LMFDB - Embedded newform 380.2.k.c.267.12

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			267.12
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.378581 - 1.36260i) q^{2} +(-1.58108 - 1.58108i) q^{3} +(-1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 + 2.75294i) q^{6} +(-1.94368 + 1.94368i) q^{7} +(2.05445 + 1.94403i) q^{8} +1.99961i q^{9} +O(q^{10})$	\(q+(-0.378581 - 1.36260i) 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} +(2.05445 + 1.94403i) q^{8} +1.99961i q^{9} +(-1.23743 + 2.91012i) q^{10} +4.18087i q^{11} +(4.34015 + 1.07773i) 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} +(2.72467 - 0.757015i) q^{18} +1.00000 q^{19} +(4.43379 + 0.584402i) q^{20} +6.14621 q^{21} +(5.69685 - 1.58280i) 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} +(1.32490 - 5.33552i) q^{28} +10.0179i q^{29} +(6.55759 - 2.64465i) q^{30} +0.276086i q^{31} +(-5.52566 - 1.21121i) 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} +(-0.378581 - 1.36260i) q^{38} -9.94801 q^{39} +(-0.882243 - 6.26272i) q^{40} -5.13494 q^{41} +(-2.32684 - 8.37482i) 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} +(-8.54812 + 2.63124i) q^{48} -0.555776i q^{49} +(6.22001 - 3.36326i) q^{50} +8.03176i q^{51} +(-2.14443 + 8.63585i) 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} +(13.6504 - 3.79259i) q^{58} -2.19430 q^{59} +(-6.08618 - 7.93415i) q^{60} -6.42875 q^{61} +(0.376195 - 0.104521i) 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} +(6.97236 + 1.73135i) q^{68} +11.7014i q^{69} +(-3.25117 - 8.06149i) q^{70} -3.20361i q^{71} +(-3.88730 + 4.10810i) 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} +(3.76613 + 13.5552i) q^{78} -3.37793 q^{79} +(-8.19957 + 3.57309i) q^{80} +11.0004 q^{81} +(1.94399 + 6.99687i) 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} +(-8.12773 + 8.58938i) q^{88} +12.4531i q^{89} +(-5.81910 - 2.47437i) q^{90} +12.2295i q^{91} +(10.1580 + 2.52240i) 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} +(-0.757299 + 0.210406i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 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 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * 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 $

$2$	−0.378581	−	1.36260i	−0.267697	−	0.963503i
$2$	−0.378581	−	1.36260i	−0.267697	−	0.963503i
$3$	−1.58108	−	1.58108i	−0.912835	−	0.912835i	0.0836591	−	0.996494i	$-0.473339\pi$
$3$	−1.58108	−	1.58108i	−0.912835	−	0.912835i	−0.996494	+	0.0836591i	$0.973339\pi$
$4$	−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	−0.971536	−	0.236894i	$-0.923871\pi$
$7$	−1.94368	+	1.94368i	−0.734642	+	0.734642i	0.236894	+	0.971536i	$0.423871\pi$
$8$	2.05445	+	1.94403i	0.726357	+	0.687318i
$9$			1.99961i			0.666537i
$10$	−1.23743	+	2.91012i	−0.391309	+	0.920259i
$11$			4.18087i			1.26058i	0.776360	+	0.630290i	$0.217064\pi$
$11$			4.18087i			1.26058i	−0.776360	+	0.630290i	$0.782936\pi$
$12$	4.34015	+	1.07773i	1.25289	+	0.311114i
$13$	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	$0.893464\pi$
$18$	2.72467	−	0.757015i	0.642210	−	0.178430i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	4.43379	+	0.584402i	0.991425	+	0.130676i
$21$	6.14621			1.34121
$22$	5.69685	−	1.58280i	1.21457	−	0.337454i
$23$	−3.70046	−	3.70046i	−0.771599	−	0.771599i	0.206787	−	0.978386i	$-0.433699\pi$
$23$	−3.70046	−	3.70046i	−0.771599	−	0.771599i	−0.978386	+	0.206787i	$0.933699\pi$
$24$	−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
$28$	1.32490	−	5.33552i	0.250382	−	1.00832i
$29$			10.0179i			1.86028i	0.367209	+	0.930139i	$0.380313\pi$
$29$			10.0179i			1.86028i	−0.367209	+	0.930139i	$0.619687\pi$
$30$	6.55759	−	2.64465i	1.19725	−	0.482845i
$31$			0.276086i			0.0495865i	0.999693	+	0.0247933i	$0.00789275\pi$
$31$			0.276086i			0.0495865i	−0.999693	+	0.0247933i	$0.992107\pi$
$32$	−5.52566	−	1.21121i	−0.976809	−	0.214114i
$33$	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	$0.539477\pi$
$38$	−0.378581	−	1.36260i	−0.0614140	−	0.221043i
$39$	−9.94801			−1.59296
$40$	−0.882243	−	6.26272i	−0.139495	−	0.990223i
$41$	−5.13494			−0.801943			−0.400971	−	0.916091i	$-0.631327\pi$
$41$	−5.13494			−0.801943			−0.400971	+	0.916091i	$0.631327\pi$
$42$	−2.32684	−	8.37482i	−0.359039	−	1.29226i
$43$	7.75925	+	7.75925i	1.18328	+	1.18328i	0.978891	+	0.204384i	$0.0655192\pi$
$43$	7.75925	+	7.75925i	1.18328	+	1.18328i	0.204384	+	0.978891i	$0.434481\pi$
$44$	−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	−0.925363	−	0.379081i	$-0.876240\pi$
$47$	−3.74512	+	3.74512i	−0.546282	+	0.546282i	0.379081	+	0.925363i	$0.376240\pi$
$48$	−8.54812	+	2.63124i	−1.23381	+	0.379787i
$49$		−	0.555776i		−	0.0793965i
$50$	6.22001	−	3.36326i	0.879642	−	0.475637i
$51$			8.03176i			1.12467i
$52$	−2.14443	+	8.63585i	−0.297378	+	1.19758i
$53$	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
$58$	13.6504	−	3.79259i	1.79238	−	0.497991i
$59$	−2.19430			−0.285674			−0.142837	−	0.989746i	$-0.545622\pi$
$59$	−2.19430			−0.285674			−0.142837	+	0.989746i	$0.545622\pi$
$60$	−6.08618	−	7.93415i	−0.785722	−	1.02429i
$61$	−6.42875			−0.823117			−0.411558	−	0.911383i	$-0.635015\pi$
