.82655i	0.210218	+	0.296998i
$167$	−11.9682	+	20.7295i	−0.926125	+	1.60410i	−0.136383	+	0.990656i	$0.543548\pi$
$167$	−11.9682	+	20.7295i	−0.926125	+	1.60410i	−0.789742	+	0.613439i	$0.789786\pi$
$168$	1.19341	+	1.15755i	0.0920736	+	0.0893071i
$169$	−0.218651	−	0.378715i	−0.0168193	−	0.0291320i
$170$	0.264566	+	2.85667i	0.0202913	+	0.219096i
$171$	−6.26595	+	0.243744i	−0.479169	+	0.0186395i
$172$	−2.75677	−	14.7555i	−0.210202	−	1.12510i
$173$	18.8921	−	10.9074i	1.43634	−	0.829273i	0.438750	−	0.898609i	$-0.355422\pi$
$173$	18.8921	−	10.9074i	1.43634	−	0.829273i	0.997593	+	0.0693364i	$0.0220882\pi$
$174$	−2.08826	−	2.95031i	−0.158311	−	0.223662i
$175$	0.241626	+	0.139503i	0.0182652	+	0.0105454i
$176$	−6.71968	+	8.34719i	−0.506515	+	0.629193i
$177$	10.8200	−	18.7408i	0.813283	−	1.40865i
$178$	1.35039	−	0.125065i	0.101216	−	0.00937401i
$179$	−16.4175			−1.22710			−0.613550	−	0.789656i	$-0.710259\pi$
$179$	−16.4175			−1.22710			−0.613550	+	0.789656i	$0.710259\pi$
$180$	−0.956517	+	2.71354i	−0.0712946	+	0.202255i
$181$	−2.06949	−	1.19482i	−0.153824	−	0.0888104i	0.421112	−	0.907009i	$-0.361640\pi$
$181$	−2.06949	−	1.19482i	−0.153824	−	0.0888104i	−0.574936	+	0.818198i	$0.694973\pi$
$182$	0.128970	+	1.39256i	0.00955992	+	0.103224i
$183$	−5.43367			−0.401668
$184$	0.942730	−	3.74592i	0.0694989	−	0.276153i
$185$	−0.220148	+	0.127102i	−0.0161856	+	0.00934475i
$186$	−10.1919	−	4.68962i	−0.747305	−	0.343860i
$187$	4.70649	−	2.71729i	0.344172	−	0.198708i
$188$	3.92851	−	3.36507i	0.286516	−	0.245423i
$189$			0.917808i			0.0667607i
$190$	0.806638	+	6.11141i	0.0585197	+	0.443368i
$191$			24.9361i			1.80431i	0.431409	+	0.902157i	$0.358017\pi$
$191$			24.9361i			1.80431i	−0.431409	+	0.902157i	$0.641983\pi$
$192$	14.8465	+	7.97812i	1.07146	+	0.575771i
$193$	21.9112	−	12.6505i	1.57721	−	0.910600i	0.581959	−	0.813218i	$-0.302287\pi$
$193$	21.9112	−	12.6505i	1.57721	−	0.910600i	0.995247	−	0.0973819i	$-0.0310468\pi$
$194$	1.20610	−	2.62119i	0.0865926	−	0.188190i
$195$	−6.46688	+	3.73366i	−0.463103	+	0.267373i
$196$	4.60252	−	13.0569i	0.328751	−	0.932633i
$197$	−11.5828			−0.825244			−0.412622	−	0.910902i	$-0.635387\pi$
$197$	−11.5828			−0.825244			−0.412622	+	0.910902i	$0.635387\pi$
$198$	5.42708	−	0.502621i	0.385686	−	0.0357197i
$199$	9.64679	+	5.56958i	0.683843	+	0.394817i	0.801301	−	0.598261i	$-0.204141\pi$
$199$	9.64679	+	5.56958i	0.683843	+	0.394817i	−0.117459	+	0.993078i	$0.537475\pi$
$200$	2.74290	+	0.690300i	0.193952	+	0.0488116i
$201$	−26.1751			−1.84625
$202$	0.299558	+	3.23449i	0.0210768	+	0.227578i
$203$	0.169240	−	0.293132i	0.0118783	−	0.0205738i
$204$	−5.56068	−	6.49176i	−0.389325	−	0.454514i
$205$	6.19954	+	3.57931i	0.432995	+	0.249990i
$206$	−21.7170	+	15.3715i	−1.51309	+	1.07098i
$207$	−1.70145	+	0.982331i	−0.118259	+	0.0682767i
$208$	5.11890	+	13.2212i	0.354932	+	0.916725i
$209$	9.87828	−	6.22735i	0.683295	−	0.430755i
$210$	−0.827745	+	0.0766605i	−0.0571198	+	0.00529007i
$211$	−10.4322	−	18.0691i	−0.718184	−	1.24393i	−0.961719	−	0.274039i	$-0.911640\pi$
$211$	−10.4322	−	18.0691i	−0.718184	−	1.24393i	0.243535	−	0.969892i	$-0.421693\pi$
$212$	−11.9236	+	10.2135i	−0.818917	+	0.701464i
$213$	−3.82941	+	6.63274i	−0.262387	+	0.454468i
$214$	−10.3135	+	7.30001i	−0.705017	+	0.499018i
$215$	6.49988	+	3.75271i	0.443288	+	0.255933i
$216$	2.54491	+	8.94948i	0.173159	+	0.608935i
$217$		−	1.05059i		−	0.0713184i
$218$	−9.73493	+	21.1568i	−0.659333	+	1.43292i
$219$	5.67719	−	9.83319i	0.383629	−	0.664465i
$220$	−0.983995	−	5.26680i	−0.0663409	−	0.355088i
$221$		−	7.19019i		−	0.483665i
$222$	0.316595	−	0.688050i	0.0212484	−	0.0461789i
$223$	−4.00014	−	6.92844i	−0.267869	−	0.463963i	0.700442	−	0.713709i	$-0.252986\pi$
$223$	−4.00014	−	6.92844i	−0.267869	−	0.463963i	−0.968311	+	0.249746i	$0.919653\pi$
$224$	−0.0975520	+	1.57528i	−0.00651797	+	0.105253i
$225$	−0.719298	−	1.24586i	−0.0479532	−	0.0830573i
$226$	10.6060	+	14.9842i	0.705499	+	0.996734i
$227$	−11.4955			−0.762986			−0.381493	−	0.924372i	$-0.624590\pi$
$227$	−11.4955			−0.762986			−0.381493	+	0.924372i	$0.624590\pi$
$228$	−12.4815	−	13.4739i	−0.826604	−	0.892332i
$229$	−10.0984			−0.667323			−0.333662	−	0.942693i	$-0.608284\pi$
$229$	−10.0984			−0.667323			−0.333662	+	0.942693i	$0.608284\pi$
$230$	1.11581	+	1.57643i	0.0735745	+	0.103947i
$231$	0.787360	+	1.36375i	0.0518045	+	0.0897280i
$232$	0.837447	−	3.32758i	0.0549811	−	0.218467i
$233$	8.22820	+	14.2517i	0.539047	+	0.933657i	0.998956	+	0.0456910i	$0.0145490\pi$
$233$	8.22820	+	14.2517i	0.539047	+	0.933657i	−0.459908	+	0.887966i	$0.652118\pi$
$234$	3.01423	−	6.55079i	0.197047	−	0.428238i
$235$			2.58635i			0.168715i
$236$	20.1937	−	3.77278i	1.31450	−	0.245587i
$237$	11.8737	−	20.5658i	0.771280	−	1.33590i
$238$	0.334587	−	0.727153i	0.0216881	−	0.0471343i
$239$			2.85325i			0.184562i	0.995733	+	0.0922808i	$0.0294158\pi$
$239$			2.85325i			0.184562i	−0.995733	+	0.0922808i	$0.970584\pi$
$240$	−7.85872	+	3.04269i	−0.507278	+	0.196405i
$241$	5.33204	+	3.07845i	0.343467	+	0.198301i	0.661804	−	0.749677i	$-0.269791\pi$
$241$	5.33204	+	3.07845i	0.343467	+	0.198301i	−0.318337	+	0.947978i	$0.603124\pi$
$242$	4.41312	−	3.12366i	0.283686	−	0.200796i
$243$	6.91242	−	11.9727i	0.443432	−	0.768047i
$244$	−3.35565	−	3.91751i	−0.214823	−	0.250793i
$245$	3.46108	+	5.99476i	0.221120	+	0.382991i
$246$	−21.2379	+	1.96692i	−1.35408	+	0.125406i
$247$	−0.600532	−	15.4380i	−0.0382109	−	0.982294i
$248$	−2.91308	−	10.2442i	−0.184981	−	0.650507i
$249$	6.04833	−	3.49201i	0.383298	−	0.221297i
$250$	−1.15432	+	0.817038i	−0.0730054	+	0.0516740i
$251$	−19.6358	−	11.3367i	−1.23940	−	0.715569i	−0.270430	−	0.962740i	$-0.587166\pi$
$251$	−19.6358	−	11.3367i	−1.23940	−	0.715569i	−0.968972	+	0.247171i	$0.920499\pi$
$252$	0.609667	−	0.522225i	0.0384054	−	0.0328971i
$253$	1.82930	−	3.16845i	0.115007	−	0.199199i
$254$	−2.31464	−	24.9924i	−0.145233	−	1.56816i
$255$	4.27388			0.267641
$256$	3.41673	+	15.6309i	0.213545	+	0.976933i
$257$	−4.93865	−	2.85133i	−0.308065	−	0.177861i	0.337995	−	0.941148i	$-0.390251\pi$
$257$	−4.93865	−	2.85133i	−0.308065	−	0.177861i	−0.646060	+	0.763287i	$0.723584\pi$
$258$	−22.2668	+	2.06221i	−1.38627	+	0.128388i
$259$	0.0709246			0.00440704
$260$	−6.68558	−	2.35665i	−0.414622	−	0.146153i
$261$	−1.51143	+	0.872626i	−0.0935553	+	0.0540142i
$262$	−0.245003	+	0.532460i	−0.0151363	+	0.0328955i
$263$	6.46225	−	3.73098i	0.398479	−	0.230062i	−0.287348	−	0.957826i	$-0.592774\pi$
$263$	6.46225	−	3.73098i	0.398479	−	0.230062i	0.685828	+	0.727764i	$0.259440\pi$
$264$	11.4589	+	11.1146i	0.705247	+	0.684057i
$265$		−	7.84996i		−	0.482219i
$266$	0.657655	−	1.58921i	0.0403234	−	0.0974404i
$267$		−	2.02033i		−	0.123642i
$268$	−16.1648	−	18.8715i	−0.987424	−	1.15276i
$269$	−3.74617	+	2.16285i	−0.228408	+	0.131872i	−0.609837	−	0.792526i	$-0.708765\pi$
$269$	−3.74617	+	2.16285i	−0.228408	+	0.131872i	0.381429	+	0.924398i	$0.375432\pi$
$270$	−4.22622	−	1.94462i	−0.257199	−	0.118346i
$271$	0.958338	−	0.553297i	0.0582149	−	0.0336104i	−0.470610	−	0.882341i	$-0.655966\pi$
