LMFDB - Embedded newform 380.2.k.d.267.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, 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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.2
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36260 - 0.378581i) q^{2} +(1.58108 + 1.58108i) q^{3} +(1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 - 2.75294i) q^{6} +(1.94368 - 1.94368i) q^{7} +(-1.94403 - 2.05445i) q^{8} +1.99961i q^{9} +O(q^{10})$	\(q+(-1.36260 - 0.378581i) q^{2} +(1.58108 + 1.58108i) q^{3} +(1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 - 2.75294i) q^{6} +(1.94368 - 1.94368i) q^{7} +(-1.94403 - 2.05445i) q^{8} +1.99961i q^{9} +(1.85470 + 2.56127i) q^{10} -4.18087i q^{11} +(1.07773 + 4.34015i) q^{12} +(3.14596 - 3.14596i) q^{13} +(-3.38430 + 1.91262i) q^{14} +(-0.560510 - 4.96829i) q^{15} +(1.87116 + 3.53536i) q^{16} +(-2.53996 - 2.53996i) q^{17} +(0.757015 - 2.72467i) q^{18} -1.00000 q^{19} +(-1.55756 - 4.19214i) q^{20} +6.14621 q^{21} +(-1.58280 + 5.69685i) q^{22} +(3.70046 + 3.70046i) q^{23} +(0.174583 - 6.32190i) q^{24} +(1.11400 + 4.87432i) q^{25} +(-5.47768 + 3.09568i) q^{26} +(1.58169 - 1.58169i) q^{27} +(5.33552 - 1.32490i) q^{28} +10.0179i q^{29} +(-1.11715 + 6.98198i) q^{30} -0.276086i q^{31} +(-1.21121 - 5.52566i) q^{32} +(6.61028 - 6.61028i) q^{33} +(2.49937 + 4.42254i) q^{34} +(-6.10771 + 0.689057i) q^{35} +(-2.06301 + 3.42604i) q^{36} +(5.28359 + 5.28359i) q^{37} +(1.36260 + 0.378581i) q^{38} +9.94801 q^{39} +(0.535264 + 6.30186i) q^{40} -5.13494 q^{41} +(-8.37482 - 2.32684i) q^{42} +(-7.75925 - 7.75925i) q^{43} +(4.31344 - 7.16331i) q^{44} +(2.78729 - 3.49617i) q^{45} +(-3.64132 - 6.44317i) q^{46} +(3.74512 - 3.74512i) q^{47} +(-2.63124 + 8.54812i) q^{48} -0.555776i q^{49} +(0.327394 - 7.06348i) q^{50} -8.03176i q^{51} +(8.63585 - 2.14443i) q^{52} +(6.04899 - 6.04899i) q^{53} +(-2.75401 + 1.55641i) q^{54} +(-5.82778 + 7.30995i) q^{55} +(-7.77175 - 0.214622i) q^{56} +(-1.58108 - 1.58108i) q^{57} +(3.79259 - 13.6504i) q^{58} +2.19430 q^{59} +(4.16547 - 9.09071i) q^{60} -6.42875 q^{61} +(-0.104521 + 0.376195i) q^{62} +(3.88660 + 3.88660i) q^{63} +(-0.441514 + 7.98781i) q^{64} +(-9.88569 + 1.11528i) q^{65} +(-11.5097 + 6.50463i) q^{66} +(5.17620 - 5.17620i) q^{67} +(-1.73135 - 6.97236i) q^{68} +11.7014i q^{69} +(8.58322 + 1.37335i) q^{70} +3.20361i q^{71} +(4.10810 - 3.88730i) q^{72} +(-6.83955 + 6.83955i) q^{73} +(-5.19914 - 9.19968i) q^{74} +(-5.94536 + 9.46799i) q^{75} +(-1.71335 - 1.03171i) q^{76} +(-8.12627 - 8.12627i) q^{77} +(-13.5552 - 3.76613i) q^{78} +3.37793 q^{79} +(1.65642 - 8.78956i) q^{80} +11.0004 q^{81} +(6.99687 + 1.94399i) q^{82} +(4.21641 + 4.21641i) q^{83} +(10.5306 + 6.34110i) q^{84} +(0.900447 + 7.98144i) q^{85} +(7.63525 + 13.5103i) q^{86} +(-15.8391 + 15.8391i) q^{87} +(-8.58938 + 8.12773i) q^{88} +12.4531i q^{89} +(-5.12154 + 3.70867i) q^{90} -12.2295i q^{91} +(2.52240 + 10.1580i) q^{92} +(0.436513 - 0.436513i) q^{93} +(-6.52093 + 3.68527i) q^{94} +(1.74843 + 1.39392i) q^{95} +(6.82148 - 10.6515i) q^{96} +(-8.49786 - 8.49786i) q^{97} +(-0.210406 + 0.757299i) q^{98} +8.36011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36260	−	0.378581i	−0.963503	−	0.267697i
$2$	−1.36260	−	0.378581i	−0.963503	−	0.267697i
$3$	1.58108	+	1.58108i	0.912835	+	0.912835i	0.996494	−	0.0836591i	$-0.0266607\pi$
$3$	1.58108	+	1.58108i	0.912835	+	0.912835i	−0.0836591	+	0.996494i	$0.526661\pi$
$4$	1.71335	+	1.03171i	0.856676	+	0.515854i
$5$	−1.74843	−	1.39392i	−0.781921	−	0.623378i
$5$	−1.74843	−	1.39392i	−0.781921	−	0.623378i
$6$	−1.55581	−	2.75294i	−0.635156	−	1.12388i
$7$	1.94368	−	1.94368i	0.734642	−	0.734642i	−0.236894	−	0.971536i	$-0.576129\pi$
$7$	1.94368	−	1.94368i	0.734642	−	0.734642i	0.971536	+	0.236894i	$0.0761294\pi$
$8$	−1.94403	−	2.05445i	−0.687318	−	0.726357i
$9$			1.99961i			0.666537i
$10$	1.85470	+	2.56127i	0.586506	+	0.809945i
$11$		−	4.18087i		−	1.26058i	−0.776360	−	0.630290i	$-0.782936\pi$
$11$		−	4.18087i		−	1.26058i	0.776360	−	0.630290i	$-0.217064\pi$
$12$	1.07773	+	4.34015i	0.311114	+	1.25289i
$13$	3.14596	−	3.14596i	0.872532	−	0.872532i	−0.120216	−	0.992748i	$-0.538359\pi$
$13$	3.14596	−	3.14596i	0.872532	−	0.872532i	0.992748	+	0.120216i	$0.0383586\pi$
$14$	−3.38430	+	1.91262i	−0.904491	+	0.511168i
$15$	−0.560510	−	4.96829i	−0.144723	−	1.28281i
$16$	1.87116	+	3.53536i	0.467789	+	0.883840i
$17$	−2.53996	−	2.53996i	−0.616032	−	0.616032i	0.328479	−	0.944511i	$-0.393464\pi$
$17$	−2.53996	−	2.53996i	−0.616032	−	0.616032i	−0.944511	+	0.328479i	$0.893464\pi$
$18$	0.757015	−	2.72467i	0.178430	−	0.642210i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.55756	−	4.19214i	−0.348281	−	0.937390i
$21$	6.14621			1.34121
$22$	−1.58280	+	5.69685i	−0.337454	+	1.21457i
$23$	3.70046	+	3.70046i	0.771599	+	0.771599i	0.978386	−	0.206787i	$-0.0663006\pi$
$23$	3.70046	+	3.70046i	0.771599	+	0.771599i	−0.206787	+	0.978386i	$0.566301\pi$
$24$	0.174583	−	6.32190i	0.0356367	−	1.29045i
$25$	1.11400	+	4.87432i	0.222800	+	0.974864i
$26$	−5.47768	+	3.09568i	−1.07426	+	0.607113i
$27$	1.58169	−	1.58169i	0.304397	−	0.304397i
$28$	5.33552	−	1.32490i	1.00832	−	0.250382i
$29$			10.0179i			1.86028i	0.367209	+	0.930139i	$0.380313\pi$
$29$			10.0179i			1.86028i	−0.367209	+	0.930139i	$0.619687\pi$
$30$	−1.11715	+	6.98198i	−0.203962	+	1.27473i
$31$		−	0.276086i		−	0.0495865i	−0.999693	−	0.0247933i	$-0.992107\pi$
$31$		−	0.276086i		−	0.0495865i	0.999693	−	0.0247933i	$-0.00789275\pi$
$32$	−1.21121	−	5.52566i	−0.214114	−	0.976809i
$33$	6.61028	−	6.61028i	1.15070	−	1.15070i
$34$	2.49937	+	4.42254i	0.428639	+	0.758459i
$35$	−6.10771	+	0.689057i	−1.03239	+	0.116472i
$36$	−2.06301	+	3.42604i	−0.343836	+	0.571006i
$37$	5.28359	+	5.28359i	0.868616	+	0.868616i	0.992319	−	0.123703i	$-0.0394770\pi$
$37$	5.28359	+	5.28359i	0.868616	+	0.868616i	−0.123703	+	0.992319i	$0.539477\pi$
$38$	1.36260	+	0.378581i	0.221043	+	0.0614140i
$39$	9.94801			1.59296
$40$	0.535264	+	6.30186i	0.0846326	+	0.996412i
$41$	−5.13494			−0.801943			−0.400971	−	0.916091i	$-0.631327\pi$
$41$	−5.13494			−0.801943			−0.400971	+	0.916091i	$0.631327\pi$
$42$	−8.37482	−	2.32684i	−1.29226	−	0.359039i
$43$	−7.75925	−	7.75925i	−1.18328	−	1.18328i	−0.978891	−	0.204384i	$-0.934481\pi$
$43$	−7.75925	−	7.75925i	−1.18328	−	1.18328i	−0.204384	−	0.978891i	$-0.565519\pi$
$44$	4.31344	−	7.16331i	0.650275	−	1.07991i
$45$	2.78729	−	3.49617i	0.415504	−	0.521179i
$46$	−3.64132	−	6.44317i	−0.536883	−	0.949993i
$47$	3.74512	−	3.74512i	0.546282	−	0.546282i	−0.379081	−	0.925363i	$-0.623760\pi$
$47$	3.74512	−	3.74512i	0.546282	−	0.546282i	0.925363	+	0.379081i	$0.123760\pi$
$48$	−2.63124	+	8.54812i	−0.379787	+	1.23381i
$49$		−	0.555776i		−	0.0793965i
$50$	0.327394	−	7.06348i	0.0463004	−	0.998928i
$51$		−	8.03176i		−	1.12467i
$52$	8.63585	−	2.14443i	1.19758	−	0.297378i