$61$	−6.42875			−0.823117			−0.411558	+	0.911383i	$0.635015\pi$
$62$	0.376195	−	0.104521i	0.0477768	−	0.0132742i
$63$	−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	−0.948663	−	0.316290i	$-0.897563\pi$
$67$	−5.17620	+	5.17620i	−0.632373	+	0.632373i	0.316290	+	0.948663i	$0.397563\pi$
$68$	6.97236	+	1.73135i	0.845523	+	0.209957i
$69$			11.7014i			1.40869i
$70$	−3.25117	−	8.06149i	−0.388589	−	0.963533i
$71$		−	3.20361i		−	0.380199i	−0.981765	−	0.190099i	$-0.939119\pi$
$71$		−	3.20361i		−	0.380199i	0.981765	−	0.190099i	$-0.0608810\pi$
$72$	−3.88730	+	4.10810i	−0.458122	+	0.484144i
$73$	−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
$78$	3.76613	+	13.5552i	0.426430	+	1.53482i
$79$	−3.37793			−0.380046			−0.190023	−	0.981780i	$-0.560856\pi$
$79$	−3.37793			−0.380046			−0.190023	+	0.981780i	$0.560856\pi$
$80$	−8.19957	+	3.57309i	−0.916740	+	0.399484i
$81$	11.0004			1.22227
$82$	1.94399	+	6.99687i	0.214678	+	0.772675i
$83$	−4.21641	−	4.21641i	−0.462811	−	0.462811i	0.436765	−	0.899576i	$-0.356124\pi$
$83$	−4.21641	−	4.21641i	−0.462811	−	0.462811i	−0.899576	+	0.436765i	$0.856124\pi$
$84$	−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
$88$	−8.12773	+	8.58938i	−0.866419	+	0.915631i
$89$			12.4531i			1.32003i	0.751254	+	0.660013i	$0.229449\pi$
$89$			12.4531i			1.32003i	−0.751254	+	0.660013i	$0.770551\pi$
$90$	−5.81910	−	2.47437i	−0.613387	−	0.260822i
$91$			12.2295i			1.28200i
$92$	10.1580	+	2.52240i	1.05904	+	0.262978i
$93$	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	$0.958875\pi$
$98$	−0.757299	+	0.210406i	−0.0764988	+	0.0212542i
$99$	−8.36011			−0.840223
$100$	−6.93755	−	7.20211i	−0.693755	−	0.720211i
$101$	−6.59302			−0.656030			−0.328015	−	0.944673i	$-0.606380\pi$
$101$	−6.59302			−0.656030			−0.328015	+	0.944673i	$0.606380\pi$
$102$	10.9441	−	3.04067i	1.08362	−	0.301071i
$103$	−7.06562	−	7.06562i	−0.696196	−	0.696196i	0.267392	−	0.963588i	$-0.413838\pi$
$103$	−7.06562	−	7.06562i	−0.696196	−	0.696196i	−0.963588	+	0.267392i	$0.913838\pi$
$104$	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	−0.859779	−	0.510666i	$-0.829399\pi$
$107$	−3.61126	+	3.61126i	−0.349114	+	0.349114i	0.510666	+	0.859779i	$0.329399\pi$
$108$	1.07815	−	4.34185i	0.103745	−	0.417794i
$109$			0.396878i			0.0380140i	0.999819	+	0.0190070i	$0.00605049\pi$
$109$			0.396878i			0.0380140i	−0.999819	+	0.0190070i	$0.993950\pi$
$110$	−12.1668	−	5.17352i	−1.16006	−	0.493276i
$111$		−	16.7075i		−	1.58581i
$112$	3.23468	+	10.5085i	0.305649	+	0.992963i
$113$	−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
$118$	0.830721	+	2.98995i	0.0764741	+	0.275248i
$119$	9.87375			0.905125
$120$	−8.50695	+	11.2967i	−0.776575	+	1.03125i
$121$	−6.47968			−0.589061
$122$	2.43380	+	8.75981i	0.220346	+	0.793076i
$123$	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	−0.347745	−	0.937589i	$-0.613053\pi$
$127$	6.64721	−	6.64721i	0.589844	−	0.589844i	0.937589	+	0.347745i	$0.113053\pi$
$128$	10.7170	−	3.62564i	0.947261	−	0.320464i
$129$		−	24.5360i		−	2.16027i
$130$	5.26221	+	13.0480i	0.461527	+	1.14439i
$131$		−	11.2454i		−	0.982519i	−0.871013	−	0.491259i	$-0.836537\pi$
$131$		−	11.2454i		−	0.982519i	0.871013	−	0.491259i	$-0.163463\pi$
$132$	−4.50586	+	18.1456i	−0.392185	+	1.57937i
$133$	−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	$0.810124\pi$
$138$	15.9444	−	4.42994i	1.35727	−	0.377101i
$139$	3.47485			0.294733			0.147366	−	0.989082i	$-0.452920\pi$
$139$	3.47485			0.294733			0.147366	+	0.989082i	$0.452920\pi$
$140$	−9.75375	+	7.48197i	−0.824342	+	0.632342i
$141$	11.8426			0.997331
$142$	−4.36524	+	1.21283i	−0.366322	+	0.101778i
$143$	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
$148$	−14.5038	−	3.60153i	−1.19220	−	0.296044i
$149$		−	3.49270i		−	0.286133i	−0.989713	−	0.143067i	$-0.954304\pi$
$149$		−	3.49270i		−	0.286133i	0.989713	−	0.143067i	$-0.0456963\pi$
$150$	−15.1519	−	4.51674i	−1.23715	−	0.368790i
$151$		−	0.0282485i		−	0.00229883i	−0.999999	−	0.00114942i	$-0.999634\pi$
$151$		−	0.0282485i		−	0.00229883i	0.999999	−	0.00114942i	$-0.000365871\pi$
$152$	2.05445	+	1.94403i	0.166638	+	0.157681i
$153$	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	$0.643306\pi$
$158$	1.27882	+	4.60276i	0.101737	+	0.366176i
$159$	−19.1278			−1.51694
$160$	7.97289	+	9.82003i	0.630313	+	0.776341i
$161$	14.3850			1.13370
$162$	−4.16454	−	14.9891i	−0.327197	−	1.17766i
$163$	−11.5447	−	11.5447i	−0.904248	−	0.904248i	0.0915524	−	0.995800i	$-0.470817\pi$
$163$	−11.5447	−	11.5447i	−0.904248	−	0.904248i	−0.995800	+	0.0915524i	$0.970817\pi$
$164$	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	$0.502094\pi$
$167$	−13.0076	+	13.0076i	−1.00656	+	1.00656i	−0.999978	+	0.00657976i	$0.997906\pi$
$168$	12.6271	+	11.9484i	0.974200	+	0.921840i
$169$		−	6.79413i		−	0.522625i
$170$	10.5346	−	4.24857i	0.807968	−	0.325851i
$171$			1.99961i			0.152914i
$172$	−21.2996	−	5.28905i	−1.62408	−	0.403286i
$173$	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
$178$	16.9686	−	4.71451i	1.27185	−	0.353368i
$179$	0.461309			0.0344798			0.0172399	−	0.999851i	$-0.494512\pi$
$179$	0.461309			0.0344798			0.0172399	+	0.999851i	$0.494512\pi$