$271$	0.958338	−	0.553297i	0.0582149	−	0.0336104i	0.528825	+	0.848731i	$0.322633\pi$
$272$	1.24628	−	8.01817i	0.0755668	−	0.486173i
$273$	2.08342			0.126095
$274$	2.83543	+	30.6157i	0.171295	+	1.84956i
$275$	2.32005	+	1.33948i	0.139904	+	0.0807738i
$276$	−5.42712	−	1.91305i	−0.326674	−	0.115152i
$277$	−27.5258			−1.65386			−0.826931	−	0.562303i	$-0.809915\pi$
$277$	−27.5258			−1.65386			−0.826931	+	0.562303i	$0.809915\pi$
$278$	8.37819	−	0.775934i	0.502490	−	0.0465375i
$279$	−2.70849	+	4.69124i	−0.162153	+	0.280857i
$280$	−0.566457	−	0.549437i	−0.0338523	−	0.0328351i
$281$	−19.3900	−	11.1948i	−1.15671	−	0.667828i	−0.206198	−	0.978510i	$-0.566109\pi$
$281$	−19.3900	−	11.1948i	−1.15671	−	0.667828i	−0.950514	+	0.310682i	$0.899442\pi$
$282$	−4.45198	−	6.28978i	−0.265111	−	0.374551i
$283$	9.94045	−	5.73912i	0.590898	−	0.341155i	−0.174554	−	0.984648i	$-0.555848\pi$
$283$	9.94045	−	5.73912i	0.590898	−	0.341155i	0.765453	+	0.643492i	$0.222515\pi$
$284$	−7.14693	+	1.33526i	−0.424092	+	0.0792330i
$285$	9.17638	−	0.356958i	0.543562	−	0.0211444i
$286$	1.23835	+	13.3712i	0.0732252	+	0.790653i
$287$	−0.998648	−	1.72971i	−0.0589483	−	0.102102i
$288$	4.49679	−	6.78268i	0.264976	−	0.399673i
$289$	6.44236	−	11.1585i	0.378963	−	0.656383i
$290$	0.991201	+	1.40038i	0.0582053	+	0.0822329i
$291$	−3.72253	−	2.14920i	−0.218219	−	0.125989i
$292$	10.5955	−	1.97955i	0.620053	−	0.115844i
$293$		−	10.3654i		−	0.605554i	−0.953061	−	0.302777i	$-0.902086\pi$
$293$		−	10.3654i		−	0.605554i	0.953061	−	0.302777i	$-0.0979138\pi$
$294$	−18.7360	−	8.62107i	−1.09271	−	0.502791i
$295$	−5.13577	+	8.89542i	−0.299016	+	0.517911i
$296$	0.691582	−	0.196661i	0.0401974	−	0.0114307i
$297$			8.81263i			0.511360i
$298$	−0.126623	−	0.0582636i	−0.00733509	−	0.00337512i
$299$	−2.42025	−	4.19200i	−0.139967	−	0.242430i
$300$	1.40080	−	3.97393i	0.0808754	−	0.229435i
$301$	−1.04703	−	1.81351i	−0.0603497	−	0.104529i
$302$	−16.5115	+	11.6870i	−0.950129	+	0.672512i
$303$	4.83914			0.278001
$304$	2.00618	−	17.3198i	0.115063	−	0.993358i
$305$	2.57911			0.147680
$306$	−3.36871	+	2.38441i	−0.192576	+	0.136307i
$307$	7.62999	+	13.2155i	0.435467	+	0.754250i	0.997334	−	0.0729772i	$-0.0232500\pi$
$307$	7.62999	+	13.2155i	0.435467	+	0.754250i	−0.561867	+	0.827228i	$0.689917\pi$
$308$	−0.496975	+	1.40987i	−0.0283178	+	0.0803346i
$309$	19.8183	+	34.3263i	1.12742	+	1.95276i
$310$	4.83762	+	2.22595i	0.274758	+	0.126425i
$311$		−	0.398787i		−	0.0226132i	−0.999936	−	0.0113066i	$-0.996401\pi$
$311$		−	0.398787i		−	0.0226132i	0.999936	−	0.0113066i	$-0.00359907\pi$
$312$	20.3153	−	5.77694i	1.15013	−	0.327055i
$313$	−3.74686	+	6.48975i	−0.211785	+	0.366823i	−0.952273	−	0.305247i	$-0.901261\pi$
$313$	−3.74686	+	6.48975i	−0.211785	+	0.366823i	0.740488	+	0.672069i	$0.234594\pi$
$314$	24.2464	+	11.1566i	1.36830	+	0.629602i
$315$			0.401377i			0.0226150i
$316$	22.1602	−	4.14018i	1.24661	−	0.232903i
$317$	4.10441	+	2.36968i	0.230526	+	0.133094i	0.610815	−	0.791773i	$-0.290842\pi$
$317$	4.10441	+	2.36968i	0.230526	+	0.133094i	−0.380288	+	0.924868i	$0.624175\pi$
$318$	13.5124	+	19.0904i	0.757738	+	1.07054i
$319$	1.62501	−	2.81460i	0.0909832	−	0.157588i
$320$	−7.04697	−	3.78685i	−0.393938	−	0.211691i
$321$	9.41182	+	16.3018i	0.525317	+	0.909875i
$322$	−0.0496933	−	0.536566i	−0.00276930	−	0.0299016i
$323$	−4.12026	+	7.82391i	−0.229257	+	0.435334i
$324$	22.1099	−	4.13079i	1.22833	−	0.229488i
$325$	3.06953	−	1.77219i	0.170267	−	0.0983037i
$326$	−16.8870	−	23.8581i	−0.935285	−	1.32138i
$327$	30.0462	+	17.3472i	1.66156	+	0.959301i
$328$	−14.5339	−	14.0972i	−0.802501	−	0.778389i
$329$	0.360804	−	0.624930i	0.0198917	−	0.0344535i
$330$	−7.94786	+	0.736080i	−0.437515	+	0.0405199i
$331$	25.4886			1.40098			0.700490	−	0.713663i	$-0.252965\pi$
$331$	25.4886			1.40098			0.700490	+	0.713663i	$0.252965\pi$
$332$	6.25288	+	2.20413i	0.343171	+	0.120967i
$333$	−0.316704	−	0.182849i	−0.0173553	−	0.0100201i
$334$	3.12171	+	33.7069i	0.170813	+	1.84436i
$335$	12.4241			0.678802
$336$	2.32334	+	0.361121i	0.126748	+	0.0197008i
$337$	−23.2710	+	13.4355i	−1.26765	+	0.731880i	−0.974543	−	0.224199i	$-0.928023\pi$
$337$	−23.2710	+	13.4355i	−1.26765	+	0.731880i	−0.293110	+	0.956079i	$0.594690\pi$
$338$	−0.561818	−	0.258511i	−0.0305589	−	0.0140612i
$339$	23.6844	−	13.6742i	1.28636	−	0.742679i
$340$	2.63940	+	3.08134i	0.143142	+	0.167109i
$341$		−	10.0875i		−	0.546271i
$342$	−7.03375	+	5.40088i	−0.380342	+	0.292046i
$343$		−	3.88436i		−	0.209736i
$344$	−15.2380	−	14.7802i	−0.821579	−	0.796893i
$345$	2.49174	−	1.43861i	0.134151	−	0.0774519i
$346$	12.8958	−	28.0262i	0.693281	−	1.50670i
$347$	−12.5255	+	7.23160i	−0.672404	+	0.388213i	−0.796987	−	0.603996i	$-0.793574\pi$
$347$	−12.5255	+	7.23160i	−0.672404	+	0.388213i	0.124583	+	0.992209i	$0.460241\pi$
$348$	−4.82103	−	1.69940i	−0.258434	−	0.0910976i
$349$	28.0396			1.50092			0.750461	−	0.660914i	$-0.229831\pi$
$349$	28.0396			1.50092			0.750461	+	0.660914i	$0.229831\pi$
$350$	0.392893	−	0.0363872i	0.0210010	−	0.00194498i
$351$	10.0974	+	5.82975i	0.538960	+	0.311169i
$352$	−0.936677	+	15.1255i	−0.0499250	+	0.806194i
$353$	−7.57661			−0.403262			−0.201631	−	0.979462i	$-0.564624\pi$
$353$	−7.57661			−0.403262			−0.201631	+	0.979462i	$0.564624\pi$
$354$	−2.82224	−	30.4732i	−0.150000	−	1.61963i
$355$	1.81765	−	3.14826i	0.0964707	−	0.167092i
$356$	1.45660	−	1.24769i	0.0771997	−	0.0661273i
$357$	−1.03268	−	0.596218i	−0.0546552	−	0.0315552i
$358$	−18.9510	+	13.4137i	−1.00159	+	0.708937i
$359$	−7.55909	+	4.36424i	−0.398954	+	0.230336i	−0.686032	−	0.727571i	$-0.740649\pi$
$359$	−7.55909	+	4.36424i	−0.398954	+	0.230336i	0.287079	+	0.957907i	$0.407316\pi$
$360$	1.11294	+	3.91380i	0.0586572	+	0.206275i
$361$	−8.19308	+	17.1427i	−0.431215	+	0.902249i
$362$	−3.36507	+	0.311651i	−0.176864	+	0.0163800i
$363$	−4.02730	−	6.97548i	−0.211378	−	0.366118i
$364$	1.28665	+	1.50209i	0.0674388	+	0.0787308i
$365$	−2.69470	+	4.66736i	−0.141047	+	0.244301i
$366$	−6.27217	+	4.43951i	−0.327852	+	0.232057i
$367$	27.6764	+	15.9790i	1.44470	+	0.834096i	0.998158	−	0.0606690i	$-0.0193234\pi$
$367$	27.6764	+	15.9790i	1.44470	+	0.834096i	0.446538	+	0.894765i	$0.352657\pi$
$368$	−1.97235	−	5.09423i	−0.102816	−	0.265555i
$369$			10.2984i			0.536111i
$370$	−0.150273	+	0.326586i	−0.00781231	+	0.0169784i
$371$	−1.09509	+	1.89676i	−0.0568544	+	0.0984746i
$372$	−15.5963	+	2.91385i	−0.808628	+	0.151076i
$373$		−	3.72186i		−	0.192711i	−0.995347	−	0.0963554i	$-0.969281\pi$
$373$		−	3.72186i		−	0.192711i	0.995347	−	0.0963554i	$-0.0307185\pi$
$374$	3.21265	−	6.98200i	0.166122	−	0.361030i
$375$	1.05340	+	1.82454i	0.0543973	+	0.0942188i
$376$	1.78536	−	7.09410i	0.0920729	−	0.365850i
$377$	−2.14996	−	3.72384i	−0.110729	−	0.191788i
$378$	0.749884	+	1.05944i	0.0385699	+	0.0544918i
$379$	25.4448			1.30701			0.653505	−	0.756922i	$-0.273298\pi$
$379$	25.4448			1.30701			0.653505	+	0.756922i	$0.273298\pi$
$380$	5.92437	+	6.39545i	0.303914	+	0.328080i
$381$	−37.3913			−1.91561
$382$	20.3738	+	28.7842i	1.04241	+	1.47273i