$53$	6.04899	−	6.04899i	0.830893	−	0.830893i	−0.156746	−	0.987639i	$-0.550100\pi$
$53$	6.04899	−	6.04899i	0.830893	−	0.830893i	0.987639	+	0.156746i	$0.0501004\pi$
$54$	−2.75401	+	1.55641i	−0.374774	+	0.211801i
$55$	−5.82778	+	7.30995i	−0.785818	+	0.985673i
$56$	−7.77175	−	0.214622i	−1.03854	−	0.0286801i
$57$	−1.58108	−	1.58108i	−0.209419	−	0.209419i
$58$	3.79259	−	13.6504i	0.497991	−	1.79238i
$59$	2.19430			0.285674			0.142837	−	0.989746i	$-0.454378\pi$
$59$	2.19430			0.285674			0.142837	+	0.989746i	$0.454378\pi$
$60$	4.16547	−	9.09071i	0.537760	−	1.17361i
$61$	−6.42875			−0.823117			−0.411558	−	0.911383i	$-0.635015\pi$
$61$	−6.42875			−0.823117			−0.411558	+	0.911383i	$0.635015\pi$
$62$	−0.104521	+	0.376195i	−0.0132742	+	0.0477768i
$63$	3.88660	+	3.88660i	0.489666	+	0.489666i
$64$	−0.441514	+	7.98781i	−0.0551892	+	0.998476i
$65$	−9.88569	+	1.11528i	−1.22617	+	0.138333i
$66$	−11.5097	+	6.50463i	−1.41674	+	0.800665i
$67$	5.17620	−	5.17620i	0.632373	−	0.632373i	−0.316290	−	0.948663i	$-0.602437\pi$
$67$	5.17620	−	5.17620i	0.632373	−	0.632373i	0.948663	+	0.316290i	$0.102437\pi$
$68$	−1.73135	−	6.97236i	−0.209957	−	0.845523i
$69$			11.7014i			1.40869i
$70$	8.58322	+	1.37335i	1.02589	+	0.164147i
$71$			3.20361i			0.380199i	0.981765	+	0.190099i	$0.0608810\pi$
$71$			3.20361i			0.380199i	−0.981765	+	0.190099i	$0.939119\pi$
$72$	4.10810	−	3.88730i	0.484144	−	0.458122i
$73$	−6.83955	+	6.83955i	−0.800509	+	0.800509i	−0.983175	−	0.182666i	$-0.941527\pi$
$73$	−6.83955	+	6.83955i	−0.800509	+	0.800509i	0.182666	+	0.983175i	$0.441527\pi$
$74$	−5.19914	−	9.19968i	−0.604388	−	1.06944i
$75$	−5.94536	+	9.46799i	−0.686511	+	1.09327i
$76$	−1.71335	−	1.03171i	−0.196535	−	0.118345i
$77$	−8.12627	−	8.12627i	−0.926074	−	0.926074i
$78$	−13.5552	−	3.76613i	−1.53482	−	0.426430i
$79$	3.37793			0.380046			0.190023	−	0.981780i	$-0.439144\pi$
$79$	3.37793			0.380046			0.190023	+	0.981780i	$0.439144\pi$
$80$	1.65642	−	8.78956i	0.185193	−	0.982702i
$81$	11.0004			1.22227
$82$	6.99687	+	1.94399i	0.772675	+	0.214678i
$83$	4.21641	+	4.21641i	0.462811	+	0.462811i	0.899576	−	0.436765i	$-0.143876\pi$
$83$	4.21641	+	4.21641i	0.462811	+	0.462811i	−0.436765	+	0.899576i	$0.643876\pi$
$84$	10.5306	+	6.34110i	1.14899	+	0.691871i
$85$	0.900447	+	7.98144i	0.0976672	+	0.865709i
$86$	7.63525	+	13.5103i	0.823330	+	1.45685i
$87$	−15.8391	+	15.8391i	−1.69813	+	1.69813i
$88$	−8.58938	+	8.12773i	−0.915631	+	0.866419i
$89$			12.4531i			1.32003i	0.751254	+	0.660013i	$0.229449\pi$
$89$			12.4531i			1.32003i	−0.751254	+	0.660013i	$0.770551\pi$
$90$	−5.12154	+	3.70867i	−0.539858	+	0.390928i
$91$		−	12.2295i		−	1.28200i
$92$	2.52240	+	10.1580i	0.262978	+	1.05904i
$93$	0.436513	−	0.436513i	0.0452643	−	0.0452643i
$94$	−6.52093	+	3.68527i	−0.672582	+	0.380106i
$95$	1.74843	+	1.39392i	0.179385	+	0.143013i
$96$	6.82148	−	10.6515i	0.696214	−	1.08712i
$97$	−8.49786	−	8.49786i	−0.862827	−	0.862827i	0.128839	−	0.991666i	$-0.458875\pi$
$97$	−8.49786	−	8.49786i	−0.862827	−	0.862827i	−0.991666	+	0.128839i	$0.958875\pi$
$98$	−0.210406	+	0.757299i	−0.0212542	+	0.0764988i
$99$	8.36011			0.840223
$100$	−3.12021	+	9.50075i	−0.312021	+	0.950075i
$101$	−6.59302			−0.656030			−0.328015	−	0.944673i	$-0.606380\pi$
$101$	−6.59302			−0.656030			−0.328015	+	0.944673i	$0.606380\pi$
$102$	−3.04067	+	10.9441i	−0.301071	+	1.08362i
$103$	7.06562	+	7.06562i	0.696196	+	0.696196i	0.963588	−	0.267392i	$-0.0861617\pi$
$103$	7.06562	+	7.06562i	0.696196	+	0.696196i	−0.267392	+	0.963588i	$0.586162\pi$
$104$	−12.5790	−	0.347378i	−1.23348	−	0.0340633i
$105$	−10.7462	−	8.56730i	−1.04872	−	0.836083i
$106$	−10.5324	+	5.95232i	−1.02300	+	0.578140i
$107$	3.61126	−	3.61126i	0.349114	−	0.349114i	−0.510666	−	0.859779i	$-0.670601\pi$
$107$	3.61126	−	3.61126i	0.349114	−	0.349114i	0.859779	+	0.510666i	$0.170601\pi$
$108$	4.34185	−	1.07815i	0.417794	−	0.103745i
$109$			0.396878i			0.0380140i	0.999819	+	0.0190070i	$0.00605049\pi$
$109$			0.396878i			0.0380140i	−0.999819	+	0.0190070i	$0.993950\pi$
$110$	10.7083	−	7.75424i	1.02100	−	0.739338i
$111$			16.7075i			1.58581i
$112$	10.5085	+	3.23468i	0.992963	+	0.305649i
$113$	−10.6308	+	10.6308i	−1.00006	+	1.00006i	−5.96926e−5		1.00000i	$0.500019\pi$
$113$	−10.6308	+	10.6308i	−1.00006	+	1.00006i	−1.00000		5.96926e-5i	$0.999981\pi$
$114$	1.55581	+	2.75294i	0.145715	+	0.257836i
$115$	−1.31186	−	11.6281i	−0.122331	−	1.08433i
$116$	−10.3356	+	17.1642i	−0.959632	+	1.59366i
$117$	6.29069	+	6.29069i	0.581575	+	0.581575i
$118$	−2.98995	−	0.830721i	−0.275248	−	0.0764741i
$119$	−9.87375			−0.905125
$120$	−9.11744	+	10.8100i	−0.832305	+	0.986816i
$121$	−6.47968			−0.589061
$122$	8.75981	+	2.43380i	0.793076	+	0.220346i
$123$	−8.11874	−	8.11874i	−0.732042	−	0.732042i
$124$	0.284840	−	0.473033i	0.0255794	−	0.0424796i
$125$	4.84665	−	10.0752i	0.433497	−	0.901155i
$126$	−3.82448	−	6.76727i	−0.340712	−	0.602876i
$127$	−6.64721	+	6.64721i	−0.589844	+	0.589844i	−0.937589	−	0.347745i	$-0.886947\pi$
$127$	−6.64721	+	6.64721i	−0.589844	+	0.589844i	0.347745	+	0.937589i	$0.386947\pi$
$128$	3.62564	−	10.7170i	0.320464	−	0.947261i
$129$		−	24.5360i		−	2.16027i
$130$	13.8925	+	2.22285i	1.21845	+	0.194957i
$131$			11.2454i			0.982519i	0.871013	+	0.491259i	$0.163463\pi$
$131$			11.2454i			0.982519i	−0.871013	+	0.491259i	$0.836537\pi$
$132$	18.1456	−	4.50586i	1.57937	−	0.392185i
$133$	−1.94368	+	1.94368i	−0.168538	+	0.168538i
$134$	−9.01269	+	5.09347i	−0.778578	+	0.440009i
$135$	−4.97022	+	0.560729i	−0.427769	+	0.0482599i
$136$	−0.280464	+	10.1560i	−0.0240496	+	0.870869i
$137$	−3.10805	−	3.10805i	−0.265539	−	0.265539i	0.561761	−	0.827300i	$-0.310124\pi$
$137$	−3.10805	−	3.10805i	−0.265539	−	0.265539i	−0.827300	+	0.561761i	$0.810124\pi$
$138$	4.42994	−	15.9444i	0.377101	−	1.35727i
$139$	−3.47485			−0.294733			−0.147366	−	0.989082i	$-0.547080\pi$
$139$	−3.47485			−0.294733			−0.147366	+	0.989082i	$0.547080\pi$
$140$	−11.1756	−	5.12077i	−0.944507	−	0.432784i
$141$	11.8426			0.997331
$142$	1.21283	−	4.36524i	0.101778	−	0.366322i
$143$	−13.1528	−	13.1528i	−1.09990	−	1.09990i
$144$	−7.06934	+	3.74158i	−0.589112	+	0.311798i
$145$	13.9641	−	17.5156i	1.15966	−	1.45459i
$146$	11.9089	−	6.73024i	0.985587	−	0.556999i
$147$	0.878724	−	0.878724i	0.0724759	−	0.0724759i
$148$	3.60153	+	14.5038i	0.296044	+	1.19220i
$149$		−	3.49270i		−	0.286133i	−0.989713	−	0.143067i	$-0.954304\pi$
$149$		−	3.49270i		−	0.286133i	0.989713	−	0.143067i	$-0.0456963\pi$
$150$	11.6855	−	10.6503i	0.954121	−	0.869592i
$151$			0.0282485i			0.00229883i	0.999999	+	0.00114942i	$0.000365871\pi$
$151$			0.0282485i			0.00229883i	−0.999999	+	0.00114942i	$0.999634\pi$
$152$	1.94403	+	2.05445i	0.157681	+	0.166638i
$153$	5.07894	−	5.07894i	0.410608	−	0.410608i
$154$	7.99640	+	14.1493i	0.644368	+	1.14018i
$155$	−0.384841	+	0.482716i	−0.0309111	+	0.0387727i
$156$	17.0445	+	10.2634i	1.36465	+	0.821733i