$180$	−1.16858	+	8.86585i	−0.0871005	+	0.660821i
$181$	7.36640			0.547540			0.273770	−	0.961795i	$-0.411729\pi$
$181$	7.36640			0.547540			0.273770	+	0.961795i	$0.411729\pi$
$182$	16.6639	−	4.62985i	1.23521	−	0.343187i
$183$	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
$188$	2.55284	−	10.2806i	0.186185	−	0.749789i
$189$		−	6.14861i		−	0.447245i
$190$	−1.23743	+	2.91012i	−0.0897724	+	0.211122i
$191$		−	7.81764i		−	0.565665i	−0.959169	−	0.282832i	$-0.908726\pi$
$191$		−	7.81764i		−	0.565665i	0.959169	−	0.282832i	$-0.0912740\pi$
$192$	11.9313	−	13.3274i	0.861065	−	0.961823i
$193$	−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	$0.728568\pi$
$198$	3.16498	+	11.3915i	0.224925	+	0.809557i
$199$	15.5573			1.10283			0.551413	−	0.834233i	$-0.314089\pi$
$199$	15.5573			1.10283			0.551413	+	0.834233i	$0.314089\pi$
$200$	−7.18716	+	12.1797i	−0.508209	+	0.861234i
$201$	16.3679			1.15451
$202$	2.49599	+	8.98364i	0.175617	+	0.632087i
$203$	−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
$208$	−5.23553	−	17.0087i	−0.363018	−	1.17934i
$209$			4.18087i			0.289197i
$210$	−7.60549	+	17.8862i	−0.524829	+	1.23426i
$211$			16.8879i			1.16261i	0.813686	+	0.581305i	$0.197458\pi$
$211$			16.8879i			1.16261i	−0.813686	+	0.581305i	$0.802542\pi$
$212$	−4.12326	+	16.6049i	−0.283187	+	1.14043i
$213$	−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
$218$	0.540786	−	0.150251i	0.0366266	−	0.0101763i
$219$	21.6277			1.46147
$220$	−2.44331	+	18.5371i	−0.164728	+	1.24977i
$221$	−15.9813			−1.07502
$222$	−22.7656	+	6.32515i	−1.52793	+	0.424516i
$223$	7.24122	+	7.24122i	0.484908	+	0.484908i	0.906695	−	0.421787i	$-0.138597\pi$
$223$	7.24122	+	7.24122i	0.484908	+	0.484908i	−0.421787	+	0.906695i	$0.638597\pi$
$224$	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	−0.695404	−	0.718619i	$-0.744774\pi$
$227$	0.349778	−	0.349778i	0.0232156	−	0.0232156i	0.718619	+	0.695404i	$0.244774\pi$
$228$	4.34015	+	1.07773i	0.287434	+	0.0713746i
$229$			10.6868i			0.706207i	0.935584	+	0.353103i	$0.114874\pi$
$229$			10.6868i			0.706207i	−0.935584	+	0.353103i	$0.885126\pi$
$230$	15.3478	−	6.18972i	1.01201	−	0.408138i
$231$			25.6965i			1.69071i
$232$	−19.4751	+	20.5813i	−1.27860	+	1.35123i
$233$	−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
$238$	−3.73802	−	13.4540i	−0.242300	−	0.872091i
$239$	10.6830			0.691028			0.345514	−	0.938414i	$-0.387705\pi$
$239$	10.6830			0.691028			0.345514	+	0.938414i	$0.387705\pi$
$240$	18.6135	+	7.31483i	1.20150	+	0.472170i
$241$	11.7625			0.757689			0.378844	−	0.925460i	$-0.376322\pi$
$241$	11.7625			0.757689			0.378844	+	0.925460i	$0.376322\pi$
$242$	2.45308	+	8.82920i	0.157690	+	0.567563i
$243$	−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
$248$	−0.536719	+	0.567204i	−0.0340817	+	0.0360175i
$249$			13.3329i			0.844941i
$250$	−15.5633	−	2.78975i	−0.984311	−	0.176439i
$251$			20.7617i			1.31047i	0.755427	+	0.655233i	$0.227430\pi$
$251$			20.7617i			1.31047i	−0.755427	+	0.655233i	$0.772570\pi$
$252$	10.6690	+	2.64928i	0.672081	+	0.166889i
$253$	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	$0.540687\pi$
$258$	−33.4327	+	9.28885i	−2.08143	+	0.578298i
$259$	−20.5392			−1.27624
$260$	15.7870	−	12.1100i	0.979070	−	0.751031i
$261$	−20.0319			−1.23994
$262$	−15.3230	+	4.25731i	−0.946660	+	0.263018i
$263$	−17.5064	−	17.5064i	−1.07949	−	1.07949i	−0.996555	−	0.0829348i	$-0.973571\pi$
$263$	−17.5064	−	17.5064i	−1.07949	−	1.07949i	−0.0829348	−	0.996555i	$-0.526429\pi$
$264$	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
$268$	3.52833	−	14.2090i	0.215527	−	0.867952i
$269$		−	16.0727i		−	0.979973i	−0.871730	−	0.489986i	$-0.837002\pi$
$269$		−	16.0727i		−	0.979973i	0.871730	−	0.489986i	$-0.162998\pi$
$270$	−2.64568	−	6.56014i	−0.161011	−	0.399237i
$271$			10.6807i			0.648808i	0.945919	+	0.324404i	$0.105164\pi$
$271$			10.6807i			0.648808i	−0.945919	+	0.324404i	$0.894836\pi$
$272$	−13.7324	+	4.22702i	−0.832647	+	0.256301i
$273$	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	$0.627657\pi$
$278$	−1.31551	−	4.73483i	−0.0788992	−	0.283976i
$279$	−0.552064			−0.0330512
$280$	13.8875	+	10.4579i	0.829938	+	0.624980i
$281$	13.8513			0.826299			0.413150	−	0.910663i	$-0.364429\pi$
$281$	13.8513			0.826299			0.413150	+	0.910663i	$0.364429\pi$
$282$	−4.48340	−	16.1368i	−0.266983	−	0.960931i
$283$	10.2962	+	10.2962i	0.612045	+	0.612045i	0.943479	−	0.331433i	$-0.107532\pi$
$283$	10.2962	+	10.2962i	0.612045	+	0.612045i	−0.331433	+	0.943479i	$0.607532\pi$
$284$	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
$288$	2.42195	−	11.0492i	0.142715	−	0.651079i
$289$		−	4.09716i		−	0.241009i
$290$	−29.1532	−	12.3964i	−1.71194	−	0.727943i
$291$			26.8715i			1.57524i
$292$	4.66214	−	18.7750i	0.272831	−	1.09872i
$293$	−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
$298$	−4.75915	+	1.32227i	−0.275690	+	0.0765970i
$299$	−23.2830			−1.34649
$300$	−0.418291	+	22.3559i	−0.0241501	+	1.29072i
$301$	−30.1630			−1.73857
$302$	−0.0384914	+	0.0106944i	−0.00221493	+	0.000615391i
$303$	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	−0.997529	−	0.0702587i	$-0.977618\pi$
$307$	−16.2471	+	16.2471i	−0.927270	+	0.927270i	0.0702587	+	0.997529i	$0.477618\pi$