$383$	9.09995	+	15.7616i	0.464986	+	0.805379i	0.999201	−	0.0399696i	$-0.0127261\pi$
$383$	9.09995	+	15.7616i	0.464986	+	0.805379i	−0.534215	+	0.845349i	$0.679393\pi$
$384$	23.6560	−	2.92091i	1.20719	−	0.149057i
$385$	−0.373724	−	0.647308i	−0.0190467	−	0.0329899i
$386$	14.9566	−	32.5050i	0.761272	−	1.65446i
$387$			10.7973i			0.548856i
$388$	−0.749394	−	4.01111i	−0.0380447	−	0.203633i
$389$	−8.29879	+	14.3739i	−0.420766	+	0.728787i	−0.996015	−	0.0891911i	$-0.971572\pi$
$389$	−8.29879	+	14.3739i	−0.420766	+	0.728787i	0.575249	+	0.817978i	$0.304905\pi$
$390$	−4.41429	+	9.59351i	−0.223526	+	0.485786i
$391$			2.77044i			0.140107i
$392$	−5.35519	−	18.8322i	−0.270478	−	0.951170i
$393$	0.756184	+	0.436583i	0.0381444	+	0.0220227i
$394$	−13.3703	+	9.46363i	−0.673585	+	0.476771i
$395$	−5.63590	+	9.76166i	−0.283573	+	0.491163i
$396$	5.85391	−	5.01432i	0.294170	−	0.251979i
$397$	7.31715	+	12.6737i	0.367237	+	0.636073i	0.989132	−	0.147027i	$-0.0469704\pi$
$397$	7.31715	+	12.6737i	0.367237	+	0.636073i	−0.621895	+	0.783100i	$0.713637\pi$
$398$	15.6860	−	1.45274i	0.786269	−	0.0728192i
$399$	−2.26705	−	1.19388i	−0.113494	−	0.0597688i
$400$	3.73018	−	1.44423i	0.186509	−	0.0722113i
$401$	22.2539	−	12.8483i	1.11131	−	0.641614i	0.172140	−	0.985073i	$-0.444932\pi$
$401$	22.2539	−	12.8483i	1.11131	−	0.641614i	0.939168	+	0.343459i	$0.111599\pi$
$402$	−30.2144	+	21.3860i	−1.50695	+	1.06664i
$403$	−11.5582	−	6.67313i	−0.575755	−	0.332412i
$404$	2.98849	+	3.48888i	0.148683	+	0.173578i
$405$	−5.62311	+	9.73952i	−0.279415	+	0.483961i
$406$	−0.0441436	−	0.476643i	−0.00219081	−	0.0236554i
$407$	0.681006			0.0337562
$408$	−11.7228	−	2.95026i	−0.580365	−	0.146060i
$409$	−20.4336	−	11.7974i	−1.01038	−	0.583342i	−0.0990755	−	0.995080i	$-0.531589\pi$
$409$	−20.4336	−	11.7974i	−1.01038	−	0.583342i	−0.911302	+	0.411738i	$0.864922\pi$
$410$	10.0807	−	0.933608i	0.497849	−	0.0461076i
$411$	45.8043			2.25936
$412$	−12.5092	+	35.4872i	−0.616282	+	1.74833i
$413$	2.48187	−	1.43291i	0.122125	−	0.0705089i
$414$	−1.16141	+	2.52407i	−0.0570801	+	0.124051i
$415$	−2.87087	+	1.65750i	−0.140925	+	0.0813633i
$416$	16.7111	+	11.0791i	0.819327	+	0.543198i
$417$		−	12.5347i		−	0.613825i
$418$	6.31469	−	15.2593i	0.308861	−	0.746355i
$419$		−	13.0060i		−	0.635385i	−0.948194	−	0.317692i	$-0.897092\pi$
$419$		−	13.0060i		−	0.635385i	0.948194	−	0.317692i	$-0.102908\pi$
$420$	−0.892846	+	0.764790i	−0.0435664	+	0.0373179i
$421$	−0.753638	+	0.435113i	−0.0367301	+	0.0212061i	−0.518253	−	0.855228i	$-0.673417\pi$
$421$	−0.753638	+	0.435113i	−0.0367301	+	0.0212061i	0.481523	+	0.876434i	$0.340084\pi$
$422$	−26.8053	−	12.3340i	−1.30486	−	0.600409i
$423$	−3.22223	+	1.86036i	−0.156670	+	0.0904536i
$424$	−5.41883	+	21.5316i	−0.263162	+	1.04567i
$425$	−2.02861			−0.0984022
$426$	0.998844	+	10.7851i	0.0483942	+	0.522538i
$427$	−0.623181	−	0.359794i	−0.0301578	−	0.0174116i
$428$	−5.94067	+	16.8531i	−0.287153	+	0.814623i
$429$	20.0047			0.965834
$430$	10.5690	−	0.978837i	0.509684	−	0.0472037i
$431$	−0.847349	+	1.46765i	−0.0408154	+	0.0706943i	−0.885711	−	0.464236i	$-0.846329\pi$
$431$	−0.847349	+	1.46765i	−0.0408154	+	0.0706943i	0.844896	+	0.534931i	$0.179662\pi$
$432$	10.2497	+	8.25126i	0.493139	+	0.396989i
$433$	−7.92050	−	4.57290i	−0.380635	−	0.219760i	0.297460	−	0.954734i	$-0.403861\pi$
$433$	−7.92050	−	4.57290i	−0.380635	−	0.219760i	−0.678094	+	0.734975i	$0.737194\pi$
$434$	−0.858369	−	1.21271i	−0.0412030	−	0.0582119i
$435$	2.21347	−	1.27795i	0.106128	−	0.0612728i
$436$	6.04869	+	32.3754i	0.289680	+	1.55050i
$437$	0.231390	+	5.94836i	0.0110689	+	0.284549i
$438$	−1.48081	−	15.9891i	−0.0707558	−	0.763989i
$439$	11.7514	+	20.3541i	0.560865	+	0.971446i	0.997421	+	0.0717695i	$0.0228646\pi$
$439$	11.7514	+	20.3541i	0.560865	+	0.971446i	−0.436556	+	0.899677i	$0.643802\pi$
$440$	−5.43902	−	5.27560i	−0.259295	−	0.251504i
$441$	−4.97909	+	8.62404i	−0.237100	+	0.410668i
$442$	−5.87466	−	8.29977i	−0.279429	−	0.394780i
$443$	13.7863	+	7.95954i	0.655008	+	0.378169i	0.790372	−	0.612627i	$-0.209887\pi$
$443$	13.7863	+	7.95954i	0.655008	+	0.378169i	−0.135364	+	0.990796i	$0.543220\pi$
$444$	−0.196713	−	1.05290i	−0.00933557	−	0.0499683i
$445$			0.958959i			0.0454590i
$446$	−10.2782	−	4.72936i	−0.486688	−	0.223941i
$447$	−0.103823	+	0.179827i	−0.00491065	+	0.00850550i
$448$	1.17446	+	1.89807i	0.0554879	+	0.0896756i
$449$		−	28.2467i		−	1.33304i	−0.745486	−	0.666521i	$-0.767783\pi$
$449$		−	28.2467i		−	1.33304i	0.745486	−	0.666521i	$-0.232217\pi$
$450$	−1.84821	−	0.850424i	−0.0871256	−	0.0400894i
$451$	−9.58884	−	16.6084i	−0.451521	−	0.782057i
$452$	24.4853	+	8.63103i	1.15169	+	0.405969i
$453$	15.0679	+	26.0984i	0.707953	+	1.22621i
$454$	−13.2695	+	9.39229i	−0.622768	+	0.440802i
$455$	−0.988906			−0.0463606
$456$	−25.4163	−	5.35536i	−1.19023	−	0.250788i
$457$	2.44512			0.114378			0.0571889	−	0.998363i	$-0.481786\pi$
$457$	2.44512			0.114378			0.0571889	+	0.998363i	$0.481786\pi$
$458$	−11.6568	+	8.25081i	−0.544686	+	0.385535i
$459$	−3.33663	−	5.77920i	−0.155740	−	0.269750i
$460$	2.57600	+	0.908036i	0.120107	+	0.0423374i
$461$	7.53507	+	13.0511i	0.350943	+	0.607852i	0.986415	−	0.164272i	$-0.0525276\pi$
$461$	7.53507	+	13.0511i	0.350943	+	0.607852i	−0.635472	+	0.772124i	$0.719194\pi$
$462$	2.02310	+	0.930894i	0.0941230	+	0.0433091i
$463$		−	20.5612i		−	0.955558i	−0.878480	−	0.477779i	$-0.841442\pi$
$463$		−	20.5612i		−	0.955558i	0.878480	−	0.477779i	$-0.158558\pi$
$464$	−1.75208	−	4.52531i	−0.0813384	−	0.210082i
$465$	3.96653	−	6.87023i	0.183943	−	0.318599i
$466$	21.1421	+	9.72818i	0.979389	+	0.450649i
$467$			21.4232i			0.991349i	0.868508	+	0.495674i	$0.165079\pi$
$467$			21.4232i			0.991349i	−0.868508	+	0.495674i	$0.834921\pi$
$468$	−1.87286	−	10.0244i	−0.0865731	−	0.463380i
$469$	−3.00199	−	1.73320i	−0.138619	−	0.0800317i
$470$	2.11315	+	2.98547i	0.0974723	+	0.137709i
$471$	19.8805	−	34.4340i	0.916044	−	1.58663i
$472$	20.2274	−	20.8540i	0.931041	−	0.959882i
$473$	−10.0534	−	17.4130i	−0.462255	−	0.800649i
$474$	−3.09707	−	33.4408i	−0.142253	−	1.53599i
$475$	−4.35560	+	0.169432i	−0.199849	+	0.00777406i
$476$	−0.207892	−	1.11274i	−0.00952872	−	0.0510022i
$477$	9.77995	−	5.64646i	0.447793	−	0.258533i
$478$	2.33122	+	3.29356i	0.106627	+	0.150644i
$479$	−18.5010	−	10.6815i	−0.845330	−	0.488052i	0.0137423	−	0.999906i	$-0.495626\pi$
$479$	−18.5010	−	10.6815i	−0.845330	−	0.488052i	−0.859072	+	0.511854i	$0.828959\pi$
$480$	−6.58546	+	9.93311i	−0.300584	+	0.453382i
$481$	0.450500	−	0.780290i	0.0205410	−	0.0355781i
$482$	8.67008	−	0.802967i	0.394911	−	0.0365742i
$483$	−0.802759			−0.0365268
$484$	2.54200	−	7.21138i	0.115545	−	0.327790i
$485$	1.76691	+	1.02013i	0.0802314	+	0.0463216i
$486$	−1.80300	−	19.4680i	−0.0817857	−	0.883085i
$487$	−9.96648			−0.451624			−0.225812	−	0.974171i	$-0.572504\pi$
$487$	−9.96648			−0.451624			−0.225812	+	0.974171i	$0.572504\pi$
$488$	−7.07424	−	1.78036i	−0.320236	−	0.0805932i
$489$	−37.7106	+	21.7722i	−1.70533	+	0.984574i
$490$	8.89313	+	4.09202i	0.401751	+	0.184859i