$157$	5.82895	+	5.82895i	0.465201	+	0.465201i	0.900356	−	0.435155i	$-0.143306\pi$
$157$	5.82895	+	5.82895i	0.465201	+	0.465201i	−0.435155	+	0.900356i	$0.643306\pi$
$158$	−4.60276	−	1.27882i	−0.366176	−	0.101737i
$159$	19.1278			1.51694
$160$	−5.58459	+	11.3496i	−0.441501	+	0.897261i
$161$	14.3850			1.13370
$162$	−14.9891	−	4.16454i	−1.17766	−	0.327197i
$163$	11.5447	+	11.5447i	0.904248	+	0.904248i	0.995800	−	0.0915524i	$-0.0291829\pi$
$163$	11.5447	+	11.5447i	0.904248	+	0.904248i	−0.0915524	+	0.995800i	$0.529183\pi$
$164$	−8.79796	−	5.29776i	−0.687006	−	0.413686i
$165$	−20.7718	+	2.34342i	−1.61708	+	0.182435i
$166$	−4.14902	−	7.34153i	−0.322027	−	0.569813i
$167$	13.0076	−	13.0076i	1.00656	−	1.00656i	0.00657976	−	0.999978i	$-0.497906\pi$
$167$	13.0076	−	13.0076i	1.00656	−	1.00656i	0.999978	−	0.00657976i	$-0.00209442\pi$
$168$	−11.9484	−	12.6271i	−0.921840	−	0.974200i
$169$		−	6.79413i		−	0.522625i
$170$	1.79467	−	11.2164i	0.137645	−	0.860258i
$171$		−	1.99961i		−	0.152914i
$172$	−5.28905	−	21.2996i	−0.403286	−	1.62408i
$173$	9.93804	−	9.93804i	0.755576	−	0.755576i	−0.219938	−	0.975514i	$-0.570586\pi$
$173$	9.93804	−	9.93804i	0.755576	−	0.755576i	0.975514	+	0.219938i	$0.0705856\pi$
$174$	27.5787	−	15.5859i	2.09073	−	1.18157i
$175$	11.6394	+	7.30886i	0.879854	+	0.552498i
$176$	14.7809	−	7.82306i	1.11415	−	0.589685i
$177$	3.46936	+	3.46936i	0.260773	+	0.260773i
$178$	4.71451	−	16.9686i	0.353368	−	1.27185i
$179$	−0.461309			−0.0344798			−0.0172399	−	0.999851i	$-0.505488\pi$
$179$	−0.461309			−0.0344798			−0.0172399	+	0.999851i	$0.505488\pi$
$180$	8.38264	−	3.11451i	0.624805	−	0.232142i
$181$	7.36640			0.547540			0.273770	−	0.961795i	$-0.411729\pi$
$181$	7.36640			0.547540			0.273770	+	0.961795i	$0.411729\pi$
$182$	−4.62985	+	16.6639i	−0.343187	+	1.23521i
$183$	−10.1643	−	10.1643i	−0.751370	−	0.751370i
$184$	0.408607	−	14.7962i	0.0301229	−	1.09079i
$185$	−1.87309	−	16.6028i	−0.137713	−	1.22067i
$186$	−0.760048	+	0.429537i	−0.0557294	+	0.0314952i
$187$	−10.6193	+	10.6193i	−0.776557	+	0.776557i
$188$	10.2806	−	2.55284i	0.749789	−	0.186185i
$189$		−	6.14861i		−	0.447245i
$190$	−1.85470	−	2.56127i	−0.134554	−	0.185814i
$191$			7.81764i			0.565665i	0.959169	+	0.282832i	$0.0912740\pi$
$191$			7.81764i			0.565665i	−0.959169	+	0.282832i	$0.908726\pi$
$192$	−13.3274	+	11.9313i	−0.961823	+	0.861065i
$193$	−17.7987	+	17.7987i	−1.28118	+	1.28118i	−0.341176	+	0.939999i	$0.610825\pi$
$193$	−17.7987	+	17.7987i	−1.28118	+	1.28118i	−0.939999	+	0.341176i	$0.889175\pi$
$194$	8.36205	+	14.7963i	0.600360	+	1.06231i
$195$	−17.3934	−	13.8667i	−1.24557	−	0.993014i
$196$	0.573398	−	0.952240i	0.0409570	−	0.0680171i
$197$	1.33547	+	1.33547i	0.0951485	+	0.0951485i	0.753079	−	0.657930i	$-0.228568\pi$
$197$	1.33547	+	1.33547i	0.0951485	+	0.0951485i	−0.657930	+	0.753079i	$0.728568\pi$
$198$	−11.3915	−	3.16498i	−0.809557	−	0.224925i
$199$	−15.5573			−1.10283			−0.551413	−	0.834233i	$-0.685911\pi$
$199$	−15.5573			−1.10283			−0.551413	+	0.834233i	$0.685911\pi$
$200$	7.84840	−	11.7645i	0.554966	−	0.831873i
$201$	16.3679			1.15451
$202$	8.98364	+	2.49599i	0.632087	+	0.175617i
$203$	19.4716	+	19.4716i	1.36664	+	1.36664i
$204$	8.28644	−	13.7612i	0.580167	−	0.963479i
$205$	8.97807	+	7.15767i	0.627056	+	0.499914i
$206$	−6.95270	−	12.3025i	−0.484417	−	0.857157i
$207$	−7.39948	+	7.39948i	−0.514299	+	0.514299i
$208$	17.0087	+	5.23553i	1.17934	+	0.363018i
$209$			4.18087i			0.289197i
$210$	11.3994	+	15.7421i	0.786630	+	1.08631i
$211$		−	16.8879i		−	1.16261i	−0.813686	−	0.581305i	$-0.802542\pi$
$211$		−	16.8879i		−	1.16261i	0.813686	−	0.581305i	$-0.197458\pi$
$212$	16.6049	−	4.12326i	1.14043	−	0.283187i
$213$	−5.06515	+	5.06515i	−0.347059	+	0.347059i
$214$	−6.28785	+	3.55354i	−0.429829	+	0.242915i
$215$	2.75075	+	24.3822i	0.187599	+	1.66285i
$216$	−6.32436	−	0.174651i	−0.430318	−	0.0118835i
$217$	−0.536623	−	0.536623i	−0.0364283	−	0.0364283i
$218$	0.150251	−	0.540786i	0.0101763	−	0.0366266i
$219$	−21.6277			−1.46147
$220$	−17.5268	+	6.51195i	−1.18166	+	0.439036i
$221$	−15.9813			−1.07502
$222$	6.32515	−	22.7656i	0.424516	−	1.52793i
$223$	−7.24122	−	7.24122i	−0.484908	−	0.484908i	0.421787	−	0.906695i	$-0.361403\pi$
$223$	−7.24122	−	7.24122i	−0.484908	−	0.484908i	−0.906695	+	0.421787i	$0.861403\pi$
$224$	−13.0943	−	8.38591i	−0.874901	−	0.560307i
$225$	−9.74674	+	2.22756i	−0.649783	+	0.148504i
$226$	18.5101	−	10.4609i	1.23127	−	0.695847i
$227$	−0.349778	+	0.349778i	−0.0232156	+	0.0232156i	−0.718619	−	0.695404i	$-0.755226\pi$
$227$	−0.349778	+	0.349778i	−0.0232156	+	0.0232156i	0.695404	+	0.718619i	$0.255226\pi$
$228$	−1.07773	−	4.34015i	−0.0713746	−	0.287434i
$229$			10.6868i			0.706207i	0.935584	+	0.353103i	$0.114874\pi$
$229$			10.6868i			0.706207i	−0.935584	+	0.353103i	$0.885126\pi$
$230$	−2.61465	+	16.3411i	−0.172405	+	1.07750i
$231$		−	25.6965i		−	1.69071i
$232$	20.5813	−	19.4751i	1.35123	−	1.27860i
$233$	−20.5613	+	20.5613i	−1.34701	+	1.34701i	−0.458128	+	0.888886i	$0.651480\pi$
$233$	−20.5613	+	20.5613i	−1.34701	+	1.34701i	−0.888886	+	0.458128i	$0.848520\pi$
$234$	−6.19016	−	10.9532i	−0.404663	−	0.716035i
$235$	−11.7685	+	1.32769i	−0.767689	+	0.0866089i
$236$	3.75961	+	2.26388i	0.244730	+	0.147366i
$237$	5.34076	+	5.34076i	0.346920	+	0.346920i
$238$	13.4540	+	3.73802i	0.872091	+	0.242300i
$239$	−10.6830			−0.691028			−0.345514	−	0.938414i	$-0.612295\pi$
$239$	−10.6830			−0.691028			−0.345514	+	0.938414i	$0.612295\pi$
$240$	16.5159	−	11.2780i	1.06610	−	0.727995i
$241$	11.7625			0.757689			0.378844	−	0.925460i	$-0.376322\pi$
$241$	11.7625			0.757689			0.378844	+	0.925460i	$0.376322\pi$
$242$	8.82920	+	2.45308i	0.567563	+	0.157690i
$243$	12.6474	+	12.6474i	0.811330	+	0.811330i
$244$	−11.0147	−	6.63259i	−0.705145	−	0.424608i
$245$	−0.774704	+	0.971733i	−0.0494940	+	0.0620818i
$246$	7.98898	+	14.1362i	0.509359	+	0.901290i
$247$	−3.14596	+	3.14596i	−0.200173	+	0.200173i
$248$	−0.567204	+	0.536719i	−0.0360175	+	0.0340817i
$249$			13.3329i			0.844941i
$250$	−10.4183	+	11.8936i	−0.658913	+	0.752219i
$251$		−	20.7617i		−	1.31047i	−0.755427	−	0.655233i	$-0.772570\pi$
$251$		−	20.7617i		−	1.31047i	0.755427	−	0.655233i	$-0.227430\pi$
$252$	2.64928	+	10.6690i	0.166889	+	0.672081i
$253$	15.4711	−	15.4711i	0.972663	−	0.972663i
$254$	11.5740	−	6.54097i	0.726216	−	0.410417i
$255$	−11.1956	+	14.0430i	−0.701095	+	0.879404i
$256$	−8.99756	+	13.2304i	−0.562347	+	0.826901i
$257$	13.8568	+	13.8568i	0.864366	+	0.864366i	0.991842	−	0.127475i	$-0.0406874\pi$
$257$	13.8568	+	13.8568i	0.864366	+	0.864366i	−0.127475	+	0.991842i	$0.540687\pi$
$258$	−9.28885	+	33.4327i	−0.578298	+	2.08143i
$259$	20.5392			1.27624
$260$	−18.0883	−	8.28828i	−1.12179	−	0.514017i
$261$	−20.0319			−1.23994
$262$	4.25731	−	15.3230i	0.263018	−	0.946660i
$263$	17.5064	+	17.5064i	1.07949	+	1.07949i	0.996555	+	0.0829348i	$0.0264293\pi$