$308$	22.3071	+	5.53922i	1.27107	+	0.315627i
$309$			22.3426i			1.27103i
$310$	−0.803442	−	0.341636i	−0.0456325	−	0.0194036i
$311$		−	28.1999i		−	1.59907i	−0.600618	−	0.799536i	$-0.705079\pi$
$311$		−	28.1999i		−	1.59907i	0.600618	−	0.799536i	$-0.294921\pi$
$312$	−20.4377	−	19.3392i	−1.15706	−	1.09487i
$313$	−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	$0.938089\pi$
$318$	7.24144	+	26.0636i	0.406080	+	1.46157i
$319$	−41.8835			−2.34503
$320$	10.3624	−	14.5815i	0.579274	−	0.815133i
$321$	11.4194			0.637366
$322$	−5.44589	−	19.6010i	−0.303488	−	1.09232i
$323$	−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
$328$	−10.5495	−	9.98247i	−0.582497	−	0.551189i
$329$		−	14.5586i		−	0.802643i
$330$	11.0569	+	27.4164i	0.608665	+	1.50922i
$331$		−	18.6160i		−	1.02323i	−0.859216	−	0.511613i	$-0.829048\pi$
$331$		−	18.6160i		−	1.02323i	0.859216	−	0.511613i	$-0.170952\pi$
$332$	11.5743	+	2.87409i	0.635222	+	0.157736i
$333$	−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	$0.711352\pi$
$338$	−9.25767	+	2.57213i	−0.503551	+	0.139905i
$339$	33.6162			1.82578
$340$	−9.77730	−	12.7460i	−0.530249	−	0.691250i
$341$	−1.15428			−0.0625077
$342$	2.72467	−	0.757015i	0.147333	−	0.0409347i
$343$	−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	−0.506009	−	0.862528i	$-0.668880\pi$
$347$	6.64122	−	6.64122i	0.356519	−	0.356519i	0.862528	+	0.506009i	$0.168880\pi$
$348$	−10.7966	+	43.4792i	−0.578759	+	2.33073i
$349$		−	7.71160i		−	0.412793i	−0.978468	−	0.206396i	$-0.933826\pi$
$349$		−	7.71160i		−	0.412793i	0.978468	−	0.206396i	$-0.0661736\pi$
$350$	−5.55260	+	18.6268i	−0.296799	+	0.995644i
$351$			9.95189i			0.531192i
$352$	5.06393	−	23.1021i	0.269908	−	1.23135i
$353$	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
$358$	−0.174643	−	0.628579i	−0.00923016	−	0.0332214i
$359$	−25.7286			−1.35791			−0.678953	−	0.734182i	$-0.737566\pi$
$359$	−25.7286			−1.35791			−0.678953	+	0.734182i	$0.737566\pi$
$360$	12.5230	−	1.76414i	0.660020	−	0.0929784i
$361$	1.00000			0.0526316
$362$	−2.78878	−	10.0375i	−0.146575	−	0.527557i
$363$	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	−0.596402	−	0.802686i	$-0.703404\pi$
$367$	3.95182	−	3.95182i	0.206283	−	0.206283i	0.802686	+	0.596402i	$0.203404\pi$
$368$	−20.0066	+	6.15833i	−1.04292	+	0.321025i
$369$		−	10.2679i		−	0.534524i
$370$	−21.9139	+	8.83780i	−1.13925	+	0.459455i
$371$			23.5146i			1.22082i
$372$	−0.297547	+	1.19826i	−0.0154271	+	0.0621267i
$373$	−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
$378$	−8.37809	+	2.32775i	−0.430922	+	0.119726i
$379$	−10.1697			−0.522380			−0.261190	−	0.965287i	$-0.584115\pi$
$379$	−10.1697			−0.522380			−0.261190	+	0.965287i	$0.584115\pi$
$380$	4.43379	+	0.584402i	0.227449	+	0.0299792i
$381$	−21.0195			−1.07686
$382$	−10.6523	+	2.95961i	−0.545020	+	0.151427i
$383$	−14.3086	−	14.3086i	−0.731138	−	0.731138i	0.239707	−	0.970845i	$-0.422949\pi$
$383$	−14.3086	−	14.3086i	−0.731138	−	0.731138i	−0.970845	+	0.239707i	$0.922949\pi$
$384$	−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
$388$	23.3271	+	5.79252i	1.18426	+	0.294070i
$389$		−	30.0276i		−	1.52246i	−0.648482	−	0.761230i	$-0.724596\pi$
$389$		−	30.0276i		−	1.52246i	0.648482	−	0.761230i	$-0.275404\pi$
$390$	12.3099	−	28.9499i	0.623338	−	1.46593i
$391$			18.7981i			0.950660i
$392$	1.08044	−	1.14181i	0.0545706	−	0.0576702i
$393$	−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	$0.829894\pi$
$398$	−5.88969	−	21.1983i	−0.295223	−	1.06258i
$399$	6.14621			0.307696
$400$	19.3169	+	5.18223i	0.965847	+	0.259111i
$401$	−16.6477			−0.831349			−0.415674	−	0.909514i	$-0.636454\pi$
$401$	−16.6477			−0.831349			−0.415674	+	0.909514i	$0.636454\pi$
$402$	−6.19659	−	22.3029i	−0.309058	−	1.11237i
$403$	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
$408$	−15.6140	+	16.5008i	−0.773006	+	0.816913i
$409$			10.2017i			0.504444i	0.967669	+	0.252222i	$0.0811613\pi$
$409$			10.2017i			0.504444i	−0.967669	+	0.252222i	$0.918839\pi$
$410$	6.35411	−	14.9433i	0.313807	−	0.737996i
$411$			9.82815i			0.484787i
$412$	19.3956	+	4.81624i	0.955551	+	0.237279i
$413$	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
$418$	5.69685	−	1.58280i	0.278642	−	0.0774172i
$419$	12.2167			0.596824			0.298412	−	0.954437i	$-0.403543\pi$
$419$	12.2167			0.596824			0.298412	+	0.954437i	$0.403543\pi$
$420$	27.2510	+	3.59186i	1.32971	+	0.175265i
$421$	−3.09851			−0.151012			−0.0755062	−	0.997145i	$-0.524057\pi$
$421$	−3.09851			−0.151012			−0.0755062	+	0.997145i	$0.524057\pi$
$422$	23.0114	−	6.39344i	1.12018	−	0.311228i
$423$	−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
$428$	2.46159	−	9.91312i	0.118986	−	0.479169i
$429$		−	41.5913i		−	2.00805i
$430$	−32.1818	+	12.9788i	−1.55195	+	0.625894i
$431$			6.40238i			0.308392i	0.988040	+	0.154196i	$0.0492787\pi$
$431$			6.40238i			0.308392i	−0.988040	+	0.154196i	$0.950721\pi$
$432$	2.63226	+	8.55145i	0.126645	+	0.411432i
$433$	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
$438$	−8.18785	−	29.4699i	−0.391230	−	1.40813i
$439$	−19.9289			−0.951155			−0.475578	−	0.879674i	$-0.657761\pi$