$491$	−1.74955	+	1.01010i	−0.0789561	+	0.0455853i	−0.538958	−	0.842332i	$-0.681182\pi$
$491$	−1.74955	+	1.01010i	−0.0789561	+	0.0455853i	0.460002	+	0.887918i	$0.347849\pi$
$492$	−22.9083	+	19.6227i	−1.03278	+	0.884658i
$493$			2.46104i			0.110840i
$494$	−13.3066	−	17.3296i	−0.598693	−	0.779698i
$495$			3.85395i			0.173222i
$496$	−11.7325	−	9.44495i	−0.526805	−	0.424091i
$497$	−0.878382	+	0.507134i	−0.0394008	+	0.0227481i
$498$	4.12859	−	8.97261i	0.185007	−	0.402072i
$499$	36.7529	−	21.2193i	1.64528	−	0.949906i	0.666374	−	0.745618i	$-0.267845\pi$
$499$	36.7529	−	21.2193i	1.64528	−	0.949906i	0.978911	−	0.204288i	$-0.0654878\pi$
$500$	−0.664897	+	1.88624i	−0.0297351	+	0.0843553i
$501$	50.4290			2.25300
$502$	−31.9285	+	2.95702i	−1.42504	+	0.131978i
$503$	9.89470	+	5.71271i	0.441183	+	0.254717i	0.704099	−	0.710102i	$-0.251351\pi$
$503$	9.89470	+	5.71271i	0.441183	+	0.254717i	−0.262916	+	0.964819i	$0.584684\pi$
$504$	0.277070	−	1.10093i	0.0123417	−	0.0490395i
$505$	−2.29692			−0.102211
$506$	−0.477146	−	5.15201i	−0.0212117	−	0.229035i
$507$	−0.460654	+	0.797877i	−0.0204584	+	0.0354350i
$508$	−23.0916	−	26.9580i	−1.02452	−	1.19607i
$509$	−7.58567	−	4.37959i	−0.336229	−	0.194122i	0.322374	−	0.946612i	$-0.395519\pi$
$509$	−7.58567	−	4.37959i	−0.336229	−	0.194122i	−0.658603	+	0.752491i	$0.728852\pi$
$510$	4.93341	−	3.49192i	0.218455	−	0.154625i
$511$	1.30222	−	0.751838i	0.0576069	−	0.0332594i
$512$	16.7151	+	15.2515i	0.738708	+	0.674025i
$513$	−7.64670	−	12.1298i	−0.337610	−	0.535542i
$514$	−8.03042	+	0.743726i	−0.354207	+	0.0328044i
$515$	−9.40684	−	16.2931i	−0.414515	−	0.717961i
$516$	−24.0181	+	20.5733i	−1.05734	+	0.905688i
$517$	3.46437	−	6.00047i	0.152363	−	0.263900i
$518$	0.0818695	−	0.0579481i	0.00359714	−	0.00254610i
$519$	−39.8019	−	22.9796i	−1.74711	−	1.00869i
$520$	−9.64276	+	2.74205i	−0.422863	+	0.120247i
$521$			31.4639i			1.37846i	0.724543	+	0.689229i	$0.242051\pi$
$521$			31.4639i			1.37846i	−0.724543	+	0.689229i	$0.757949\pi$
$522$	−1.03170	+	2.24219i	−0.0451564	+	0.0981378i
$523$	−1.12879	+	1.95512i	−0.0493585	+	0.0854913i	−0.889649	−	0.456645i	$-0.849051\pi$
$523$	−1.12879	+	1.95512i	−0.0493585	+	0.0854913i	0.840291	+	0.542136i	$0.182384\pi$
$524$	0.152230	+	0.814805i	0.00665019	+	0.0355949i
$525$		−	0.587809i		−	0.0256541i
$526$	4.41113	−	9.58664i	0.192334	−	0.417997i
$527$	3.81933	+	6.61527i	0.166373	+	0.288166i
$528$	22.3083	+	3.46742i	0.970843	+	0.150900i
$529$	−10.5675	−	18.3034i	−0.459455	−	0.795799i
$530$	−6.41372	−	9.06134i	−0.278594	−	0.393600i
$531$	−14.7766			−0.641249
$532$	−0.539299	−	2.37178i	−0.0233816	−	0.102830i
$533$	−25.3729			−1.09902
$534$	−1.65069	−	2.33210i	−0.0714323	−	0.100920i
$535$	−4.46736	−	7.73770i	−0.193141	−	0.334530i
$536$	−34.0781	−	8.57637i	−1.47195	−	0.370443i
$537$	17.2942	+	29.9544i	0.746298	+	1.29263i
$538$	−2.55714	+	5.55739i	−0.110246	+	0.239596i
$539$		−	18.5442i		−	0.798756i
$540$	−6.46722	+	1.20827i	−0.278305	+	0.0519957i
$541$	19.0229	−	32.9486i	0.817857	−	1.41657i	−0.0894010	−	0.995996i	$-0.528495\pi$
$541$	19.0229	−	32.9486i	0.817857	−	1.41657i	0.907258	−	0.420574i	$-0.138171\pi$
$542$	0.654161	−	1.42168i	0.0280986	−	0.0610663i
$543$			5.03450i			0.216051i
$544$	−5.11255	−	10.2738i	−0.219199	−	0.440484i
$545$	−14.2615	−	8.23391i	−0.610897	−	0.352702i
$546$	2.40493	−	1.70224i	0.102922	−	0.0728490i
$547$	−18.1943	+	31.5135i	−0.777933	+	1.34742i	0.155198	+	0.987883i	$0.450399\pi$
$547$	−18.1943	+	31.5135i	−0.777933	+	1.34742i	−0.933131	+	0.359537i	$0.882935\pi$
$548$	28.2872	+	33.0236i	1.20837	+	1.41070i
$549$	1.85515	+	3.21321i	0.0791758	+	0.137137i
$550$	3.77248	−	0.349383i	0.160859	−	0.0148978i
$551$	0.205548	+	5.28406i	0.00875666	+	0.225109i
$552$	−7.82765	+	2.22590i	−0.333167	+	0.0947406i
$553$	2.72356	−	1.57245i	0.115818	−	0.0668673i
$554$	−31.7735	+	22.4896i	−1.34992	+	0.955491i
$555$	0.463807	+	0.267779i	0.0196875	+	0.0113666i
$556$	9.03712	−	7.74098i	0.383259	−	0.328291i
$557$	5.49620	−	9.51969i	0.232881	−	0.403362i	−0.725774	−	0.687934i	$-0.758518\pi$
$557$	5.49620	−	9.51969i	0.232881	−	0.403362i	0.958655	+	0.284571i	$0.0918513\pi$
$558$	0.706467	+	7.62811i	0.0299071	+	0.322924i
$559$	−26.6021			−1.12515
$560$	−1.10278	−	0.171408i	−0.0466010	−	0.00724329i
$561$	−9.91561	−	5.72478i	−0.418638	−	0.241701i
$562$	−31.5288	+	2.92000i	−1.32996	+	0.123173i
$563$	−6.59388			−0.277899			−0.138949	−	0.990299i	$-0.544373\pi$
$563$	−6.59388			−0.277899			−0.138949	+	0.990299i	$0.544373\pi$
$564$	−10.2780	−	3.62297i	−0.432781	−	0.152554i
$565$	−11.2419	+	6.49050i	−0.472950	+	0.273058i
$566$	6.78535	−	14.7465i	0.285209	−	0.619841i
$567$	2.71738	−	1.56888i	0.114119	−	0.0658869i
$568$	−7.15886	+	7.38062i	−0.300379	+	0.309684i
$569$		−	45.9998i		−	1.92841i	−0.265157	−	0.964205i	$-0.585424\pi$
$569$		−	45.9998i		−	1.92841i	0.265157	−	0.964205i	$-0.414576\pi$
$570$	10.3008	−	7.90949i	0.431453	−	0.331292i
$571$			5.91950i			0.247723i	0.992299	+	0.123862i	$0.0395279\pi$
$571$			5.91950i			0.247723i	−0.992299	+	0.123862i	$0.960472\pi$
$572$	12.3542	+	14.4228i	0.516555	+	0.603046i
$573$	45.4969	−	26.2677i	1.90066	−	1.09735i
$574$	−2.56600	−	1.18070i	−0.107103	−	0.0492814i
$575$	−1.18271	+	0.682840i	−0.0493226	+	0.0284764i
$576$	−0.350990	−	11.5034i	−0.0146246	−	0.479309i
$577$	3.74081			0.155732			0.0778660	−	0.996964i	$-0.475189\pi$
$577$	3.74081			0.155732			0.0778660	+	0.996964i	$0.475189\pi$
$578$	−1.68039	−	18.1441i	−0.0698951	−	0.754696i
$579$	−46.1626	−	26.6520i	−1.91845	−	1.10762i
$580$	2.28832	+	0.806629i	0.0950174	+	0.0334934i
$581$	0.924902			0.0383714
$582$	−6.05296	+	0.560587i	−0.250903	+	0.0232371i
$583$	−10.5149	+	18.2123i	−0.435482	+	0.754277i
$584$	10.6132	−	10.9419i	0.439176	−	0.452781i
$585$	4.41581	+	2.54947i	0.182571	+	0.105408i
$586$	−8.46894	−	11.9650i	−0.349849	−	0.494269i
$587$	−21.8583	+	12.6199i	−0.902190	+	0.520880i	−0.877910	−	0.478825i	$-0.841063\pi$
$587$	−21.8583	+	12.6199i	−0.902190	+	0.520880i	−0.0242802	+	0.999705i	$0.507729\pi$
$588$	−28.6711	+	5.35661i	−1.18237	+	0.220903i
$589$	8.75294	+	13.8846i	0.360659	+	0.572103i
$590$	1.33959	+	14.4643i	0.0551499	+	0.595484i
$591$	12.2014	+	21.1334i	0.501897	+	0.869311i
$592$	0.637625	−	0.792058i	0.0262062	−	0.0325534i
$593$	−11.3980	+	19.7419i	−0.468059	+	0.810702i	−0.999334	−	0.0364977i	$-0.988380\pi$
$593$	−11.3980	+	19.7419i	−0.468059	+	0.810702i	0.531275	+	0.847200i	$0.321713\pi$
$594$	7.20025	+	10.1726i	0.295430	+	0.417385i
$595$	0.490166	+	0.282997i	0.0200948	+	0.0116018i
$596$	−0.193767	+	0.0362015i	−0.00793701	+	0.00148287i
$597$		−	23.4679i		−	0.960479i
$598$	−6.21876	−	2.86146i	−0.254304	−	0.117014i
$599$	−15.0211	+	26.0173i	−0.613745	+	1.06304i	0.376859	+	0.926271i	$0.377004\pi$
$599$	−15.0211	+	26.0173i	−0.613745	+	1.06304i	−0.990603	+	0.136766i	$0.956329\pi$
$600$	−1.62988	−	5.73169i	−0.0665397	−	0.233995i
$601$		−	29.7085i		−	1.21184i	−0.795527	−	0.605918i	$-0.792806\pi$
$601$		−	29.7085i		−	1.21184i	0.795527	−	0.605918i	$-0.207194\pi$
$602$	−2.69031	−	1.23790i	−0.109649	−	0.0504530i
$603$	8.93663	+	15.4787i	0.363928	+	0.630342i