$263$	17.5064	+	17.5064i	1.07949	+	1.07949i	0.0829348	+	0.996555i	$0.473571\pi$
$264$	−26.4310	−	0.729910i	−1.62672	−	0.0449229i
$265$	−19.0080	+	2.14444i	−1.16765	+	0.131732i
$266$	3.38430	−	1.91262i	0.207504	−	0.117270i
$267$	−19.6893	+	19.6893i	−1.20497	+	1.20497i
$268$	14.2090	−	3.52833i	0.867952	−	0.215527i
$269$		−	16.0727i		−	0.979973i	−0.871730	−	0.489986i	$-0.837002\pi$
$269$		−	16.0727i		−	0.979973i	0.871730	−	0.489986i	$-0.162998\pi$
$270$	6.98470	+	1.11758i	0.425076	+	0.0680140i
$271$		−	10.6807i		−	0.648808i	−0.945919	−	0.324404i	$-0.894836\pi$
$271$		−	10.6807i		−	0.648808i	0.945919	−	0.324404i	$-0.105164\pi$
$272$	4.22702	−	13.7324i	0.256301	−	0.832647i
$273$	19.3357	−	19.3357i	1.17025	−	1.17025i
$274$	3.05838	+	5.41168i	0.184764	+	0.326932i
$275$	20.3789	−	4.65748i	1.22889	−	0.280857i
$276$	−12.0725	+	20.0487i	−0.726677	+	1.20679i
$277$	8.82550	+	8.82550i	0.530273	+	0.530273i	0.920654	−	0.390381i	$-0.127657\pi$
$277$	8.82550	+	8.82550i	0.530273	+	0.530273i	−0.390381	+	0.920654i	$0.627657\pi$
$278$	4.73483	+	1.31551i	0.283976	+	0.0788992i
$279$	0.552064			0.0330512
$280$	13.2892	+	11.2084i	0.794181	+	0.669831i
$281$	13.8513			0.826299			0.413150	−	0.910663i	$-0.364429\pi$
$281$	13.8513			0.826299			0.413150	+	0.910663i	$0.364429\pi$
$282$	−16.1368	−	4.48340i	−0.960931	−	0.266983i
$283$	−10.2962	−	10.2962i	−0.612045	−	0.612045i	0.331433	−	0.943479i	$-0.392468\pi$
$283$	−10.2962	−	10.2962i	−0.612045	−	0.612045i	−0.943479	+	0.331433i	$0.892468\pi$
$284$	−3.30519	+	5.48891i	−0.196127	+	0.325707i
$285$	0.560510	+	4.96829i	0.0332018	+	0.294296i
$286$	12.9426	+	22.9015i	0.765314	+	1.35419i
$287$	−9.98068	+	9.98068i	−0.589141	+	0.589141i
$288$	11.0492	−	2.42195i	0.651079	−	0.142715i
$289$		−	4.09716i		−	0.241009i
$290$	−25.6585	+	18.5802i	−1.50672	+	1.09106i
$291$		−	26.8715i		−	1.57524i
$292$	−18.7750	+	4.66214i	−1.09872	+	0.272831i
$293$	−8.39088	+	8.39088i	−0.490201	+	0.490201i	−0.908369	−	0.418169i	$-0.862672\pi$
$293$	−8.39088	+	8.39088i	−0.490201	+	0.490201i	0.418169	+	0.908369i	$0.362672\pi$
$294$	−1.53002	+	0.864680i	−0.0892324	+	0.0504292i
$295$	−3.83658	−	3.05867i	−0.223374	−	0.178083i
$296$	0.583416	−	21.1263i	0.0339104	−	1.22794i
$297$	−6.61285	−	6.61285i	−0.383717	−	0.383717i
$298$	−1.32227	+	4.75915i	−0.0765970	+	0.275690i
$299$	23.2830			1.34649
$300$	−19.9547	+	10.0881i	−1.15209	+	0.582439i
$301$	−30.1630			−1.73857
$302$	0.0106944	−	0.0384914i	0.000615391	−	0.00221493i
$303$	−10.4241	−	10.4241i	−0.598847	−	0.598847i
$304$	−1.87116	−	3.53536i	−0.107318	−	0.202767i
$305$	11.2402	+	8.96113i	0.643612	+	0.513113i
$306$	−8.84335	+	4.99777i	−0.505541	+	0.285703i
$307$	16.2471	−	16.2471i	0.927270	−	0.927270i	−0.0702587	−	0.997529i	$-0.522382\pi$
$307$	16.2471	−	16.2471i	0.927270	−	0.927270i	0.997529	+	0.0702587i	$0.0223825\pi$
$308$	−5.53922	−	22.3071i	−0.315627	−	1.27107i
$309$			22.3426i			1.27103i
$310$	0.707131	−	0.512055i	0.0401623	−	0.0290828i
$311$			28.1999i			1.59907i	0.600618	+	0.799536i	$0.294921\pi$
$311$			28.1999i			1.59907i	−0.600618	+	0.799536i	$0.705079\pi$
$312$	−19.3392	−	20.4377i	−1.09487	−	1.15706i
$313$	−4.82974	+	4.82974i	−0.272993	+	0.272993i	−0.830304	−	0.557311i	$-0.811833\pi$
$313$	−4.82974	+	4.82974i	−0.272993	+	0.272993i	0.557311	+	0.830304i	$0.311833\pi$
$314$	−5.73579	−	10.1492i	−0.323689	−	0.572755i
$315$	−1.37785	−	12.2130i	−0.0776328	−	0.688126i
$316$	5.78758	+	3.48503i	0.325577	+	0.196049i
$317$	−14.0276	−	14.0276i	−0.787868	−	0.787868i	0.193276	−	0.981144i	$-0.438089\pi$
$317$	−14.0276	−	14.0276i	−0.787868	−	0.787868i	−0.981144	+	0.193276i	$0.938089\pi$
$318$	−26.0636	−	7.24144i	−1.46157	−	0.406080i
$319$	41.8835			2.34503
$320$	11.9063	−	13.3507i	0.665582	−	0.746325i
$321$	11.4194			0.637366
$322$	−19.6010	−	5.44589i	−1.09232	−	0.303488i
$323$	2.53996	+	2.53996i	0.141327	+	0.141327i
$324$	18.8475	+	11.3492i	1.04709	+	0.630511i
$325$	18.8390	+	11.8298i	1.04500	+	0.656201i
$326$	−11.3602	−	20.1013i	−0.629181	−	1.11331i
$327$	−0.627495	+	0.627495i	−0.0347006	+	0.0347006i
$328$	9.98247	+	10.5495i	0.551189	+	0.582497i
$329$		−	14.5586i		−	0.802643i
$330$	29.1908	+	4.67065i	1.60690	+	0.257111i
$331$			18.6160i			1.02323i	0.859216	+	0.511613i	$0.170952\pi$
$331$			18.6160i			1.02323i	−0.859216	+	0.511613i	$0.829048\pi$
$332$	2.87409	+	11.5743i	0.157736	+	0.635222i
$333$	−10.5651	+	10.5651i	−0.578965	+	0.578965i
$334$	−22.6486	+	12.7997i	−1.23927	+	0.700369i
$335$	−16.2654	+	1.83502i	−0.888673	+	0.100258i
$336$	11.5005	+	21.7291i	0.627405	+	1.18542i
$337$	3.14441	+	3.14441i	0.171287	+	0.171287i	0.787545	−	0.616258i	$-0.211352\pi$
$337$	3.14441	+	3.14441i	0.171287	+	0.171287i	−0.616258	+	0.787545i	$0.711352\pi$
$338$	−2.57213	+	9.25767i	−0.139905	+	0.503551i
$339$	−33.6162			−1.82578
$340$	−6.69174	+	14.6040i	−0.362910	+	0.792014i
$341$	−1.15428			−0.0625077
$342$	−0.757015	+	2.72467i	−0.0409347	+	0.147333i
$343$	12.5255	+	12.5255i	0.676314	+	0.676314i
$344$	−0.856780	+	31.0252i	−0.0461945	+	1.67277i
$345$	16.3108	−	20.4591i	0.878144	−	1.10148i
$346$	−17.3039	+	9.77921i	−0.930265	+	0.525734i
$347$	−6.64122	+	6.64122i	−0.356519	+	0.356519i	−0.862528	−	0.506009i	$-0.831120\pi$
$347$	−6.64122	+	6.64122i	−0.356519	+	0.356519i	0.506009	+	0.862528i	$0.331120\pi$
$348$	−43.4792	+	10.7966i	−2.33073	+	0.578759i
$349$		−	7.71160i		−	0.412793i	−0.978468	−	0.206396i	$-0.933826\pi$
$349$		−	7.71160i		−	0.412793i	0.978468	−	0.206396i	$-0.0661736\pi$
$350$	−13.0928	−	14.3655i	−0.699839	−	0.767868i
$351$		−	9.95189i		−	0.531192i
$352$	−23.1021	+	5.06393i	−1.23135	+	0.269908i
$353$	0.937561	−	0.937561i	0.0499014	−	0.0499014i	−0.681716	−	0.731617i	$-0.738766\pi$
$353$	0.937561	−	0.937561i	0.0499014	−	0.0499014i	0.731617	+	0.681716i	$0.238766\pi$
$354$	−3.41391	−	6.04078i	−0.181447	−	0.321064i
$355$	4.46556	−	5.60128i	0.237007	−	0.297285i
$356$	−12.8480	+	21.3366i	−0.680941	+	1.13084i
$357$	−15.6112	−	15.6112i	−0.826230	−	0.826230i
$358$	0.628579	+	0.174643i	0.0332214	+	0.00923016i
$359$	25.7286			1.35791			0.678953	−	0.734182i	$-0.262434\pi$
$359$	25.7286			1.35791			0.678953	+	0.734182i	$0.262434\pi$
$360$	−12.6013	+	1.07032i	−0.664145	+	0.0564108i
$361$	1.00000			0.0526316
$362$	−10.0375	−	2.78878i	−0.527557	−	0.146575i
$363$	−10.2449	−	10.2449i	−0.537716	−	0.537716i
$364$	12.6172	−	20.9534i	0.661324	−	1.09826i
$365$	21.4922	−	2.42470i	1.12495	−	0.126915i
$366$	10.0019	+	17.6980i	0.522808	+	0.925087i
$367$	−3.95182	+	3.95182i	−0.206283	+	0.206283i	−0.802686	−	0.596402i	$-0.796596\pi$
$367$	−3.95182	+	3.95182i	−0.206283	+	0.206283i	0.596402	+	0.802686i	$0.296596\pi$
$368$	−6.15833	+	20.0066i	−0.321025	+	1.04292i
$369$		−	10.2679i		−	0.534524i
$370$	−3.73325	+	23.3321i	−0.194082	+	1.21298i
$371$		−	23.5146i		−	1.22082i
$372$	1.19826	−	0.297547i	0.0621267	−	0.0154271i
$373$	−8.10059	+	8.10059i	−0.419433	+	0.419433i	−0.885008	−	0.465575i	$-0.845847\pi$