$439$	−19.9289			−0.951155			−0.475578	+	0.879674i	$0.657761\pi$
$440$	26.1836	−	3.68854i	1.24825	−	0.175844i
$441$	1.11133			0.0529207
$442$	6.05020	+	21.7760i	0.287779	+	1.03578i
$443$	1.19044	+	1.19044i	0.0565597	+	0.0565597i	0.734821	−	0.678261i	$-0.237266\pi$
$443$	1.19044	+	1.19044i	0.0565597	+	0.0565597i	−0.678261	+	0.734821i	$0.737266\pi$
$444$	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
$448$	−16.3839	−	14.6676i	−0.774066	−	0.692978i
$449$			31.3174i			1.47796i	0.673728	+	0.738980i	$0.264692\pi$
$449$			31.3174i			1.47796i	−0.673728	+	0.738980i	$0.735308\pi$
$450$	6.72521	+	12.4376i	0.317029	+	0.586314i
$451$		−	21.4685i		−	1.01091i
$452$	7.24641	−	29.1821i	0.340842	−	1.37261i
$453$	−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	$0.976375\pi$
$458$	14.5619	−	4.04584i	0.680432	−	0.189050i
$459$	8.03489			0.375037
$460$	−14.2445	−	18.5696i	−0.664153	−	0.865813i
$461$	−13.6317			−0.634894			−0.317447	−	0.948276i	$-0.602825\pi$
$461$	−13.6317			−0.634894			−0.317447	+	0.948276i	$0.602825\pi$
$462$	35.0141	−	9.72822i	1.62900	−	0.452598i
$463$	26.2755	+	26.2755i	1.22113	+	1.22113i	0.967231	+	0.253897i	$0.0817123\pi$
$463$	26.2755	+	26.2755i	1.22113	+	1.22113i	0.253897	+	0.967231i	$0.418288\pi$
$464$	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	−0.620206	−	0.784439i	$-0.712951\pi$
$467$	3.54910	−	3.54910i	0.164233	−	0.164233i	0.784439	+	0.620206i	$0.212951\pi$
$468$	−17.2683	−	4.28801i	−0.798229	−	0.198214i
$469$		−	20.1217i		−	0.929135i
$470$	−6.26442	−	15.5330i	−0.288956	−	0.716486i
$471$		−	18.4320i		−	0.849303i
$472$	−4.50808	−	4.26578i	−0.207501	−	0.196349i
$473$	−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
$478$	−4.04439	−	14.5567i	−0.184986	−	0.665807i
$479$	28.6474			1.30893			0.654465	−	0.756092i	$-0.272894\pi$
$479$	28.6474			1.30893			0.654465	+	0.756092i	$0.272894\pi$
$480$	2.92046	−	28.1320i	0.133300	−	1.28404i
$481$	33.2439			1.51579
$482$	−4.45306	−	16.0276i	−0.202831	−	0.730035i
$483$	−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	$-0.334218\pi$
$487$	30.1230	−	30.1230i	1.36500	−	1.36500i	0.867412	−	0.497590i	$-0.165782\pi$
$488$	−13.2075	−	12.4977i	−0.597877	−	0.565743i
$489$			36.5060i			1.65086i
$490$	1.61737	+	0.687732i	0.0730654	+	0.0310685i
$491$		−	11.8932i		−	0.536731i	−0.963317	−	0.268366i	$-0.913516\pi$
$491$		−	11.8932i		−	0.536731i	0.963317	−	0.268366i	$-0.0864836\pi$
$492$	−22.2864	−	5.53409i	−1.00475	−	0.249496i
$493$	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
$498$	18.1675	−	5.04760i	0.814103	−	0.226188i
$499$	18.1037			0.810432			0.405216	−	0.914221i	$-0.367196\pi$
$499$	18.1037			0.810432			0.405216	+	0.914221i	$0.367196\pi$
$500$	2.09067	+	22.2627i	0.0934975	+	0.995620i
$501$	41.1320			1.83764
$502$	28.2899	−	7.85999i	1.26264	−	0.350808i
$503$	−16.2494	−	16.2494i	−0.724524	−	0.724524i	0.244999	−	0.969523i	$-0.421212\pi$
$503$	−16.2494	−	16.2494i	−0.724524	−	0.724524i	−0.969523	+	0.244999i	$0.921212\pi$
$504$	−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
$508$	−4.53103	+	18.2470i	−0.201032	+	0.809579i
$509$			43.7904i			1.94097i	0.241155	+	0.970487i	$0.422474\pi$
$509$			43.7904i			1.94097i	−0.241155	+	0.970487i	$0.577526\pi$
$510$	−23.3734	−	9.93872i	−1.03499	−	0.440094i
$511$		−	26.5878i		−	1.17617i
$512$	−14.6215	+	17.2688i	−0.646183	+	0.763183i
$513$	−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
$518$	7.77575	+	27.9867i	0.341647	+	1.22966i
$519$	−31.4256			−1.37943
$520$	−22.4778	−	16.9268i	−0.985715	−	0.742288i
$521$	34.0703			1.49265			0.746323	−	0.665584i	$-0.231817\pi$
$521$	34.0703			1.49265			0.746323	+	0.665584i	$0.231817\pi$
$522$	7.58370	+	27.2954i	0.331929	+	1.19469i
$523$	16.2536	+	16.2536i	0.710720	+	0.710720i	0.966686	−	0.255966i	$-0.0823934\pi$
$523$	16.2536	+	16.2536i	0.710720	+	0.710720i	−0.255966	+	0.966686i	$0.582393\pi$
$524$	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
$528$	−11.0009	−	35.7386i	−0.478751	−	1.55532i
$529$			4.38682i			0.190731i
$530$	10.1181	+	25.0885i	0.439501	+	1.08977i
$531$		−	4.38775i		−	0.190412i
$532$	1.32490	−	5.33552i	0.0574416	−	0.231324i
$533$	−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
$538$	−21.9007	+	6.08484i	−0.944207	+	0.262336i
$539$	2.32363			0.100086
$540$	−7.93724	+	6.08855i	−0.341564	+	0.262009i
$541$	2.52042			0.108361			0.0541807	−	0.998531i	$-0.482745\pi$
$541$	2.52042			0.108361			0.0541807	+	0.998531i	$0.482745\pi$
$542$	14.5535	−	4.04352i	0.625128	−	0.173684i
$543$	−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	−0.951200	−	0.308576i	$-0.900148\pi$
$547$	−15.0297	+	15.0297i	−0.642623	+	0.642623i	0.308576	+	0.951200i	$0.400148\pi$
$548$	8.53180	+	2.11859i	0.364460	+	0.0905016i
$549$		−	12.8550i		−	0.548638i
$550$	14.0613	+	26.0050i	0.599578	+	1.10886i
$551$			10.0179i			0.426777i
$552$	−22.7479	+	24.0400i	−0.968215	+	1.02321i
$553$	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	$0.461679\pi$
$558$	0.209001	+	0.752242i	0.00884772	+	0.0318450i
$559$	48.8206			2.06489
$560$	8.99240	−	22.8823i	0.379998	−	0.966953i
$561$	−33.5797			−1.41774
$562$	−5.24384	−	18.8738i	−0.221198	−	0.796142i
$563$	30.1923	+	30.1923i	1.27246	+	1.27246i	0.944796	+	0.327660i	$0.106260\pi$