$604$	−9.51076	+	26.9810i	−0.386987	+	1.09784i
$605$	1.91157	+	3.31094i	0.0777165	+	0.134609i
$606$	5.58590	−	3.95376i	0.226912	−	0.160611i
$607$	4.14818			0.168369			0.0841847	−	0.996450i	$-0.473171\pi$
$607$	4.14818			0.168369			0.0841847	+	0.996450i	$0.473171\pi$
$608$	−11.8352	−	21.6317i	−0.479979	−	0.877280i
$609$	−0.713109			−0.0288966
$610$	2.97711	−	2.10723i	0.120540	−	0.0853194i
$611$	−4.58352	−	7.93889i	−0.185429	−	0.321173i
$612$	−1.94040	+	5.50472i	−0.0784362	+	0.222515i
$613$	−5.07665	−	8.79302i	−0.205044	−	0.355147i	0.745103	−	0.666950i	$-0.232400\pi$
$613$	−5.07665	−	8.79302i	−0.205044	−	0.355147i	−0.950147	+	0.311803i	$0.899067\pi$
$614$	19.6050	+	9.02092i	0.791195	+	0.364055i
$615$		−	15.0818i		−	0.608155i
$616$	0.578248	+	2.03348i	0.0232983	+	0.0819313i
$617$	4.99604	−	8.65340i	0.201133	−	0.348373i	−0.747761	−	0.663968i	$-0.768871\pi$
$617$	4.99604	−	8.65340i	0.201133	−	0.348373i	0.948894	+	0.315596i	$0.102204\pi$
$618$	50.9225	+	23.4311i	2.04840	+	0.942539i
$619$		−	14.3326i		−	0.576077i	−0.957619	−	0.288038i	$-0.906997\pi$
$619$		−	14.3326i		−	0.576077i	0.957619	−	0.288038i	$-0.0930031\pi$
$620$	7.40283	−	1.38307i	0.297305	−	0.0555454i
$621$	−3.89061	−	2.24625i	−0.156125	−	0.0901387i
$622$	−0.325825	−	0.460327i	−0.0130644	−	0.0184574i
$623$	0.133778	−	0.231710i	0.00535969	−	0.00928325i
$624$	18.7304	−	23.2668i	0.749814	−	0.931419i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.977311	+	10.5526i	0.0390612	+	0.421765i
$627$	−21.7678	−	11.4634i	−0.869323	−	0.457806i
$628$	37.1034	−	6.93202i	1.48059	−	0.276618i
$629$	−0.446595	+	0.257842i	−0.0178069	+	0.0102808i
$630$	0.327940	+	0.463316i	0.0130654	+	0.0184589i
$631$	−39.9653	−	23.0740i	−1.59099	−	0.918561i	−0.993137	−	0.116958i	$-0.962686\pi$
$631$	−39.9653	−	23.0740i	−1.59099	−	0.918561i	−0.597857	−	0.801603i	$-0.703981\pi$
$632$	22.1972	−	22.8848i	0.882956	−	0.910308i
$633$	−21.9786	+	38.0680i	−0.873570	+	1.51307i
$634$	6.67391	−	0.618095i	0.265055	−	0.0245477i
$635$	17.7479			0.704305
$636$	31.1952	+	10.9962i	1.23697	+	0.436029i
$637$	−21.2478	−	12.2674i	−0.841867	−	0.486052i
$638$	−0.423859	−	4.57664i	−0.0167808	−	0.181191i
$639$	5.22972			0.206884
$640$	−11.2284	+	1.38642i	−0.443843	+	0.0548032i
$641$	38.0203	−	21.9510i	1.50171	−	0.867013i	0.501712	−	0.865035i	$-0.332704\pi$
$641$	38.0203	−	21.9510i	1.50171	−	0.867013i	0.999998	−	0.00197812i	$-0.000629655\pi$
$642$	24.1834	+	11.1276i	0.954442	+	0.439171i
$643$	−6.01499	+	3.47276i	−0.237208	+	0.136952i	−0.613893	−	0.789389i	$-0.710397\pi$
$643$	−6.01499	+	3.47276i	−0.237208	+	0.136952i	0.376685	+	0.926341i	$0.377064\pi$
$644$	−0.495757	−	0.578766i	−0.0195355	−	0.0228066i
$645$		−	15.8124i		−	0.622612i
$646$	1.63636	+	12.3977i	0.0643816	+	0.487780i
$647$		−	42.6465i		−	1.67661i	−0.545205	−	0.838303i	$-0.683548\pi$
$647$		−	42.6465i		−	1.67661i	0.545205	−	0.838303i	$-0.316452\pi$
$648$	22.1468	−	22.8329i	0.870009	−	0.896960i
$649$	23.8305	−	13.7585i	0.935429	−	0.540070i
$650$	2.09526	−	4.55360i	0.0821829	−	0.178607i
$651$	−1.91684	+	1.10669i	−0.0751267	+	0.0433744i
$652$	−38.9859	−	13.7425i	−1.52681	−	0.538196i
$653$	−2.00713			−0.0785452			−0.0392726	−	0.999229i	$-0.512504\pi$
$653$	−2.00713			−0.0785452			−0.0392726	+	0.999229i	$0.512504\pi$
$654$	48.8561	−	4.52474i	1.91043	−	0.176931i
$655$	−0.358926	−	0.207226i	−0.0140244	−	0.00809698i
$656$	−28.2947	−	4.39790i	−1.10472	−	0.171709i
$657$	−7.75317			−0.302480
$658$	−0.0941101	−	1.01616i	−0.00366879	−	0.0396140i
$659$	−6.05584	+	10.4890i	−0.235902	+	0.408594i	−0.959534	−	0.281591i	$-0.909138\pi$
$659$	−6.05584	+	10.4890i	−0.235902	+	0.408594i	0.723633	+	0.690185i	$0.242471\pi$
$660$	−8.57295	+	7.34338i	−0.333702	+	0.285841i
$661$	33.2302	+	19.1855i	1.29251	+	0.746228i	0.979098	−	0.203390i	$-0.0651961\pi$
$661$	33.2302	+	19.1855i	1.29251	+	0.746228i	0.313408	+	0.949619i	$0.398529\pi$
$662$	29.4219	−	20.8251i	1.14352	−	0.809392i
$663$	−13.1188	+	7.57414i	−0.509492	+	0.294155i
$664$	9.01866	−	2.56458i	0.349992	−	0.0995250i
$665$	1.07606	+	0.566681i	0.0417280	+	0.0219749i
$666$	−0.514971	+	0.0476933i	−0.0199547	+	0.00184808i
$667$	0.828397	+	1.43483i	0.0320757	+	0.0555567i
$668$	31.1432	+	36.3578i	1.20497	+	1.40673i
$669$	−8.42748	+	14.5968i	−0.325825	+	0.564346i
$670$	14.3414	−	10.1510i	0.554055	−	0.392166i
$671$	−5.98367	−	3.45468i	−0.230997	−	0.133366i
$672$	2.97692	−	1.48141i	0.114837	−	0.0571466i
$673$			5.52880i			0.213120i	0.994306	+	0.106560i	$0.0339835\pi$
$673$			5.52880i			0.213120i	−0.994306	+	0.106560i	$0.966016\pi$
$674$	−15.8848	+	34.5222i	−0.611859	+	1.32974i
$675$	1.64478	−	2.84885i	0.0633077	−	0.109652i
$676$	−0.859730	+	0.160623i	−0.0330665	+	0.00617781i
$677$			8.23531i			0.316509i	0.987398	+	0.158254i	$0.0505866\pi$
$677$			8.23531i			0.316509i	−0.987398	+	0.158254i	$0.949413\pi$
$678$	16.1669	−	35.1354i	0.620888	−	1.34937i
$679$	−0.284622	−	0.492979i	−0.0109228	−	0.0189188i
$680$	5.56428	+	1.40035i	0.213380	+	0.0537011i
$681$	12.1094	+	20.9741i	0.464033	+	0.803728i
$682$	−8.24190	−	11.6442i	−0.315599	−	0.445880i
$683$	26.2516			1.00449			0.502245	−	0.864725i	$-0.332508\pi$
$683$	26.2516			1.00449			0.502245	+	0.864725i	$0.332508\pi$
$684$	−3.70645	+	11.9812i	−0.141720	+	0.458112i
$685$	−21.7412			−0.830689
$686$	−3.17367	−	4.48379i	−0.121171	−	0.171192i
$687$	10.6377	+	18.4250i	0.405853	+	0.702957i
$688$	−29.6655	−	4.61096i	−1.13099	−	0.175791i
$689$	13.9117	+	24.0957i	0.529992	+	0.917973i
$690$	1.70086	−	3.69645i	0.0647507	−	0.140722i
$691$			26.1638i			0.995319i	0.867373	+	0.497659i	$0.165807\pi$
$691$			26.1638i			0.995319i	−0.867373	+	0.497659i	$0.834193\pi$
$692$	−8.01265	−	42.8875i	−0.304595	−	1.63034i
$693$	0.537637	−	0.931215i	0.0204231	−	0.0353739i
$694$	−8.54991	+	18.5814i	−0.324550	+	0.705340i
$695$			5.94963i			0.225682i
$696$	−6.95348	+	1.97732i	−0.263571	+	0.0749500i
$697$	12.5765	+	7.26103i	0.476368	+	0.275031i
$698$	32.3665	−	22.9094i	1.22509	−	0.867133i
$699$	17.3352	−	30.0254i	0.655676	−	1.13566i
$700$	0.423793	−	0.363011i	0.0160179	−	0.0137205i
$701$	0.555704	+	0.962508i	0.0209887	+	0.0363534i	0.876329	−	0.481713i	$-0.159985\pi$
$701$	0.555704	+	0.962508i	0.0209887	+	0.0363534i	−0.855340	+	0.518067i	$0.826652\pi$
$702$	16.4187	−	1.52060i	0.619686	−	0.0573913i
$703$	−0.937342	+	0.590908i	−0.0353525	+	0.0222865i
$704$	11.2769	+	18.2250i	0.425015	+	0.686880i
$705$	4.71890	−	2.72446i	0.177724	−	0.102609i
$706$	−8.74581	+	6.19038i	−0.329153	+	0.232978i
$707$	0.554995	+	0.320427i	0.0208727	+	0.0120509i
$708$	−28.1556	−	32.8699i	−1.05815	−	1.23533i
$709$	−14.4368	+	25.0052i	−0.542185	+	0.939091i	0.456594	+	0.889675i	$0.349069\pi$
$709$	−14.4368	+	25.0052i	−0.542185	+	0.939091i	−0.998778	+	0.0494160i	$0.984264\pi$
$710$	−0.474105	−	5.11918i	−0.0177929	−	0.192119i
$711$	−16.2156			−0.608131
$712$	0.661970	−	2.63033i	0.0248084	−	0.0985756i
$713$	4.45346	+	2.57121i	0.166783	+	0.0962925i
$714$	−1.67917	+	0.155514i	−0.0628415	+	0.00581998i
$715$	−9.49530			−0.355104
$716$	−10.9159	+	30.9674i	−0.407948	+	1.15731i