$373$	−8.10059	+	8.10059i	−0.419433	+	0.419433i	0.465575	+	0.885008i	$0.345847\pi$
$374$	18.4900	−	10.4495i	0.956098	−	0.540333i
$375$	23.5926	−	8.26677i	1.21832	−	0.426894i
$376$	−14.9748	−	0.413538i	−0.772265	−	0.0213266i
$377$	31.5159	+	31.5159i	1.62315	+	1.62315i
$378$	−2.32775	+	8.37809i	−0.119726	+	0.430922i
$379$	10.1697			0.522380			0.261190	−	0.965287i	$-0.415885\pi$
$379$	10.1697			0.522380			0.261190	+	0.965287i	$0.415885\pi$
$380$	1.55756	+	4.19214i	0.0799011	+	0.215052i
$381$	−21.0195			−1.07686
$382$	2.95961	−	10.6523i	0.151427	−	0.545020i
$383$	14.3086	+	14.3086i	0.731138	+	0.731138i	0.970845	−	0.239707i	$-0.0770515\pi$
$383$	14.3086	+	14.3086i	0.731138	+	0.731138i	−0.239707	+	0.970845i	$0.577051\pi$
$384$	22.6769	−	11.2120i	1.15722	−	0.572162i
$385$	2.88086	+	25.5355i	0.146822	+	1.30141i
$386$	30.9907	−	17.5142i	1.57738	−	0.891450i
$387$	15.5155	−	15.5155i	0.788696	−	0.788696i
$388$	−5.79252	−	23.3271i	−0.294070	−	1.18426i
$389$		−	30.0276i		−	1.52246i	−0.648482	−	0.761230i	$-0.724596\pi$
$389$		−	30.0276i		−	1.52246i	0.648482	−	0.761230i	$-0.275404\pi$
$390$	18.4505	+	25.4795i	0.934279	+	1.29021i
$391$		−	18.7981i		−	0.950660i
$392$	−1.14181	+	1.08044i	−0.0576702	+	0.0545706i
$393$	−17.7799	+	17.7799i	−0.896878	+	0.896878i
$394$	−1.31413	−	2.32530i	−0.0662049	−	0.117147i
$395$	−5.90606	−	4.70854i	−0.297166	−	0.236913i
$396$	14.3238	+	8.62520i	0.719799	+	0.433432i
$397$	−6.99848	−	6.99848i	−0.351244	−	0.351244i	0.509329	−	0.860572i	$-0.329894\pi$
$397$	−6.99848	−	6.99848i	−0.351244	−	0.351244i	−0.860572	+	0.509329i	$0.829894\pi$
$398$	21.1983	+	5.88969i	1.06258	+	0.295223i
$399$	−6.14621			−0.307696
$400$	−15.1480	+	13.0590i	−0.757401	+	0.652950i
$401$	−16.6477			−0.831349			−0.415674	−	0.909514i	$-0.636454\pi$
$401$	−16.6477			−0.831349			−0.415674	+	0.909514i	$0.636454\pi$
$402$	−22.3029	−	6.19659i	−1.11237	−	0.309058i
$403$	−0.868555	−	0.868555i	−0.0432658	−	0.0432658i
$404$	−11.2962	−	6.80207i	−0.562005	−	0.338416i
$405$	−19.2334	−	15.3336i	−0.955715	−	0.761934i
$406$	−19.1604	−	33.9035i	−0.950914	−	1.68260i
$407$	22.0900	−	22.0900i	1.09496	−	1.09496i
$408$	−16.5008	+	15.6140i	−0.816913	+	0.773006i
$409$			10.2017i			0.504444i	0.967669	+	0.252222i	$0.0811613\pi$
$409$			10.2017i			0.504444i	−0.967669	+	0.252222i	$0.918839\pi$
$410$	−9.52375	−	13.1520i	−0.470345	−	0.649529i
$411$		−	9.82815i		−	0.484787i
$412$	4.81624	+	19.3956i	0.237279	+	0.955551i
$413$	4.26502	−	4.26502i	0.209868	−	0.209868i
$414$	12.8838	−	7.28122i	0.633206	−	0.357852i
$415$	−1.49477	−	13.2494i	−0.0733752	−	0.650388i
$416$	−21.1939	−	13.5731i	−1.03912	−	0.665475i
$417$	−5.49400	−	5.49400i	−0.269043	−	0.269043i
$418$	1.58280	−	5.69685i	0.0774172	−	0.278642i
$419$	−12.2167			−0.596824			−0.298412	−	0.954437i	$-0.596457\pi$
$419$	−12.2167			−0.596824			−0.298412	+	0.954437i	$0.596457\pi$
$420$	−9.57309	−	25.7658i	−0.467119	−	1.25724i
$421$	−3.09851			−0.151012			−0.0755062	−	0.997145i	$-0.524057\pi$
$421$	−3.09851			−0.151012			−0.0755062	+	0.997145i	$0.524057\pi$
$422$	−6.39344	+	23.0114i	−0.311228	+	1.12018i
$423$	7.48878	+	7.48878i	0.364117	+	0.364117i
$424$	−24.1867	−	0.667933i	−1.17461	−	0.0324377i
$425$	9.55109	−	15.2101i	0.463296	−	0.737799i
$426$	8.81935	−	4.98420i	0.427299	−	0.241485i
$427$	−12.4954	+	12.4954i	−0.604696	+	0.604696i
$428$	9.91312	−	2.46159i	0.479169	−	0.118986i
$429$		−	41.5913i		−	2.00805i
$430$	5.48249	−	34.2646i	0.264389	−	1.65239i
$431$		−	6.40238i		−	0.308392i	−0.988040	−	0.154196i	$-0.950721\pi$
$431$		−	6.40238i		−	0.308392i	0.988040	−	0.154196i	$-0.0492787\pi$
$432$	8.55145	+	2.63226i	0.411432	+	0.126645i
$433$	17.5962	−	17.5962i	0.845621	−	0.845621i	−0.143962	−	0.989583i	$-0.545984\pi$
$433$	17.5962	−	17.5962i	0.845621	−	0.845621i	0.989583	+	0.143962i	$0.0459843\pi$
$434$	0.528046	+	0.934356i	0.0253470	+	0.0448505i
$435$	49.7718	−	5.61514i	2.38638	−	0.269225i
$436$	−0.409463	+	0.679992i	−0.0196097	+	0.0325657i
$437$	−3.70046	−	3.70046i	−0.177017	−	0.177017i
$438$	29.4699	+	8.18785i	1.40813	+	0.391230i
$439$	19.9289			0.951155			0.475578	−	0.879674i	$-0.342239\pi$
$439$	19.9289			0.951155			0.475578	+	0.879674i	$0.342239\pi$
$440$	26.3473	−	2.23787i	1.25606	−	0.106686i
$441$	1.11133			0.0529207
$442$	21.7760	+	6.05020i	1.03578	+	0.287779i
$443$	−1.19044	−	1.19044i	−0.0565597	−	0.0565597i	0.678261	−	0.734821i	$-0.262734\pi$
$443$	−1.19044	−	1.19044i	−0.0565597	−	0.0565597i	−0.734821	+	0.678261i	$0.762734\pi$
$444$	−17.2373	+	28.6259i	−0.818045	+	1.35852i
$445$	17.3586	−	21.7734i	0.822876	−	1.03216i
$446$	7.12549	+	12.6083i	0.337402	+	0.597019i
$447$	5.52223	−	5.52223i	0.261192	−	0.261192i
$448$	14.6676	+	16.3839i	0.692978	+	0.774066i
$449$			31.3174i			1.47796i	0.673728	+	0.738980i	$0.264692\pi$
$449$			31.3174i			1.47796i	−0.673728	+	0.738980i	$0.735308\pi$
$450$	14.1242	+	0.654660i	0.665822	+	0.0308609i
$451$			21.4685i			1.01091i
$452$	−29.1821	+	7.24641i	−1.37261	+	0.340842i
$453$	−0.0446631	+	0.0446631i	−0.00209846	+	0.00209846i
$454$	0.609026	−	0.344187i	0.0285830	−	0.0161535i
$455$	−17.0469	+	21.3823i	−0.799169	+	1.00242i
$456$	−0.174583	+	6.32190i	−0.00817561	+	0.296050i
$457$	−19.7335	−	19.7335i	−0.923096	−	0.923096i	0.0741508	−	0.997247i	$-0.476375\pi$
$457$	−19.7335	−	19.7335i	−0.923096	−	0.923096i	−0.997247	+	0.0741508i	$0.976375\pi$
$458$	4.04584	−	14.5619i	0.189050	−	0.680432i
$459$	−8.03489			−0.375037
$460$	9.74915	−	21.2765i	0.454557	−	0.992023i
$461$	−13.6317			−0.634894			−0.317447	−	0.948276i	$-0.602825\pi$
$461$	−13.6317			−0.634894			−0.317447	+	0.948276i	$0.602825\pi$
$462$	−9.72822	+	35.0141i	−0.452598	+	1.62900i
$463$	−26.2755	−	26.2755i	−1.22113	−	1.22113i	−0.967231	−	0.253897i	$-0.918288\pi$
$463$	−26.2755	−	26.2755i	−1.22113	−	1.22113i	−0.253897	−	0.967231i	$-0.581712\pi$
$464$	−35.4169	+	18.7450i	−1.64419	+	0.870217i
$465$	−1.37167	+	0.154749i	−0.0636099	+	0.00717632i
$466$	35.8009	−	20.2327i	1.65844	−	0.937260i
$467$	−3.54910	+	3.54910i	−0.164233	+	0.164233i	−0.784439	−	0.620206i	$-0.787049\pi$
$467$	−3.54910	+	3.54910i	−0.164233	+	0.164233i	0.620206	+	0.784439i	$0.287049\pi$
$468$	4.28801	+	17.2683i	0.198214	+	0.798229i
$469$		−	20.1217i		−	0.929135i
$470$	16.5383	+	2.64621i	0.762856	+	0.122060i
$471$			18.4320i			0.849303i
$472$	−4.26578	−	4.50808i	−0.196349	−	0.207501i
$473$	−32.4404	+	32.4404i	−1.49161	+	1.49161i
$474$	−5.25541	−	9.29923i	−0.241389	−	0.427128i
$475$	−1.11400	−	4.87432i	−0.0511137	−	0.223649i
$476$	−16.9172	−	10.1868i	−0.775399	−	0.466913i
$477$	12.0956	+	12.0956i	0.553821	+	0.553821i
$478$	14.5567	+	4.04439i	0.665807	+	0.184986i
$479$	−28.6474			−1.30893			−0.654465	−	0.756092i	$-0.727106\pi$
$479$	−28.6474			−1.30893			−0.654465	+	0.756092i	$0.727106\pi$
$480$	−26.7742	+	9.11485i	−1.22207	+	0.416034i
$481$	33.2439			1.51579
$482$	−16.0276	−	4.45306i	−0.730035	−	0.202831i