$563$	30.1923	+	30.1923i	1.27246	+	1.27246i	0.327660	+	0.944796i	$0.393740\pi$
$564$	−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
$568$	6.22791	−	6.58165i	0.261317	−	0.276160i
$569$			14.6606i			0.614603i	0.951612	+	0.307302i	$0.0994261\pi$
$569$			14.6606i			0.614603i	−0.951612	+	0.307302i	$0.900574\pi$
$570$	6.55759	−	2.64465i	0.274667	−	0.110772i
$571$		−	16.3003i		−	0.682145i	−0.940037	−	0.341072i	$-0.889210\pi$
$571$		−	16.3003i		−	0.682145i	0.940037	−	0.341072i	$-0.110790\pi$
$572$	−36.1054	−	8.96556i	−1.50964	−	0.374869i
$573$	−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	$0.974600\pi$
$578$	−5.58279	+	1.55111i	−0.232213	+	0.0645176i
$579$	56.2821			2.33901
$580$	−5.85448	+	44.4172i	−0.243094	+	1.84433i
$581$	16.3907			0.680001
$582$	36.6151	−	10.1731i	1.51775	−	0.421687i
$583$	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	−0.872990	−	0.487737i	$-0.837822\pi$
$587$	−9.33394	+	9.33394i	−0.385253	+	0.385253i	0.487737	+	0.872990i	$0.337822\pi$
$588$	0.598977	−	2.41215i	0.0247014	−	0.0994755i
$589$			0.276086i			0.0113759i
$590$	2.71529	−	6.38567i	0.111787	−	0.262894i
$591$		−	4.22297i		−	0.173710i
$592$	28.5658	−	8.79298i	1.17405	−	0.361389i
$593$	−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
$598$	8.81450	+	31.7254i	0.360452	+	1.29735i
$599$	6.30551			0.257636			0.128818	−	0.991668i	$-0.458882\pi$
$599$	6.30551			0.257636			0.128818	+	0.991668i	$0.458882\pi$
$600$	30.6205	−	7.89356i	1.25008	−	0.322253i
$601$	−28.6173			−1.16732			−0.583662	−	0.811996i	$-0.698381\pi$
$601$	−28.6173			−1.16732			−0.583662	+	0.811996i	$0.698381\pi$
$602$	11.4191	+	41.1001i	0.465409	+	1.67511i
$603$	−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	−0.979480	−	0.201543i	$-0.935405\pi$
$607$	−19.1663	+	19.1663i	−0.777937	+	0.777937i	0.201543	+	0.979480i	$0.435405\pi$
$608$	−5.52566	−	1.21121i	−0.224095	−	0.0491212i
$609$			61.5721i			2.49503i
$610$	7.95511	−	18.7084i	0.322093	−	0.757481i
$611$			23.5640i			0.953297i
$612$	−3.46203	+	13.9420i	−0.139944	+	0.563572i
$613$	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	$0.965666\pi$
$618$	30.4440	−	8.45848i	1.22464	−	0.340250i
$619$	−46.0944			−1.85269			−0.926345	−	0.376677i	$-0.877067\pi$
$619$	−46.0944			−1.85269			−0.926345	+	0.376677i	$0.877067\pi$
$620$	−0.161345	+	1.22411i	−0.00647978	+	0.0491613i
$621$	11.7060			0.469745
$622$	−38.4252	+	10.6760i	−1.54071	+	0.428067i
$623$	−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
$628$	−16.0008	−	3.97327i	−0.638502	−	0.158551i
$629$		−	26.8402i		−	1.07019i
$630$	16.1198	−	6.50107i	0.642230	−	0.259009i
$631$		−	22.0131i		−	0.876327i	−0.898895	−	0.438164i	$-0.855629\pi$
$631$		−	22.0131i		−	0.876327i	0.898895	−	0.438164i	$-0.144371\pi$
$632$	−6.93977	−	6.56678i	−0.276049	−	0.261213i
$633$	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
$638$	15.8563	+	57.0705i	0.627757	+	2.25944i
$639$	6.40597			0.253416
$640$	−23.7918	−	8.59947i	−0.940453	−	0.339924i
$641$	14.7965			0.584427			0.292213	−	0.956353i	$-0.405608\pi$
$641$	14.7965			0.584427			0.292213	+	0.956353i	$0.405608\pi$
$642$	−4.32315	−	15.5600i	−0.170621	−	0.614104i
$643$	30.6307	+	30.6307i	1.20796	+	1.20796i	0.971688	+	0.236268i	$0.0759242\pi$
$643$	30.6307	+	30.6307i	1.20796	+	1.20796i	0.236268	+	0.971688i	$0.424076\pi$
$644$	−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	$0.584480\pi$
$647$	−31.2175	+	31.2175i	−1.22728	+	1.22728i	−0.964987	+	0.262298i	$0.915520\pi$
$648$	22.5997	+	21.3851i	0.887801	+	0.840085i
$649$		−	9.17409i		−	0.360115i
$650$	8.98722	−	30.1486i	0.352508	−	1.18252i
$651$			1.69688i			0.0665061i
$652$	31.6908	+	7.86935i	1.24111	+	0.308188i
$653$	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
$658$	−19.8376	+	5.51162i	−0.773349	+	0.214865i
$659$	−4.02042			−0.156613			−0.0783066	−	0.996929i	$-0.524951\pi$
$659$	−4.02042			−0.156613			−0.0783066	+	0.996929i	$0.524951\pi$
$660$	33.1716	−	25.4455i	1.29120	−	0.990465i
$661$	−18.3750			−0.714705			−0.357352	−	0.933970i	$-0.616321\pi$
$661$	−18.3750			−0.714705			−0.357352	+	0.933970i	$0.616321\pi$
$662$	−25.3661	+	7.04765i	−0.985882	+	0.273915i
$663$	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
$668$	8.86655	−	35.7067i	0.343057	−	1.38153i
$669$		−	22.8979i		−	0.885282i
$670$	−8.65817	−	21.4685i	−0.334494	−	0.829401i
$671$		−	26.8778i		−	1.03760i
$672$	−33.9619	−	7.44438i	−1.31011	−	0.287173i
$673$	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	$0.674093\pi$
$678$	−12.7264	−	45.8054i	−0.488756	−	1.75914i
$679$	33.0342			1.26774
$680$	−13.6662	+	18.1479i	−0.524076	+	0.695942i
$681$	−1.10605			−0.0423840
$682$	0.436988	+	1.57282i	0.0167332	+	0.0602264i
$683$	18.0817	+	18.0817i	0.691878	+	0.691878i	0.962645	−	0.270767i	$-0.0872773\pi$
$683$	18.0817	+	18.0817i	0.691878	+	0.691878i	−0.270767	+	0.962645i	$0.587277\pi$
$684$	−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
$688$	41.9505	−	12.9130i	1.59935	−	0.492303i
$689$		−	38.0598i		−	1.44996i
$690$	−34.0525	−	14.4797i	−1.29636	−	0.551231i
$691$		−	3.20982i		−	0.122107i	−0.998134	−	0.0610536i	$-0.980554\pi$
$691$		−	3.20982i		−	0.122107i	0.998134	−	0.0610536i	$-0.0194460\pi$