$717$	5.20588	−	3.00561i	0.194417	−	0.112247i
$718$	−5.15984	+	11.2138i	−0.192563	+	0.418495i
$719$	3.08073	−	1.77866i	0.114892	−	0.0663329i	−0.441453	−	0.897284i	$-0.645537\pi$
$719$	3.08073	−	1.77866i	0.114892	−	0.0663329i	0.556345	+	0.830952i	$0.312203\pi$
$720$	4.48241	+	3.60845i	0.167050	+	0.134479i
$721$			5.24913i			0.195488i
$722$	4.54886	+	26.4822i	0.169291	+	0.985566i
$723$		−	12.9714i		−	0.482410i
$724$	−3.62972	+	3.10913i	−0.134898	+	0.115550i
$725$	−1.05063	+	0.606582i	−0.0390194	+	0.0225279i
$726$	−10.3480	−	4.76146i	−0.384051	−	0.176715i
$727$	−25.5582	+	14.7560i	−0.947900	+	0.547271i	−0.892428	−	0.451190i	$-0.851000\pi$
$727$	−25.5582	+	14.7560i	−0.947900	+	0.547271i	−0.0554723	+	0.998460i	$0.517666\pi$
$728$	2.71247	+	0.682642i	0.100531	+	0.0253004i
$729$	4.61256			0.170835
$730$	0.702872	+	7.58929i	0.0260145	+	0.280892i
$731$	13.1857	+	7.61279i	0.487692	+	0.281569i
$732$	−3.61283	+	10.2492i	−0.133534	+	0.378822i
$733$	−28.7112			−1.06047			−0.530236	−	0.847850i	$-0.677897\pi$
$733$	−28.7112			−1.06047			−0.530236	+	0.847850i	$0.677897\pi$
$734$	45.0028	−	4.16787i	1.66108	−	0.153839i
$735$	7.29179	−	12.6298i	0.268962	−	0.465855i
$736$	−6.43890	−	4.26887i	−0.237341	−	0.157353i
$737$	−28.8246	−	16.6419i	−1.06177	−	0.613011i
$738$	8.41415	+	11.8876i	0.309729	+	0.437587i
$739$	−32.7772	+	18.9239i	−1.20573	+	0.696127i	−0.961823	−	0.273672i	$-0.911762\pi$
$739$	−32.7772	+	18.9239i	−1.20573	+	0.696127i	−0.243905	+	0.969799i	$0.578428\pi$
$740$	0.0933704	+	0.499762i	0.00343237	+	0.0183716i
$741$	−27.5346	+	17.3580i	−1.01151	+	0.637663i
$742$	0.285638	+	3.08419i	0.0104861	+	0.113224i
$743$	24.6050	+	42.6172i	0.902672	+	1.56347i	0.824012	+	0.566572i	$0.191731\pi$
$743$	24.6050	+	42.6172i	0.902672	+	1.56347i	0.0786592	+	0.996902i	$0.474936\pi$
$744$	−15.6223	+	16.1062i	−0.572742	+	0.590484i
$745$	0.0492800	−	0.0853554i	0.00180548	−	0.00312718i
$746$	−3.04090	−	4.29621i	−0.111335	−	0.157295i
$747$	−4.13002	−	2.38447i	−0.151109	−	0.0872430i
$748$	−1.99614	−	10.6843i	−0.0729863	−	0.390657i
$749$			2.49284i			0.0910864i
$750$	2.70668	+	1.24543i	0.0988338	+	0.0454767i
$751$	−7.25003	+	12.5574i	−0.264557	+	0.458227i	−0.967448	−	0.253072i	$-0.918559\pi$
$751$	−7.25003	+	12.5574i	−0.264557	+	0.458227i	0.702890	+	0.711298i	$0.251893\pi$
$752$	−3.73528	−	9.64754i	−0.136212	−	0.351810i
$753$			47.7684i			1.74078i
$754$	−5.52426	−	2.54190i	−0.201182	−	0.0925704i
$755$	−7.15206	−	12.3877i	−0.260290	−	0.450836i
$756$	1.73121	+	0.610247i	0.0629634	+	0.0221945i
$757$	2.53642	+	4.39322i	0.0921879	+	0.159674i	0.908432	−	0.418034i	$-0.137281\pi$
$757$	2.53642	+	4.39322i	0.0921879	+	0.159674i	−0.816244	+	0.577708i	$0.803947\pi$
$758$	29.3713	−	20.7894i	1.06682	−	0.755103i
$759$	−7.70795			−0.279781
$760$	12.0639	+	2.54194i	0.437605	+	0.0922059i
$761$	−46.1745			−1.67383			−0.836913	−	0.547336i	$-0.815642\pi$
$761$	−46.1745			−1.67383			−0.836913	+	0.547336i	$0.815642\pi$
$762$	−43.1614	+	30.5501i	−1.56357	+	1.10671i
$763$	2.29731	+	3.97906i	0.0831682	+	0.144051i
$764$	47.0356	+	16.5799i	1.70169	+	0.599841i
$765$	−1.45918	−	2.52737i	−0.0527566	−	0.0913772i
$766$	23.3820	+	10.7589i	0.844828	+	0.388733i
$767$		−	36.4063i		−	1.31456i
$768$	24.9201	−	22.6996i	0.899226	−	0.819100i
$769$	8.19104	−	14.1873i	0.295377	−	0.511607i	−0.679696	−	0.733494i	$-0.737888\pi$
$769$	8.19104	−	14.1873i	0.295377	−	0.511607i	0.975072	+	0.221887i	$0.0712216\pi$
$770$	−0.960271	−	0.441853i	−0.0346058	−	0.0159233i
$771$			12.0144i			0.432687i
$772$	−9.29313	−	49.7412i	−0.334467	−	1.79022i
$773$	−39.4479	−	22.7753i	−1.41884	−	0.819170i	−0.422646	−	0.906295i	$-0.638899\pi$
$773$	−39.4479	−	22.7753i	−1.41884	−	0.819170i	−0.996197	+	0.0871250i	$0.972232\pi$
$774$	8.82178	+	12.4635i	0.317092	+	0.447990i
$775$	−1.88273	+	3.26098i	−0.0676297	+	0.117138i
$776$	−4.14227	−	4.01781i	−0.148699	−	0.144231i
$777$	−0.0747119	−	0.129405i	−0.00268028	−	0.00464237i
$778$	2.16461	+	23.3725i	0.0776051	+	0.837945i
$779$	27.6092	+	14.5397i	0.989203	+	0.520937i
$780$	2.74277	+	14.6806i	0.0982070	+	0.525650i
$781$	−8.43407	+	4.86941i	−0.301795	+	0.174241i
$782$	2.26355	+	3.19796i	0.0809445	+	0.114359i
$783$	−3.45612	−	1.99539i	−0.123512	−	0.0713094i
$784$	−21.5682	−	17.3629i	−0.770294	−	0.620105i
$785$	−9.43635	+	16.3442i	−0.336798	+	0.583351i
$786$	1.22958	−	0.113876i	0.0438577	−	0.00406182i
$787$	35.2039			1.25488			0.627442	−	0.778663i	$-0.284102\pi$
$787$	35.2039			1.25488			0.627442	+	0.778663i	$0.284102\pi$
$788$	−7.70140	+	21.8481i	−0.274351	+	0.778305i
$789$	−13.6146	−	7.86042i	−0.484694	−	0.279838i
$790$	1.47004	+	15.8728i	0.0523016	+	0.564729i
$791$	3.62178			0.128776
$792$	2.66038	−	10.5710i	0.0945325	−	0.375623i
$793$	−7.91666	+	4.57069i	−0.281129	+	0.162310i
$794$	18.8012	+	8.65105i	0.667229	+	0.307014i
$795$	−14.3226	+	8.26914i	−0.507969	+	0.293276i
$796$	16.9197	−	14.4930i	0.599702	−	0.513690i
$797$			33.3694i			1.18201i	0.806670	+	0.591003i	$0.201268\pi$
$797$			33.3694i			1.18201i	−0.806670	+	0.591003i	$0.798732\pi$
$798$	−3.59234	+	0.474149i	−0.127168	+	0.0167847i
$799$			5.24671i			0.185615i
$800$	3.12582	−	4.71479i	0.110514	−	0.166693i
$801$	−1.19473	+	0.689777i	−0.0422137	+	0.0243721i
$802$	15.1905	−	33.0133i	0.536396	−	1.16574i
$803$	12.5037	−	7.21901i	0.441246	−	0.254754i
$804$	−17.4037	+	49.3726i	−0.613782	+	1.74124i
$805$	0.381033			0.0134296
$806$	−18.7940	+	1.74058i	−0.661991	+	0.0613094i
$807$	7.89243	+	4.55669i	0.277827	+	0.160403i
$808$	6.30021	+	1.58556i	0.221641	+	0.0557799i
$809$	25.3227			0.890298			0.445149	−	0.895457i	$-0.353151\pi$
$809$	25.3227			0.890298			0.445149	+	0.895457i	$0.353151\pi$
$810$	1.46670	+	15.8368i	0.0515347	+	0.556448i
$811$	−22.6019	+	39.1476i	−0.793659	+	1.37466i	0.130028	+	0.991510i	$0.458493\pi$
$811$	−22.6019	+	39.1476i	−0.793659	+	1.37466i	−0.923687	+	0.383148i	$0.874840\pi$
$812$	−0.440391	−	0.514130i	−0.0154547	−	0.0180424i
$813$	−2.01902	−	1.16568i	−0.0708103	−	0.0408823i
$814$	0.786097	−	0.556408i	0.0275527	−	0.0195021i
$815$	17.8995	−	10.3343i	0.626992	−	0.361994i
$816$	−15.9423	+	6.17245i	−0.558092	+	0.216079i
$817$	28.9467	+	15.2440i	1.01272	+	0.533321i
$818$	−33.2258	+	3.07716i	−1.16171	+	0.107590i
$819$	−0.711318	−	1.23204i	−0.0248554	−	0.0430509i
$820$	10.8735	−	9.31398i	0.379719	−	0.325258i
$821$	−12.4324	+	21.5335i	−0.433893	+	0.751524i	−0.997205	−	0.0747200i	$-0.976194\pi$
$821$	−12.4324	+	21.5335i	−0.433893	+	0.751524i	0.563312	+	0.826244i	$0.309527\pi$
$822$	52.8727	−	37.4239i	1.84415	−	1.30531i
$823$	−21.6261	−	12.4858i	−0.753837	−	0.435228i	0.0732417	−	0.997314i	$-0.476666\pi$
$823$	−21.6261	−	12.4858i	−0.753837	−	0.435228i	−0.827079	+	0.562086i	$0.809999\pi$
$824$	14.5548	+	51.1839i	0.507042	+	1.78308i
$825$		−	5.64404i		−	0.196500i
$826$	1.69413	−	3.68182i	0.0589462	−	0.128107i
$827$	15.5687	−	26.9657i	0.541375	−	0.937689i	−0.457450	−	0.889235i	$-0.651237\pi$
$827$	15.5687	−	26.9657i	0.541375	−	0.937689i	0.998825	−	0.0484542i	$-0.0154295\pi$
$828$	0.721628	+	3.86249i	0.0250783	+	0.134231i