$483$	22.7438	+	22.7438i	1.03488	+	1.03488i
$484$	−11.1020	−	6.68514i	−0.504635	−	0.303870i
$485$	3.01259	+	26.7032i	0.136795	+	1.21253i
$486$	−12.4453	−	22.0214i	−0.564528	−	0.998910i
$487$	−30.1230	+	30.1230i	−1.36500	+	1.36500i	−0.497590	+	0.867412i	$0.665782\pi$
$487$	−30.1230	+	30.1230i	−1.36500	+	1.36500i	−0.867412	+	0.497590i	$0.834218\pi$
$488$	12.4977	+	13.2075i	0.565743	+	0.597877i
$489$			36.5060i			1.65086i
$490$	1.42349	−	1.03079i	0.0643068	−	0.0465666i
$491$			11.8932i			0.536731i	0.963317	+	0.268366i	$0.0864836\pi$
$491$			11.8932i			0.536731i	−0.963317	+	0.268366i	$0.913516\pi$
$492$	−5.53409	−	22.2864i	−0.249496	−	1.00475i
$493$	25.4451	−	25.4451i	1.14599	−	1.14599i
$494$	5.47768	−	3.09568i	0.246453	−	0.139281i
$495$	−14.6170	−	11.6533i	−0.656987	−	0.523776i
$496$	0.976064	−	0.516600i	0.0438266	−	0.0231960i
$497$	6.22679	+	6.22679i	0.279310	+	0.279310i
$498$	5.04760	−	18.1675i	0.226188	−	0.814103i
$499$	−18.1037			−0.810432			−0.405216	−	0.914221i	$-0.632804\pi$
$499$	−18.1037			−0.810432			−0.405216	+	0.914221i	$0.632804\pi$
$500$	18.6987	−	12.2621i	0.836232	−	0.548376i
$501$	41.1320			1.83764
$502$	−7.85999	+	28.2899i	−0.350808	+	1.26264i
$503$	16.2494	+	16.2494i	0.724524	+	0.724524i	0.969523	−	0.244999i	$-0.0787877\pi$
$503$	16.2494	+	16.2494i	0.724524	+	0.724524i	−0.244999	+	0.969523i	$0.578788\pi$
$504$	0.429160	−	15.5405i	0.0191163	−	0.692228i
$505$	11.5274	+	9.19011i	0.512963	+	0.408955i
$506$	−26.9381	+	15.2239i	−1.19754	+	0.676784i
$507$	10.7420	−	10.7420i	0.477071	−	0.477071i
$508$	−18.2470	+	4.53103i	−0.809579	+	0.201032i
$509$			43.7904i			1.94097i	0.241155	+	0.970487i	$0.422474\pi$
$509$			43.7904i			1.94097i	−0.241155	+	0.970487i	$0.577526\pi$
$510$	20.5715	−	14.8965i	0.910922	−	0.659627i
$511$			26.5878i			1.17617i
$512$	17.2688	−	14.6215i	0.763183	−	0.646183i
$513$	−1.58169	+	1.58169i	−0.0698335	+	0.0698335i
$514$	−13.6354	−	24.1273i	−0.601431	−	1.06421i
$515$	−2.50485	−	22.2026i	−0.110377	−	0.978364i
$516$	25.3140	−	42.0387i	1.11438	−	1.85065i
$517$	−15.6579	−	15.6579i	−0.688632	−	0.688632i
$518$	−27.9867	−	7.77575i	−1.22966	−	0.341647i
$519$	31.4256			1.37943
$520$	21.5093	+	18.1415i	0.943246	+	0.795557i
$521$	34.0703			1.49265			0.746323	−	0.665584i	$-0.231817\pi$
$521$	34.0703			1.49265			0.746323	+	0.665584i	$0.231817\pi$
$522$	27.2954	+	7.58370i	1.19469	+	0.331929i
$523$	−16.2536	−	16.2536i	−0.710720	−	0.710720i	0.255966	−	0.966686i	$-0.417607\pi$
$523$	−16.2536	−	16.2536i	−0.710720	−	0.710720i	−0.966686	+	0.255966i	$0.917607\pi$
$524$	−11.6020	+	19.2674i	−0.506837	+	0.841701i
$525$	6.84687	+	29.9586i	0.298822	+	1.30750i
$526$	−17.2266	−	30.4818i	−0.751115	−	1.32907i
$527$	−0.701249	+	0.701249i	−0.0305469	+	0.0305469i
$528$	35.7386	+	11.0009i	1.55532	+	0.478751i
$529$			4.38682i			0.190731i
$530$	26.7121	+	4.27406i	1.16030	+	0.185653i
$531$			4.38775i			0.190412i
$532$	−5.33552	+	1.32490i	−0.231324	+	0.0574416i
$533$	−16.1543	+	16.1543i	−0.699721	+	0.699721i
$534$	34.2827	−	19.3747i	1.48356	−	0.838423i
$535$	−11.3478	+	1.28023i	−0.490609	+	0.0553493i
$536$	−20.6969	−	0.571558i	−0.893970	−	0.0246876i
$537$	−0.729365	−	0.729365i	−0.0314744	−	0.0314744i
$538$	−6.08484	+	21.9007i	−0.262336	+	0.944207i
$539$	−2.32363			−0.100086
$540$	−9.09426	−	4.16710i	−0.391354	−	0.179323i
$541$	2.52042			0.108361			0.0541807	−	0.998531i	$-0.482745\pi$
$541$	2.52042			0.108361			0.0541807	+	0.998531i	$0.482745\pi$
$542$	−4.04352	+	14.5535i	−0.173684	+	0.625128i
$543$	11.6469	+	11.6469i	0.499814	+	0.499814i
$544$	−10.9586	+	17.1114i	−0.469844	+	0.733647i
$545$	0.553215	−	0.693913i	0.0236971	−	0.0297240i
$546$	−33.6670	+	19.0267i	−1.44081	+	0.814268i
$547$	15.0297	−	15.0297i	0.642623	−	0.642623i	−0.308576	−	0.951200i	$-0.599852\pi$
$547$	15.0297	−	15.0297i	0.642623	−	0.642623i	0.951200	+	0.308576i	$0.0998525\pi$
$548$	−2.11859	−	8.53180i	−0.0905016	−	0.364460i
$549$		−	12.8550i		−	0.548638i
$550$	−29.5315	−	1.36879i	−1.25923	−	0.0583654i
$551$		−	10.0179i		−	0.426777i
$552$	24.0400	−	22.7479i	1.02321	−	0.968215i
$553$	6.56560	−	6.56560i	0.279198	−	0.279198i
$554$	−8.68445	−	15.3668i	−0.368967	−	0.652872i
$555$	23.2889	−	29.2119i	0.988557	−	1.23998i
$556$	−5.95364	−	3.58503i	−0.252491	−	0.152039i
$557$	26.2644	+	26.2644i	1.11286	+	1.11286i	0.992762	+	0.120098i	$0.0383209\pi$
$557$	26.2644	+	26.2644i	1.11286	+	1.11286i	0.120098	+	0.992762i	$0.461679\pi$
$558$	−0.752242	−	0.209001i	−0.0318450	−	0.00884772i
$559$	−48.8206			−2.06489
$560$	−13.8645	−	20.3036i	−0.585883	−	0.857984i
$561$	−33.5797			−1.41774
$562$	−18.8738	−	5.24384i	−0.796142	−	0.221198i
$563$	−30.1923	−	30.1923i	−1.27246	−	1.27246i	−0.944796	−	0.327660i	$-0.893740\pi$
$563$	−30.1923	−	30.1923i	−1.27246	−	1.27246i	−0.327660	−	0.944796i	$-0.606260\pi$
$564$	20.2906	+	12.2182i	0.854390	+	0.514477i
$565$	33.4056	−	3.76874i	1.40538	−	0.158552i
$566$	10.1316	+	17.9275i	0.425865	+	0.753550i
$567$	21.3812	−	21.3812i	0.897927	−	0.897927i
$568$	6.58165	−	6.22791i	0.276160	−	0.261317i
$569$			14.6606i			0.614603i	0.951612	+	0.307302i	$0.0994261\pi$
$569$			14.6606i			0.614603i	−0.951612	+	0.307302i	$0.900574\pi$
$570$	1.11715	−	6.98198i	0.0467922	−	0.292443i
$571$			16.3003i			0.682145i	0.940037	+	0.341072i	$0.110790\pi$
$571$			16.3003i			0.682145i	−0.940037	+	0.341072i	$0.889210\pi$
$572$	−8.96556	−	36.1054i	−0.374869	−	1.50964i
$573$	−12.3603	+	12.3603i	−0.516359	+	0.516359i
$574$	17.3782	−	9.82117i	0.725350	−	0.409928i
$575$	−13.9149	+	22.1595i	−0.580293	+	0.924117i
$576$	−15.9725	−	0.882855i	−0.665521	−	0.0367856i
$577$	−22.0297	−	22.0297i	−0.917107	−	0.917107i	0.0797106	−	0.996818i	$-0.474600\pi$
$577$	−22.0297	−	22.0297i	−0.917107	−	0.917107i	−0.996818	+	0.0797106i	$0.974600\pi$
$578$	−1.55111	+	5.58279i	−0.0645176	+	0.232213i
$579$	−56.2821			−2.33901
$580$	41.9964	−	15.6035i	1.74381	−	0.647898i
$581$	16.3907			0.680001
$582$	−10.1731	+	36.6151i	−0.421687	+	1.51775i
$583$	−25.2901	−	25.2901i	−1.04741	−	1.04741i
$584$	27.3478	+	0.755227i	1.13166	+	0.0312515i
$585$	−2.23012	−	19.7675i	−0.0922043	−	0.817286i
$586$	14.6100	−	8.25678i	0.603535	−	0.341084i
$587$	9.33394	−	9.33394i	0.385253	−	0.385253i	−0.487737	−	0.872990i	$-0.662178\pi$
$587$	9.33394	−	9.33394i	0.385253	−	0.385253i	0.872990	+	0.487737i	$0.162178\pi$
$588$	2.41215	−	0.598977i	0.0994755	−	0.0247014i
$589$			0.276086i			0.0113759i
$590$	4.06976	+	5.62020i	0.167549	+	0.231380i
$591$			4.22297i			0.173710i
$592$	−8.79298	+	28.5658i	−0.361389	+	1.17405i
$593$	−6.90298	+	6.90298i	−0.283472	+	0.283472i	−0.834492	−	0.551020i	$-0.814239\pi$
$593$	−6.90298	+	6.90298i	−0.283472	+	0.283472i	0.551020	+	0.834492i	$0.314239\pi$
$594$	6.50717	+	11.5142i	0.266992	+	0.472432i
$595$	17.2635	+	13.7632i	0.707736	+	0.564235i
$596$	3.60345	−	5.98423i	0.147603	−	0.245123i
$597$	−24.5972	−	24.5972i	−1.00670	−	1.00670i
$598$	−31.7254	−	8.81450i	−1.29735	−	0.360452i