$692$	−6.77421	+	27.2805i	−0.257517	+	1.03705i
$693$	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
$698$	−10.5078	+	2.91947i	−0.397727	+	0.110503i
$699$	65.0179			2.45920
$700$	27.4830	+	0.514222i	1.03876	+	0.0194357i
$701$	1.08890			0.0411273			0.0205637	−	0.999789i	$-0.493454\pi$
$701$	1.08890			0.0411273			0.0205637	+	0.999789i	$0.493454\pi$
$702$	13.5604	−	3.76760i	0.511806	−	0.142199i
$703$	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
$708$	−9.52361	−	2.36487i	−0.357919	−	0.0888772i
$709$		−	39.2212i		−	1.47298i	−0.676446	−	0.736492i	$-0.736481\pi$
$709$		−	39.2212i		−	1.47298i	0.676446	−	0.736492i	$-0.263519\pi$
$710$	9.32288	+	3.96423i	0.349881	+	0.148775i
$711$		−	6.75454i		−	0.253315i
$712$	−24.2092	+	25.5843i	−0.907278	+	0.958811i
$713$	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
$718$	9.74038	+	35.0578i	0.363508	+	1.30835i
$719$	−18.4618			−0.688509			−0.344255	−	0.938876i	$-0.611868\pi$
$719$	−18.4618			−0.688509			−0.344255	+	0.938876i	$0.611868\pi$
$720$	−7.14479	−	16.3960i	−0.266271	−	0.611041i
$721$	27.4666			1.02291
$722$	−0.378581	−	1.36260i	−0.0140893	−	0.0507107i
$723$	−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	−0.988635	−	0.150334i	$-0.951965\pi$
$727$	−22.6031	+	22.6031i	−0.838301	+	0.838301i	0.150334	+	0.988635i	$0.451965\pi$
$728$	−23.7744	+	25.1248i	−0.881139	+	0.931188i
$729$			6.99182i			0.258956i
$730$	−11.4404	−	28.3673i	−0.423430	−	1.04992i
$731$		−	39.4165i		−	1.45787i
$732$	−27.9018	−	6.92847i	−1.03128	−	0.256084i
$733$	−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
$738$	−13.9910	+	3.88723i	−0.515016	+	0.143091i
$739$	−2.93089			−0.107814			−0.0539072	−	0.998546i	$-0.517168\pi$
$739$	−2.93089			−0.107814			−0.0539072	+	0.998546i	$0.517168\pi$
$740$	20.3386	+	26.5140i	0.747660	+	0.974675i
$741$	−9.94801			−0.365449
$742$	32.0410	−	8.90218i	1.17626	−	0.326809i
$743$	−7.25703	−	7.25703i	−0.266234	−	0.266234i	0.561346	−	0.827581i	$-0.310284\pi$
$743$	−7.25703	−	7.25703i	−0.266234	−	0.266234i	−0.827581	+	0.561346i	$0.810284\pi$
$744$	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
$748$	−7.23856	+	29.1505i	−0.264668	+	1.06585i
$749$		−	14.0383i		−	0.512947i
$750$	20.1960	+	29.0176i	0.737454	+	1.05957i
$751$		−	49.3852i		−	1.80209i	−0.433725	−	0.901045i	$-0.642801\pi$
$751$		−	49.3852i		−	1.80209i	0.433725	−	0.901045i	$-0.357199\pi$
$752$	6.23265	+	20.2481i	0.227281	+	0.738371i
$753$	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	$0.967317\pi$
$758$	3.85004	+	13.8572i	0.139840	+	0.503315i
$759$	−48.9222			−1.77576
$760$	−0.882243	−	6.26272i	−0.0320023	−	0.227173i
$761$	−1.97888			−0.0717342			−0.0358671	−	0.999357i	$-0.511419\pi$
$761$	−1.97888			−0.0717342			−0.0358671	+	0.999357i	$0.511419\pi$
$762$	7.95758	+	28.6411i	0.288273	+	1.03756i
$763$	−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
$768$	−6.69248	+	35.1441i	−0.241494	+	1.26816i
$769$		−	28.4422i		−	1.02565i	−0.858492	−	0.512827i	$-0.828598\pi$
$769$		−	28.4422i		−	1.02565i	0.858492	−	0.512827i	$-0.171402\pi$
$770$	33.7040	−	13.5927i	1.21461	−	0.489848i
$771$		−	43.8175i		−	1.57805i
$772$	12.1324	−	48.8584i	0.436653	−	1.75845i
$773$	−3.06324	+	3.06324i	−0.110177	+	0.110177i	−0.760046	−	0.649869i	$-0.774824\pi$
$773$	−3.06324	+	3.06324i	−0.110177	+	0.110177i	0.649869	+	0.760046i	$0.274824\pi$
$774$	27.0153	+	15.2675i	0.971043	+	0.548779i
$775$	−1.34573	+	0.307559i	−0.0483401	+	0.0110479i
$776$	−0.938338	−	33.9785i	−0.0336844	−	1.21976i
$777$	32.4740	+	32.4740i	1.16500	+	1.16500i
$778$	−40.9156	+	11.3679i	−1.46690	+	0.407559i
$779$	−5.13494			−0.183978
$780$	−44.1074	−	5.81363i	−1.57930	−	0.208162i
$781$	13.3939			0.479271
$782$	25.6142	−	7.11660i	0.915964	−	0.254489i
$783$	−15.8452	−	15.8452i	−0.566263	−	0.566263i
$784$	−1.96487	−	1.03994i	−0.0701738	−	0.0371408i
$785$	−2.06643	−	18.3166i	−0.0737541	−	0.653746i
$786$	30.9580	+	17.4958i	1.10424	+	0.624053i
$787$	4.18760	−	4.18760i	0.149272	−	0.149272i	−0.628521	−	0.777793i	$-0.716339\pi$
$787$	4.18760	−	4.18760i	0.149272	−	0.149272i	0.777793	+	0.628521i	$0.216339\pi$
$788$	−3.66596	−	0.910317i	−0.130594	−	0.0324287i
$789$			55.3579i			1.97079i
$790$	4.17994	−	9.83016i	0.148715	−	0.349741i
$791$		−	41.3256i		−	1.46937i
$792$	−17.1754	−	16.2523i	−0.610302	−	0.577500i
$793$	−20.2246	+	20.2246i	−0.718196	+	0.718196i
$794$	−6.88663	+	12.1856i	−0.244397	+	0.432451i
$795$	33.4437	+	26.6626i	1.18612	+	0.945625i
$796$	−26.6551	+	16.0506i	−0.944765	+	0.568897i
$797$	3.16145	+	3.16145i	0.111984	+	0.111984i	0.760879	−	0.648894i	$-0.224768\pi$
$797$	3.16145	+	3.16145i	0.111984	+	0.111984i	−0.648894	+	0.760879i	$0.724768\pi$
$798$	−2.32684	−	8.37482i	−0.0823692	−	0.296466i
$799$	19.0249			0.673054
$800$	−0.251734	−	28.2832i	−0.00890013	−	0.999960i
$801$	−24.9014			−0.879846
$802$	6.30252	+	22.6842i	0.222550	+	0.801007i
$803$	−28.5953	−	28.5953i	−1.00911	−	1.00911i
$804$	−28.0440	+	16.8869i	−0.989037	+	0.595556i
$805$	−25.1512	−	20.0515i	−0.886462	−	0.706722i
$806$	0.854674	−	1.51231i	0.0301046	−	0.0532689i
$807$	−25.4123	+	25.4123i	−0.894554	+	0.894554i
$808$	−13.5450	−	12.8170i	−0.476512	−	0.450901i