$829$			13.6171i			0.472943i	0.971638	+	0.236471i	$0.0759910\pi$
$829$			13.6171i			0.472943i	−0.971638	+	0.236471i	$0.924009\pi$
$830$	−1.95965	+	4.25888i	−0.0680206	+	0.147828i
$831$	28.9956	+	50.2218i	1.00585	+	1.74218i
$832$	28.3419	−	0.864763i	0.982580	−	0.0299803i
$833$	7.02119	+	12.1611i	0.243270	+	0.421355i
$834$	−10.2413	−	14.4690i	−0.354627	−	0.501020i
$835$	−23.9363			−0.828351
$836$	−5.17825	−	22.7734i	−0.179094	−	0.787634i
$837$	−12.3867			−0.428148
$838$	−10.6264	−	15.0131i	−0.367083	−	0.518617i
$839$	−26.4196	−	45.7601i	−0.912107	−	1.57982i	−0.811083	−	0.584931i	$-0.801121\pi$
$839$	−26.4196	−	45.7601i	−0.912107	−	1.57982i	−0.101024	−	0.994884i	$-0.532212\pi$
$840$	−0.405765	+	1.61230i	−0.0140002	+	0.0556296i
$841$	−13.7641	−	23.8401i	−0.474625	−	0.822074i
$842$	−0.514434	+	1.11801i	−0.0177285	+	0.0385292i
$843$			47.1705i			1.62464i
$844$	−41.0191	+	7.66359i	−1.41194	+	0.263792i
$845$	0.218651	−	0.378715i	0.00752184	−	0.0130282i
$846$	−2.19950	+	4.78013i	−0.0756202	+	0.164344i
$847$		−	1.06668i		−	0.0366516i
$848$	11.3371	+	29.2817i	0.389318	+	1.00554i
$849$	−20.9425	−	12.0912i	−0.718745	−	0.414968i
$850$	−2.34166	+	1.65745i	−0.0803184	+	0.0568502i
$851$	−0.173581	+	0.300652i	−0.00595029	+	0.0103062i
$852$	9.96480	+	11.6333i	0.341388	+	0.398550i
$853$	−23.0843	−	39.9831i	−0.790390	−	1.36900i	−0.925725	−	0.378196i	$-0.876544\pi$
$853$	−23.0843	−	39.9831i	−0.790390	−	1.36900i	0.135335	−	0.990800i	$-0.456789\pi$
$854$	−1.01331	+	0.0938467i	−0.0346749	+	0.00321137i
$855$	−3.34406	−	5.30460i	−0.114365	−	0.181414i
$856$	6.91218	+	24.3075i	0.236253	+	0.830814i
$857$	38.0306	−	21.9570i	1.29910	−	0.750036i	0.318852	−	0.947804i	$-0.396703\pi$
$857$	38.0306	−	21.9570i	1.29910	−	0.750036i	0.980249	+	0.197768i	$0.0633693\pi$
$858$	23.0917	−	16.3446i	0.788339	−	0.557995i
$859$	−4.07813	−	2.35451i	−0.139144	−	0.0803349i	0.428812	−	0.903394i	$-0.358932\pi$
$859$	−4.07813	−	2.35451i	−0.139144	−	0.0803349i	−0.567956	+	0.823059i	$0.692266\pi$
$860$	11.4003	−	9.76519i	0.388746	−	0.332990i
$861$	−2.10395	+	3.64415i	−0.0717024	+	0.124192i
$862$	0.221018	+	2.38645i	0.00752790	+	0.0812829i
$863$	38.0611			1.29562			0.647808	−	0.761803i	$-0.275686\pi$
$863$	38.0611			1.29562			0.647808	+	0.761803i	$0.275686\pi$
$864$	18.5730	+	1.15017i	0.631866	+	0.0391295i
$865$	18.8921	+	10.9074i	0.642352	+	0.370862i
$866$	−12.8790	+	1.19277i	−0.437646	+	0.0405320i
$867$	−27.1455			−0.921910
$868$	−1.98166	−	0.698531i	−0.0672619	−	0.0237097i
$869$	26.1512	−	15.0984i	0.887117	−	0.512177i
$870$	1.51091	−	3.28364i	0.0512247	−	0.111326i
$871$	−38.1362	+	22.0179i	−1.29220	+	0.746050i
$872$	33.4341	+	32.4295i	1.13222	+	1.09820i
$873$			2.93510i			0.0993382i
$874$	5.12714	+	6.67724i	0.173428	+	0.225861i
$875$			0.279006i			0.00943212i
$876$	−14.7730	−	17.2466i	−0.499134	−	0.582709i
$877$	18.4503	−	10.6523i	0.623023	−	0.359703i	−0.155022	−	0.987911i	$-0.549545\pi$
$877$	18.4503	−	10.6523i	0.623023	−	0.359703i	0.778045	+	0.628208i	$0.216211\pi$
$878$	30.1949	+	13.8937i	1.01903	+	0.468889i
$879$	−18.9121	+	10.9189i	−0.637890	+	0.368286i
$880$	−10.5887	−	1.64582i	−0.356946	−	0.0554807i
$881$	37.5723			1.26584			0.632922	−	0.774215i	$-0.281855\pi$
$881$	37.5723			1.26584			0.632922	+	0.774215i	$0.281855\pi$
$882$	1.29872	+	14.0230i	0.0437302	+	0.472178i
$883$	7.86545	+	4.54112i	0.264693	+	0.152821i	0.626474	−	0.779443i	$-0.284498\pi$
$883$	7.86545	+	4.54112i	0.264693	+	0.152821i	−0.361780	+	0.932263i	$0.617831\pi$
$884$	−13.5625	−	4.78074i	−0.456155	−	0.160794i
$885$	21.6401			0.727422
$886$	22.4170	−	2.07612i	0.753115	−	0.0697487i
$887$	18.2317	−	31.5783i	0.612162	−	1.06030i	−0.378714	−	0.925514i	$-0.623633\pi$
$887$	18.2317	−	31.5783i	0.612162	−	1.06030i	0.990875	−	0.134781i	$-0.0430332\pi$
$888$	−1.08733	−	1.05466i	−0.0364883	−	0.0353919i
$889$	−4.28836	−	2.47589i	−0.143827	−	0.0830386i
$890$	0.783506	+	1.10694i	0.0262632	+	0.0371048i
$891$	26.0918	−	15.0641i	0.874109	−	0.504667i
$892$	−15.7284	+	2.93853i	−0.526626	+	0.0983894i
$893$	0.438210	+	11.2651i	0.0146641	+	0.376973i
$894$	0.0270806	+	0.292404i	0.000905711	+	0.00977946i
$895$	−8.20874	−	14.2180i	−0.274388	−	0.475254i
$896$	2.90650	+	1.23140i	0.0970992	+	0.0411383i
$897$	−5.09898	+	8.83169i	−0.170250	+	0.294882i
$898$	−23.0786	−	32.6056i	−0.770143	−	1.08806i
$899$	3.95611	+	2.28406i	0.131944	+	0.0761777i
$900$	−2.82825	+	0.528402i	−0.0942751	+	0.0176134i
$901$		−	15.9245i		−	0.530523i
$902$	−24.6382	−	11.3369i	−0.820364	−	0.377476i
$903$	−2.20588	+	3.82069i	−0.0734070	+	0.127145i
$904$	35.3157	−	10.0425i	1.17458	−	0.334009i
$905$		−	2.38964i		−	0.0794345i
$906$	38.7166	+	17.8148i	1.28627	+	0.591857i
$907$	5.96287	+	10.3280i	0.197994	+	0.342936i	0.947878	−	0.318634i	$-0.103224\pi$
$907$	5.96287	+	10.3280i	0.197994	+	0.342936i	−0.749884	+	0.661569i	$0.769891\pi$
$908$	−7.64334	+	21.6834i	−0.253653	+	0.719588i
$909$	−1.65217	−	2.86164i	−0.0547989	−	0.0949145i
$910$	−1.14151	+	0.807974i	−0.0378407	+	0.0267841i
$911$	37.1988			1.23245			0.616225	−	0.787570i	$-0.288661\pi$
$911$	37.1988			1.23245			0.616225	+	0.787570i	$0.288661\pi$
$912$	−33.7140	+	14.5843i	−1.11638	+	0.482934i
$913$	8.88075			0.293910
$914$	2.82244	−	1.99775i	0.0933580	−	0.0660798i
$915$	−2.71683	−	4.70569i	−0.0898157	−	0.155565i
$916$	−6.71442	+	19.0481i	−0.221851	+	0.629367i
$917$	0.0578172	+	0.100142i	0.00190929	+	0.00330699i
$918$	−8.57336	−	3.94488i	−0.282963	−	0.130201i
$919$		−	28.8153i		−	0.950529i	−0.879843	−	0.475264i	$-0.842352\pi$
$919$		−	28.8153i		−	0.950529i	0.879843	−	0.475264i	$-0.157648\pi$
$920$	3.71543	−	1.05653i	0.122494	−	0.0348329i
$921$	16.0748	−	27.8425i	0.529684	−	0.917440i
$922$	19.3611	+	8.90870i	0.637625	+	0.293392i
$923$			12.8849i			0.424112i
$924$	3.09587	−	0.578401i	0.101847	−	0.0190280i
$925$	−0.220148	−	0.127102i	−0.00723841	−	0.00417910i
$926$	−16.7992	−	23.7341i	−0.552058	−	0.779951i
$927$	13.5326	−	23.4392i	0.444470	−	0.769845i
$928$	−5.71982	−	3.79213i	−0.187762	−	0.124483i
$929$	9.52383	+	16.4958i	0.312467	+	0.541208i	0.978896	−	0.204360i	$-0.0655114\pi$
$929$	9.52383	+	16.4958i	0.312467	+	0.541208i	−0.666429	+	0.745568i	$0.732178\pi$
$930$	−1.03461	−	11.1712i	−0.0339262	−	0.366319i
$931$	16.0908	+	25.5244i	0.527354	+	0.836528i
$932$	32.3530	−	6.04450i	1.05976	−	0.197994i
$933$	−0.727603	+	0.420082i	−0.0238207	+	0.0137529i
$934$	17.5036	+	24.7292i	0.572735	+	0.809164i
$935$	4.70649	+	2.71729i	0.153919	+	0.0888649i
$936$	−10.3522	−	10.0412i	−0.338373	−	0.328206i
$937$	−5.89444	+	10.2095i	−0.192563	+	0.333529i	−0.946099	−	0.323878i	$-0.895013\pi$
$937$	−5.89444	+	10.2095i	−0.192563	+	0.333529i	0.753536	+	0.657407i	$0.228347\pi$
$938$	−4.88134	+	0.452079i	−0.159381	+	0.0147609i
$939$	15.7878			0.515214
$940$	4.87849	+	1.71966i	0.159119	+	0.0560890i
$941$	−19.4954	−	11.2557i	−0.635531	−	0.366924i	0.147360	−	0.989083i	$-0.452922\pi$
$941$	−19.4954	−	11.2557i	−0.635531	−	0.366924i	−0.782891	+	0.622159i	$0.786256\pi$
$942$	−5.18551	−	55.9908i	−0.168953	−	1.82428i
$943$	9.77638			0.318363