$599$	−6.30551			−0.257636			−0.128818	−	0.991668i	$-0.541118\pi$
$599$	−6.30551			−0.257636			−0.128818	+	0.991668i	$0.541118\pi$
$600$	31.0095	−	6.19161i	1.26596	−	0.252771i
$601$	−28.6173			−1.16732			−0.583662	−	0.811996i	$-0.698381\pi$
$601$	−28.6173			−1.16732			−0.583662	+	0.811996i	$0.698381\pi$
$602$	41.1001	+	11.4191i	1.67511	+	0.465409i
$603$	10.3504	+	10.3504i	0.421500	+	0.421500i
$604$	−0.0291442	+	0.0483997i	−0.00118586	+	0.00196936i
$605$	11.3292	+	9.03212i	0.460599	+	0.367208i
$606$	10.2575	+	18.1502i	0.416681	+	0.737301i
$607$	19.1663	−	19.1663i	0.777937	−	0.777937i	−0.201543	−	0.979480i	$-0.564595\pi$
$607$	19.1663	−	19.1663i	0.777937	−	0.777937i	0.979480	+	0.201543i	$0.0645954\pi$
$608$	1.21121	+	5.52566i	0.0491212	+	0.224095i
$609$			61.5721i			2.49503i
$610$	−11.9234	−	16.4658i	−0.482763	−	0.666679i
$611$		−	23.5640i		−	0.953297i
$612$	13.9420	−	3.46203i	0.563572	−	0.139944i
$613$	4.87008	−	4.87008i	0.196701	−	0.196701i	−0.601883	−	0.798584i	$-0.705583\pi$
$613$	4.87008	−	4.87008i	0.196701	−	0.196701i	0.798584	+	0.601883i	$0.205583\pi$
$614$	−28.2891	+	15.9874i	−1.14166	+	0.645200i
$615$	2.87819	+	25.5119i	0.116060	+	1.02874i
$616$	−0.897307	+	32.4927i	−0.0361535	+	1.30917i
$617$	−22.0210	−	22.0210i	−0.886533	−	0.886533i	0.107655	−	0.994188i	$-0.465666\pi$
$617$	−22.0210	−	22.0210i	−0.886533	−	0.886533i	−0.994188	+	0.107655i	$0.965666\pi$
$618$	8.45848	−	30.4440i	0.340250	−	1.22464i
$619$	46.0944			1.85269			0.926345	−	0.376677i	$-0.122933\pi$
$619$	46.0944			1.85269			0.926345	+	0.376677i	$0.122933\pi$
$620$	−1.15739	+	0.430020i	−0.0464819	+	0.0172700i
$621$	11.7060			0.469745
$622$	10.6760	−	38.4252i	0.428067	−	1.54071i
$623$	24.2048	+	24.2048i	0.969747	+	0.969747i
$624$	18.6143	+	35.1698i	0.745167	+	1.40792i
$625$	−22.5180	+	10.8600i	−0.900721	+	0.434399i
$626$	8.40945	−	4.75255i	0.336109	−	0.189950i
$627$	−6.61028	+	6.61028i	−0.263989	+	0.263989i
$628$	3.97327	+	16.0008i	0.158551	+	0.638502i
$629$		−	26.8402i		−	1.07019i
$630$	−2.74617	+	17.1631i	−0.109410	+	0.683794i
$631$			22.0131i			0.876327i	0.898895	+	0.438164i	$0.144371\pi$
$631$			22.0131i			0.876327i	−0.898895	+	0.438164i	$0.855629\pi$
$632$	−6.56678	−	6.93977i	−0.261213	−	0.276049i
$633$	26.7011	−	26.7011i	1.06127	−	1.06127i
$634$	13.8034	+	24.4246i	0.548203	+	0.970024i
$635$	20.8878	−	2.35651i	0.828907	−	0.0935153i
$636$	32.7727	+	19.7344i	1.29952	+	0.782518i
$637$	−1.74845	−	1.74845i	−0.0692760	−	0.0692760i
$638$	−57.0705	−	15.8563i	−2.25944	−	0.627757i
$639$	−6.40597			−0.253416
$640$	−21.2778	+	13.6841i	−0.841079	+	0.540912i
$641$	14.7965			0.584427			0.292213	−	0.956353i	$-0.405608\pi$
$641$	14.7965			0.584427			0.292213	+	0.956353i	$0.405608\pi$
$642$	−15.5600	−	4.32315i	−0.614104	−	0.170621i
$643$	−30.6307	−	30.6307i	−1.20796	−	1.20796i	−0.971688	−	0.236268i	$-0.924076\pi$
$643$	−30.6307	−	30.6307i	−1.20796	−	1.20796i	−0.236268	−	0.971688i	$-0.575924\pi$
$644$	24.6466	+	14.8411i	0.971212	+	0.584823i
$645$	−34.2011	+	42.8993i	−1.34667	+	1.68916i
$646$	−2.49937	−	4.42254i	−0.0983364	−	0.174002i
$647$	31.2175	−	31.2175i	1.22728	−	1.22728i	0.262298	−	0.964987i	$-0.415520\pi$
$647$	31.2175	−	31.2175i	1.22728	−	1.22728i	0.964987	−	0.262298i	$-0.0844803\pi$
$648$	−21.3851	−	22.5997i	−0.840085	−	0.887801i
$649$		−	9.17409i		−	0.360115i
$650$	−21.1915	−	23.2514i	−0.831198	−	0.911995i
$651$		−	1.69688i		−	0.0665061i
$652$	7.86935	+	31.6908i	0.308188	+	1.24111i
$653$	2.80916	−	2.80916i	0.109931	−	0.109931i	−0.650002	−	0.759933i	$-0.725232\pi$
$653$	2.80916	−	2.80916i	0.109931	−	0.109931i	0.759933	+	0.650002i	$0.225232\pi$
$654$	1.09258	−	0.617466i	0.0427233	−	0.0241448i
$655$	15.6752	−	19.6618i	0.612481	−	0.768252i
$656$	−9.60827	−	18.1539i	−0.375140	−	0.708790i
$657$	−13.6764	−	13.6764i	−0.533569	−	0.533569i
$658$	−5.51162	+	19.8376i	−0.214865	+	0.773349i
$659$	4.02042			0.156613			0.0783066	−	0.996929i	$-0.475049\pi$
$659$	4.02042			0.156613			0.0783066	+	0.996929i	$0.475049\pi$
$660$	−38.0071	−	17.4153i	−1.47942	−	0.677890i
$661$	−18.3750			−0.714705			−0.357352	−	0.933970i	$-0.616321\pi$
$661$	−18.3750			−0.714705			−0.357352	+	0.933970i	$0.616321\pi$
$662$	7.04765	−	25.3661i	0.273915	−	0.985882i
$663$	−25.2676	−	25.2676i	−0.981312	−	0.981312i
$664$	0.465578	−	16.8592i	0.0180679	−	0.654264i
$665$	6.10771	−	0.689057i	0.236847	−	0.0267205i
$666$	18.3958	−	10.3963i	0.712821	−	0.402847i
$667$	−37.0708	+	37.0708i	−1.43539	+	1.43539i
$668$	35.7067	−	8.86655i	1.38153	−	0.343057i
$669$		−	22.8979i		−	0.885282i
$670$	22.8579	+	3.65737i	0.883078	+	0.141296i
$671$			26.8778i			1.03760i
$672$	−7.44438	−	33.9619i	−0.287173	−	1.31011i
$673$	31.9937	−	31.9937i	1.23327	−	1.23327i	0.270565	−	0.962702i	$-0.412789\pi$
$673$	31.9937	−	31.9937i	1.23327	−	1.23327i	0.962702	−	0.270565i	$-0.0872105\pi$
$674$	−3.09416	−	5.47499i	−0.119183	−	0.210889i
$675$	9.47168	+	5.94768i	0.364565	+	0.228926i
$676$	7.00956	−	11.6407i	0.269598	−	0.447721i
$677$	8.69191	+	8.69191i	0.334057	+	0.334057i	0.854125	−	0.520068i	$-0.174093\pi$
$677$	8.69191	+	8.69191i	0.334057	+	0.334057i	−0.520068	+	0.854125i	$0.674093\pi$
$678$	45.8054	+	12.7264i	1.75914	+	0.488756i
$679$	−33.0342			−1.26774
$680$	14.6470	−	17.3661i	0.561685	−	0.665958i
$681$	−1.10605			−0.0423840
$682$	1.57282	+	0.436988i	0.0602264	+	0.0167332i
$683$	−18.0817	−	18.0817i	−0.691878	−	0.691878i	0.270767	−	0.962645i	$-0.412723\pi$
$683$	−18.0817	−	18.0817i	−0.691878	−	0.691878i	−0.962645	+	0.270767i	$0.912723\pi$
$684$	2.06301	−	3.42604i	0.0788813	−	0.130998i
$685$	1.10184	+	9.76658i	0.0420992	+	0.373162i
$686$	−12.3253	−	21.8092i	−0.470583	−	0.832678i
$687$	−16.8967	+	16.8967i	−0.644650	+	0.644650i
$688$	12.9130	−	41.9505i	0.492303	−	1.59935i
$689$		−	38.0598i		−	1.44996i
$690$	−29.9705	+	21.7026i	−1.14096	+	0.826203i
$691$			3.20982i			0.122107i	0.998134	+	0.0610536i	$0.0194460\pi$
$691$			3.20982i			0.122107i	−0.998134	+	0.0610536i	$0.980554\pi$
$692$	27.2805	−	6.77421i	1.03705	−	0.257517i
$693$	16.2494	−	16.2494i	0.617263	−	0.617263i
$694$	11.5636	−	6.53508i	0.438947	−	0.248068i
$695$	6.07552	+	4.84365i	0.230458	+	0.183730i
$696$	63.3321	+	1.74896i	2.40060	+	0.0662941i
$697$	13.0426	+	13.0426i	0.494022	+	0.494022i
$698$	−2.91947	+	10.5078i	−0.110503	+	0.397727i
$699$	−65.0179			−2.45920
$700$	12.4017	+	24.5311i	0.468741	+	0.927188i
$701$	1.08890			0.0411273			0.0205637	−	0.999789i	$-0.493454\pi$
$701$	1.08890			0.0411273			0.0205637	+	0.999789i	$0.493454\pi$
$702$	−3.76760	+	13.5604i	−0.142199	+	0.511806i
$703$	−5.28359	−	5.28359i	−0.199274	−	0.199274i
$704$	33.3960	+	1.84591i	1.25866	+	0.0695704i
$705$	−20.7060	−	16.5077i	−0.779834	−	0.621714i
$706$	−1.63246	+	0.922577i	−0.0614386	+	0.0347217i
$707$	−12.8147	+	12.8147i	−0.481947	+	0.481947i
$708$	2.36487	+	9.52361i	0.0888772	+	0.357919i
$709$		−	39.2212i		−	1.47298i	−0.676446	−	0.736492i	$-0.736481\pi$
$709$		−	39.2212i		−	1.47298i	0.676446	−	0.736492i	$-0.263519\pi$
$710$	−8.20531	+	5.94172i	−0.307940	+	0.222989i
$711$			6.75454i			0.253315i
$712$	25.5843	−	24.2092i	0.958811	−	0.907278i
$713$	1.02165	−	1.02165i	0.0382609	−	0.0382609i
$714$	15.3617	+	27.1818i	0.574896	+	1.01726i
$715$	4.66284	+	41.3308i	0.174380	+	1.54568i
$716$	−0.790385	−	0.475936i	−0.0295381	−	0.0177866i
$717$	−16.8907	−	16.8907i	−0.630795	−	0.630795i
$718$	−35.0578	−	9.74038i	−1.30835	−	0.363508i
$719$	18.4618			0.688509			0.344255	−	0.938876i	$-0.388132\pi$
$719$	18.4618			0.688509			0.344255	+	0.938876i	$0.388132\pi$
$720$	17.5757	+	3.31219i	0.655007	+	0.123438i
$721$	27.4666			1.02291
$722$	−1.36260	−	0.378581i	−0.0507107	−	0.0140893i
$723$	18.5974	+	18.5974i	0.691645	+	0.691645i
$724$	12.6212	+	7.59998i	0.469065	+	0.282451i
$725$	−48.8305	+	11.1599i	−1.81352	+	0.414469i
$726$	10.0811	+	17.8382i	0.374146	+	0.662036i
$727$	22.6031	−	22.6031i	0.838301	−	0.838301i	−0.150334	−	0.988635i	$-0.548035\pi$
$727$	22.6031	−	22.6031i	0.838301	−	0.838301i	0.988635	+	0.150334i	$0.0480350\pi$
$728$	−25.1248	+	23.7744i	−0.931188	+	0.881139i
$729$			6.99182i			0.258956i
$730$	−30.2032	−	4.83265i	−1.11787	−	0.178864i
$731$			39.4165i			1.45787i
$732$	−6.92847	−	27.9018i	−0.256084	−	1.03128i
$733$	−10.3459	+	10.3459i	−0.382136	+	0.382136i	−0.871871	−	0.489735i	$-0.837093\pi$
$733$	−10.3459	+	10.3459i	−0.382136	+	0.382136i	0.489735	+	0.871871i	$0.337093\pi$
$734$	6.88083	−	3.88866i	0.253976	−	0.143533i
$735$	−2.76125	+	0.311518i	−0.101850	+	0.0114905i
$736$	15.9655	−	24.9296i	0.588494	−	0.918915i
$737$	−21.6410	−	21.6410i	−0.797157	−	0.797157i
$738$	−3.88723	+	13.9910i	−0.143091	+	0.515016i
$739$	2.93089			0.107814			0.0539072	−	0.998546i	$-0.482832\pi$
$739$	2.93089			0.107814			0.0539072	+	0.998546i	$0.482832\pi$
$740$	13.9200	−	30.3790i	0.511710	−	1.11675i
$741$	−9.94801			−0.365449
$742$	−8.90218	+	32.0410i	−0.326809	+	1.17626i
$743$	7.25703	+	7.25703i	0.266234	+	0.266234i	0.827581	−	0.561346i	$-0.189716\pi$
$743$	7.25703	+	7.25703i	0.266234	+	0.266234i	−0.561346	+	0.827581i	$0.689716\pi$
$744$	−1.74539	−	0.0482000i	−0.0639890	−	0.00176710i
$745$	−4.86853	+	6.10673i	−0.178369	+	0.223733i
$746$	14.1046	−	7.97113i	0.516406	−	0.291844i
$747$	−8.43118	+	8.43118i	−0.308481	+	0.308481i
$748$	−29.1505	+	7.23856i	−1.06585	+	0.264668i
$749$		−	14.0383i		−	0.512947i
$750$	−35.2769	+	2.33257i	−1.28813	+	0.0851735i
$751$			49.3852i			1.80209i	0.433725	+	0.901045i	$0.357199\pi$
$751$			49.3852i			1.80209i	−0.433725	+	0.901045i	$0.642801\pi$
$752$	20.2481	+	6.23265i	0.738371	+	0.227281i
$753$	32.8258	−	32.8258i	1.19624	−	1.19624i
$754$	−31.0122	−	54.8749i	−1.12940	−	1.99842i
$755$	0.0393761	−	0.0493905i	0.00143304	−	0.00179750i
$756$	6.34357	−	10.5347i	0.230713	−	0.383145i
$757$	−24.5487	−	24.5487i	−0.892236	−	0.892236i	0.102497	−	0.994733i	$-0.467317\pi$
$757$	−24.5487	−	24.5487i	−0.892236	−	0.892236i	−0.994733	+	0.102497i	$0.967317\pi$
$758$	−13.8572	−	3.85004i	−0.503315	−	0.139840i
$759$	48.9222			1.77576
$760$	−0.535264	−	6.30186i	−0.0194161	−	0.228593i
$761$	−1.97888			−0.0717342			−0.0358671	−	0.999357i	$-0.511419\pi$
$761$	−1.97888			−0.0717342			−0.0358671	+	0.999357i	$0.511419\pi$
$762$	28.6411	+	7.95758i	1.03756	+	0.288273i
$763$	0.771404	+	0.771404i	0.0279267	+	0.0279267i
$764$	−8.06553	+	13.3944i	−0.291801	+	0.484592i
$765$	−15.9598	+	1.80054i	−0.577027	+	0.0650988i
$766$	−14.0800	−	24.9139i	−0.508730	−	0.900177i
$767$	6.90318	−	6.90318i	0.249260	−	0.249260i
$768$	−35.1441	+	6.69248i	−1.26816	+	0.241494i
$769$		−	28.4422i		−	1.02565i	−0.858492	−	0.512827i	$-0.828598\pi$
$769$		−	28.4422i		−	1.02565i	0.858492	−	0.512827i	$-0.171402\pi$
$770$	5.74181	−	35.8853i	0.206921	−	1.29322i
$771$			43.8175i			1.57805i

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36260 - 0.378581i) q^{2} +(1.58108 + 1.58108i) q^{3} +(1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 - 2.75294i) q^{6} +(1.94368 - 1.94368i) q^{7} +(-1.94403 - 2.05445i) q^{8} +1.99961i q^{9} +O(q^{10})\)	\(q+(-1.36260 - 0.378581i) q^{2} +(1.58108 + 1.58108i) q^{3} +(1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 - 2.75294i) q^{6} +(1.94368 - 1.94368i) q^{7} +(-1.94403 - 2.05445i) q^{8} +1.99961i q^{9} +(1.85470 + 2.56127i) q^{10} -4.18087i q^{11} +(1.07773 + 4.34015i) q^{12} +(3.14596 - 3.14596i) q^{13} +(-3.38430 + 1.91262i) q^{14} +(-0.560510 - 4.96829i) q^{15} +(1.87116 + 3.53536i) q^{16} +(-2.53996 - 2.53996i) q^{17} +(0.757015 - 2.72467i) q^{18} -1.00000 q^{19} +(-1.55756 - 4.19214i) q^{20} +6.14621 q^{21} +(-1.58280 + 5.69685i) q^{22} +(3.70046 + 3.70046i) q^{23} +(0.174583 - 6.32190i) q^{24} +(1.11400 + 4.87432i) q^{25} +(-5.47768 + 3.09568i) q^{26} +(1.58169 - 1.58169i) q^{27} +(5.33552 - 1.32490i) q^{28} +10.0179i q^{29} +(-1.11715 + 6.98198i) q^{30} -0.276086i q^{31} +(-1.21121 - 5.52566i) q^{32} +(6.61028 - 6.61028i) q^{33} +(2.49937 + 4.42254i) q^{34} +(-6.10771 + 0.689057i) q^{35} +(-2.06301 + 3.42604i) q^{36} +(5.28359 + 5.28359i) q^{37} +(1.36260 + 0.378581i) q^{38} +9.94801 q^{39} +(0.535264 + 6.30186i) q^{40} -5.13494 q^{41} +(-8.37482 - 2.32684i) q^{42} +(-7.75925 - 7.75925i) q^{43} +(4.31344 - 7.16331i) q^{44} +(2.78729 - 3.49617i) q^{45} +(-3.64132 - 6.44317i) q^{46} +(3.74512 - 3.74512i) q^{47} +(-2.63124 + 8.54812i) q^{48} -0.555776i q^{49} +(0.327394 - 7.06348i) q^{50} -8.03176i q^{51} +(8.63585 - 2.14443i) q^{52} +(6.04899 - 6.04899i) q^{53} +(-2.75401 + 1.55641i) q^{54} +(-5.82778 + 7.30995i) q^{55} +(-7.77175 - 0.214622i) q^{56} +(-1.58108 - 1.58108i) q^{57} +(3.79259 - 13.6504i) q^{58} +2.19430 q^{59} +(4.16547 - 9.09071i) q^{60} -6.42875 q^{61} +(-0.104521 + 0.376195i) q^{62} +(3.88660 + 3.88660i) q^{63} +(-0.441514 + 7.98781i) q^{64} +(-9.88569 + 1.11528i) q^{65} +(-11.5097 + 6.50463i) q^{66} +(5.17620 - 5.17620i) q^{67} +(-1.73135 - 6.97236i) q^{68} +11.7014i q^{69} +(8.58322 + 1.37335i) q^{70} +3.20361i q^{71} +(4.10810 - 3.88730i) q^{72} +(-6.83955 + 6.83955i) q^{73} +(-5.19914 - 9.19968i) q^{74} +(-5.94536 + 9.46799i) q^{75} +(-1.71335 - 1.03171i) q^{76} +(-8.12627 - 8.12627i) q^{77} +(-13.5552 - 3.76613i) q^{78} +3.37793 q^{79} +(1.65642 - 8.78956i) q^{80} +11.0004 q^{81} +(6.99687 + 1.94399i) q^{82} +(4.21641 + 4.21641i) q^{83} +(10.5306 + 6.34110i) q^{84} +(0.900447 + 7.98144i) q^{85} +(7.63525 + 13.5103i) q^{86} +(-15.8391 + 15.8391i) q^{87} +(-8.58938 + 8.12773i) q^{88} +12.4531i q^{89} +(-5.12154 + 3.70867i) q^{90} -12.2295i q^{91} +(2.52240 + 10.1580i) q^{92} +(0.436513 - 0.436513i) q^{93} +(-6.52093 + 3.68527i) q^{94} +(1.74843 + 1.39392i) q^{95} +(6.82148 - 10.6515i) q^{96} +(-8.49786 - 8.49786i) q^{97} +(-0.210406 + 0.757299i) q^{98} +8.36011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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