$944$	6.31033	−	40.5987i	0.205384	−	1.32137i
$945$	−0.794845	+	0.458904i	−0.0258563	+	0.0149281i
$946$	−25.8318	−	11.8861i	−0.839866	−	0.386450i
$947$	−36.2235	+	20.9137i	−1.17711	+	0.679603i	−0.955343	−	0.295498i	$-0.904515\pi$
$947$	−36.2235	+	20.9137i	−1.17711	+	0.679603i	−0.221763	+	0.975101i	$0.571181\pi$
$948$	−30.8974	−	36.0708i	−1.00350	−	1.17153i
$949$		−	19.1022i		−	0.620082i
$950$	−4.88932	+	3.75427i	−0.158630	+	0.121805i
$951$		−	9.98487i		−	0.323782i
$952$	−1.14912	−	1.11459i	−0.0372433	−	0.0361242i
$953$	50.6437	−	29.2392i	1.64051	−	0.947150i	0.659860	−	0.751389i	$-0.270616\pi$
$953$	50.6437	−	29.2392i	1.64051	−	0.947150i	0.980652	−	0.195761i	$-0.0627177\pi$
$954$	6.67579	−	14.5084i	0.216137	−	0.469727i
$955$	−21.5953	+	12.4681i	−0.698808	+	0.403457i
$956$	5.38193	+	1.89712i	0.174064	+	0.0613572i
$957$	−6.84714			−0.221337
$958$	−30.0832	+	2.78611i	−0.971944	+	0.0900152i
$959$	5.25324	+	3.03296i	0.169636	+	0.0979395i
$960$	0.514018	+	16.8465i	0.0165899	+	0.543720i
$961$	−16.8213			−0.542623
$962$	−0.117506	−	1.26878i	−0.00378855	−	0.0409070i
$963$	6.42673	−	11.1314i	0.207098	−	0.358705i
$964$	9.35197	−	8.01066i	0.301207	−	0.258006i
$965$	21.9112	+	12.6505i	0.705348	+	0.407233i
$966$	−0.926639	+	0.655885i	−0.0298141	+	0.0211028i
$967$	50.7915	−	29.3245i	1.63334	−	0.943011i	0.650291	−	0.759685i	$-0.274647\pi$
$967$	50.7915	−	29.3245i	1.63334	−	0.943011i	0.983052	−	0.183325i	$-0.0586862\pi$
$968$	−2.95770	−	10.4011i	−0.0950642	−	0.334305i
$969$	18.6153	−	0.724130i	0.598010	−	0.0232624i
$970$	2.87306	−	0.266085i	0.0922485	−	0.00854347i
$971$	−10.8529	−	18.7978i	−0.348286	−	0.603250i	0.637659	−	0.770319i	$-0.279903\pi$
$971$	−10.8529	−	18.7978i	−0.348286	−	0.603250i	−0.985945	+	0.167069i	$0.946570\pi$
$972$	−17.9873	−	20.9991i	−0.576943	−	0.673546i
$973$	0.829991	−	1.43759i	0.0266083	−	0.0460869i
$974$	−11.5045	+	8.14299i	−0.368627	+	0.260918i
$975$	−6.46688	−	3.73366i	−0.207106	−	0.119573i
$976$	−9.62054	+	3.72482i	−0.307946	+	0.119229i
$977$			28.1786i			0.901514i	0.892647	+	0.450757i	$0.148846\pi$
$977$			28.1786i			0.901514i	−0.892647	+	0.450757i	$0.851154\pi$
$978$	−25.7413	+	55.9431i	−0.823115	+	1.78886i
$979$	1.28451	−	2.22483i	0.0410531	−	0.0711060i
$980$	13.6088	−	2.54254i	0.434718	−	0.0812183i
$981$		−	23.6905i		−	0.756380i
$982$	−1.19424	+	2.59543i	−0.0381098	+	0.0828235i
$983$	8.53614	+	14.7850i	0.272261	+	0.471569i	0.969440	−	0.245327i	$-0.0788954\pi$
$983$	8.53614	+	14.7850i	0.272261	+	0.471569i	−0.697180	+	0.716896i	$0.745562\pi$
$984$	−10.4109	+	41.3677i	−0.331889	+	1.31875i
$985$	−5.79142	−	10.0310i	−0.184530	−	0.319616i
$986$	2.01076	+	2.84082i	0.0640358	+	0.0904702i
$987$	−1.52028			−0.0483911
$988$	−29.5190	−	9.13190i	−0.939126	−	0.290524i
$989$	10.2500			0.325931
$990$	3.14882	+	4.44868i	0.100076	+	0.141388i
$991$	−19.3586	−	33.5301i	−0.614946	−	1.06512i	−0.990394	−	0.138274i	$-0.955845\pi$
$991$	−19.3586	−	33.5301i	−0.614946	−	1.06512i	0.375448	−	0.926843i	$-0.377489\pi$
$992$	−21.2599	−	1.31656i	−0.675004	−	0.0418008i
$993$	−26.8496	−	46.5049i	−0.852048	−	1.47579i
$994$	−0.599584	+	1.30307i	−0.0190176	+	0.0413307i
$995$			11.1392i			0.353135i
$996$	−2.56526	−	13.7305i	−0.0812833	−	0.435066i
$997$	3.82350	−	6.62250i	0.121092	−	0.209737i	−0.799107	−	0.601189i	$-0.794694\pi$
$997$	3.82350	−	6.62250i	0.121092	−	0.209737i	0.920198	+	0.391452i	$0.128027\pi$
$998$	25.0875	−	54.5223i	0.794131	−	1.72587i
$999$		−	0.836223i		−	0.0264569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.17	✓	40
4.3	odd	2	inner	380.2.n.a.31.18	yes	40
19.8	odd	6	inner	380.2.n.a.331.18	yes	40
76.27	even	6	inner	380.2.n.a.331.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.17	✓	40	1.1	even	1	trivial
380.2.n.a.31.18	yes	40	4.3	odd	2	inner
380.2.n.a.331.17	yes	40	76.27	even	6	inner
380.2.n.a.331.18	yes	40	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15432 - 0.817038i) q^{2} +(-1.05340 - 1.82454i) q^{3} +(0.664897 - 1.88624i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.70668 - 1.24543i) q^{6} -0.279006i q^{7} +(-0.773631 - 2.72057i) q^{8} +(-0.719298 + 1.24586i) q^{9} +O(q^{10})\)	\(q+(1.15432 - 0.817038i) q^{2} +(-1.05340 - 1.82454i) q^{3} +(0.664897 - 1.88624i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.70668 - 1.24543i) q^{6} -0.279006i q^{7} +(-0.773631 - 2.72057i) q^{8} +(-0.719298 + 1.24586i) q^{9} +(1.28473 + 0.591149i) q^{10} -2.67897i q^{11} +(-4.14193 + 0.773835i) q^{12} +(-3.06953 - 1.77219i) q^{13} +(-0.227959 - 0.322061i) q^{14} +(1.05340 - 1.82454i) q^{15} +(-3.11582 - 2.50831i) q^{16} +(1.01431 + 1.75683i) q^{17} +(0.187618 + 2.02581i) q^{18} +(2.32453 + 3.68735i) q^{19} +(1.96598 - 0.367304i) q^{20} +(-0.509057 + 0.293904i) q^{21} +(-2.18882 - 3.09238i) q^{22} +(1.18271 + 0.682840i) q^{23} +(-4.14885 + 4.27736i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-4.99116 + 0.462250i) q^{26} -3.28956 q^{27} +(-0.526273 - 0.185510i) q^{28} +(1.05063 + 0.606582i) q^{29} +(-0.274763 - 2.96677i) q^{30} +3.76546 q^{31} +(-5.64604 - 0.349641i) q^{32} +(-4.88788 + 2.82202i) q^{33} +(2.60623 + 1.19921i) q^{34} +(0.241626 - 0.139503i) q^{35} +(1.87174 + 2.18514i) q^{36} +0.254205i q^{37} +(5.69596 + 2.35714i) q^{38} +7.46731i q^{39} +(1.96927 - 2.03027i) q^{40} +(6.19954 - 3.57931i) q^{41} +(-0.347483 + 0.755178i) q^{42} +(6.49988 - 3.75271i) q^{43} +(-5.05318 - 1.78124i) q^{44} -1.43860 q^{45} +(1.92313 - 0.178108i) q^{46} +(2.23985 + 1.29318i) q^{47} +(-1.29431 + 8.32720i) q^{48} +6.92216 q^{49} +(0.130417 + 1.40819i) q^{50} +(2.13694 - 3.70129i) q^{51} +(-5.38371 + 4.61156i) q^{52} +(-6.79826 - 3.92498i) q^{53} +(-3.79720 + 2.68770i) q^{54} +(2.32005 - 1.33948i) q^{55} +(-0.759055 + 0.215848i) q^{56} +(4.27905 - 8.12545i) q^{57} +(1.70836 - 0.158218i) q^{58} +(5.13577 + 8.89542i) q^{59} +(-2.74112 - 3.20010i) q^{60} +(1.28956 - 2.23358i) q^{61} +(4.34654 - 3.07653i) q^{62} +(0.347602 + 0.200688i) q^{63} +(-6.80299 + 4.20943i) q^{64} -3.54439i q^{65} +(-3.33647 + 7.25109i) q^{66} +(6.21206 - 10.7596i) q^{67} +(3.98822 - 0.745118i) q^{68} -2.87721i q^{69} +(0.164934 - 0.358449i) q^{70} +(-1.81765 - 3.14826i) q^{71} +(3.94592 + 0.993063i) q^{72} +(2.69470 + 4.66736i) q^{73} +(0.207695 + 0.293433i) q^{74} +2.10680 q^{75} +(8.50081 - 1.93293i) q^{76} -0.747447 q^{77} +(6.10108 + 8.61965i) q^{78} +(5.63590 + 9.76166i) q^{79} +(0.614351 - 3.95254i) q^{80} +(5.62311 + 9.73952i) q^{81} +(4.23181 - 9.19692i) q^{82} +3.31499i q^{83} +(0.215905 + 1.15562i) q^{84} +(-1.01431 + 1.75683i) q^{85} +(4.43682 - 9.64247i) q^{86} -2.55589i q^{87} +(-7.28831 + 2.07253i) q^{88} +(0.830483 + 0.479480i) q^{89} +(-1.66060 + 1.17539i) q^{90} +(-0.494453 + 0.856417i) q^{91} +(2.07438 - 1.77687i) q^{92} +(-3.96653 - 6.87023i) q^{93} +(3.64207 - 0.337305i) q^{94} +(-2.03107 + 3.85678i) q^{95} +(5.30960 + 10.6697i) q^{96} +(1.76691 - 1.02013i) q^{97} +(7.99036 - 5.65567i) q^{98} +(3.33762 + 1.92697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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