$809$		−	11.2620i		−	0.395951i	−0.980207	−	0.197975i	$-0.936563\pi$
$809$		−	11.2620i		−	0.395951i	0.980207	−	0.197975i	$-0.0634366\pi$
$810$	−13.6122	+	32.0124i	−0.478283	+	1.12480i
$811$			24.7854i			0.870334i	0.900350	+	0.435167i	$0.143311\pi$
$811$			24.7854i			0.870334i	−0.900350	+	0.435167i	$0.856689\pi$
$812$	53.4507	+	13.2727i	1.87575	+	0.465780i
$813$	16.8870	−	16.8870i	0.592254	−	0.592254i
$814$	38.4626	+	21.7369i	1.34812	+	0.761880i
$815$	4.09272	+	36.2773i	0.143362	+	1.27074i
$816$	28.3952	+	15.0287i	0.994030	+	0.526109i
$817$	7.75925	+	7.75925i	0.271462	+	0.271462i
$818$	13.9009	−	3.86219i	0.486033	−	0.135038i
$819$	−24.4542			−0.854498
$820$	−22.7672	−	3.00087i	−0.795066	−	0.104795i
$821$	−12.3025			−0.429361			−0.214681	−	0.976684i	$-0.568871\pi$
$821$	−12.3025			−0.429361			−0.214681	+	0.976684i	$0.568871\pi$
$822$	13.3918	−	3.72075i	0.467094	−	0.129776i
$823$	8.19530	+	8.19530i	0.285670	+	0.285670i	0.835365	−	0.549695i	$-0.185256\pi$
$823$	8.19530	+	8.19530i	0.285670	+	0.285670i	−0.549695	+	0.835365i	$0.685256\pi$
$824$	−0.780189	−	28.2517i	−0.0271792	−	0.984195i
$825$	39.5845	+	24.8568i	1.37815	+	0.865402i
$826$	−7.42616	−	4.19685i	−0.258389	−	0.146027i
$827$	2.75835	−	2.75835i	0.0959173	−	0.0959173i	−0.657520	−	0.753437i	$-0.728394\pi$
$827$	2.75835	−	2.75835i	0.0959173	−	0.0959173i	0.753437	+	0.657520i	$0.228394\pi$
$828$	−5.04381	+	20.3120i	−0.175285	+	0.705892i
$829$			48.6050i			1.68812i	0.536248	+	0.844061i	$0.319841\pi$
$829$			48.6050i			1.68812i	−0.536248	+	0.844061i	$0.680159\pi$
$830$	17.4877	−	7.05274i	0.607008	−	0.244804i
$831$		−	27.9076i		−	0.968104i
$832$	26.5183	+	23.7403i	0.919357	+	0.823048i
$833$	−1.41165	+	1.41165i	−0.0489108	+	0.0489108i
$834$	−5.40620	+	9.56605i	−0.187201	+	0.331245i
$835$	40.8743	−	4.61135i	1.41451	−	0.159582i
$836$	−4.31344	−	7.16331i	−0.149183	−	0.247748i
$837$	−0.436683	−	0.436683i	−0.0150940	−	0.0150940i
$838$	−4.62501	−	16.6465i	−0.159768	−	0.575042i
$839$	5.60755			0.193594			0.0967971	−	0.995304i	$-0.469140\pi$
$839$	5.60755			0.193594			0.0967971	+	0.995304i	$0.469140\pi$
$840$	−5.42245	−	38.4920i	−0.187092	−	1.32810i
$841$	−71.3583			−2.46063
$842$	1.17304	+	4.22203i	0.0404256	+	0.145501i
$843$	−21.9000	−	21.9000i	−0.754275	−	0.754275i
$844$	−17.4234	−	28.9349i	−0.599738	−	0.995981i
$845$	−9.47044	+	11.8790i	−0.325793	+	0.408651i
$846$	−7.36910	+	13.0393i	−0.253355	+	0.448301i
$847$	12.5944	−	12.5944i	0.432749	−	0.432749i
$848$	−10.0668	−	32.7040i	−0.345694	−	1.12306i
$849$		−	32.5582i		−	1.11739i
$850$	−24.3412	−	7.25604i	−0.834895	−	0.248880i
$851$		−	39.1034i		−	1.34045i
$852$	3.45263	−	13.9042i	0.118285	−	0.476349i
$853$	35.1335	−	35.1335i	1.20295	−	1.20295i	0.229682	−	0.973266i	$-0.426232\pi$
$853$	35.1335	−	35.1335i	1.20295	−	1.20295i	0.973266	−	0.229682i	$-0.0737685\pi$
$854$	−21.7568	−	12.2957i	−0.744502	−	0.420751i
$855$	2.78729	−	3.49617i	0.0953232	−	0.119567i
$856$	−14.4395	+	0.398757i	−0.493533	+	0.0136292i
$857$	14.1447	+	14.1447i	0.483173	+	0.483173i	0.906143	−	0.422971i	$-0.139013\pi$
$857$	14.1447	+	14.1447i	0.483173	+	0.483173i	−0.422971	+	0.906143i	$0.639013\pi$
$858$	−56.6723	+	15.7457i	−1.93476	+	0.537549i
$859$	37.7363			1.28755			0.643774	−	0.765216i	$-0.277368\pi$
$859$	37.7363			1.28755			0.643774	+	0.765216i	$0.277368\pi$
$860$	29.8684	+	38.9374i	1.01850	+	1.32775i
$861$	−31.5604			−1.07558
$862$	8.72388	−	2.42382i	0.297137	−	0.0825557i
$863$	16.5929	+	16.5929i	0.564828	+	0.564828i	0.930675	−	0.365847i	$-0.119221\pi$
$863$	16.5929	+	16.5929i	0.564828	+	0.564828i	−0.365847	+	0.930675i	$0.619221\pi$
$864$	10.6557	−	6.82414i	0.362513	−	0.232162i
$865$	−31.2287	+	3.52315i	−1.06181	+	0.119791i
$866$	−30.6382	−	17.3150i	−1.04113	−	0.588388i
$867$	−6.47793	+	6.47793i	−0.220002	+	0.220002i
$868$	1.47306	+	0.365786i	0.0499990	+	0.0124156i
$869$		−	14.1227i		−	0.479079i
$870$	26.4938	+	65.6932i	0.898225	+	2.22721i
$871$			32.5682i			1.10353i
$872$	−0.771542	+	0.815366i	−0.0261277	+	0.0276118i
$873$	16.9924	−	16.9924i	0.575106	−	0.575106i
$874$	−3.64132	+	6.44317i	−0.123169	+	0.217943i
$875$	10.1627	+	29.0033i	0.343561	+	0.980491i
$876$	−37.0559	+	22.3135i	−1.25200	+	0.753903i
$877$	15.9676	+	15.9676i	0.539187	+	0.539187i	0.923290	−	0.384104i	$-0.125489\pi$
$877$	15.9676	+	15.9676i	0.539187	+	0.539187i	−0.384104	+	0.923290i	$0.625489\pi$
$878$	7.54471	+	27.1551i	0.254622	+	0.916441i
$879$	26.5333			0.894945
$880$	−14.9386	−	34.2814i	−0.503581	−	1.15562i
$881$	−26.4663			−0.891672			−0.445836	−	0.895115i	$-0.647094\pi$
$881$	−26.4663			−0.891672			−0.445836	+	0.895115i	$0.647094\pi$
$882$	−0.420730	−	1.51430i	−0.0141667	−	0.0509893i
$883$	−32.8945	−	32.8945i	−1.10699	−	1.10699i	−0.993544	−	0.113444i	$-0.963812\pi$
$883$	−32.8945	−	32.8945i	−1.10699	−	1.10699i	−0.113444	−	0.993544i	$-0.536188\pi$
$884$	27.3815	−	16.4880i	0.920940	−	0.554551i
$885$	−1.22993	−	10.9019i	−0.0413436	−	0.366464i
$886$	1.17142	−	2.07278i	0.0393546	−	0.0696363i
$887$	8.60196	−	8.60196i	0.288826	−	0.288826i	−0.547790	−	0.836616i	$-0.684531\pi$
$887$	8.60196	−	8.60196i	0.288826	−	0.288826i	0.836616	+	0.547790i	$0.184531\pi$
$888$	32.4799	−	34.3247i	1.08995	−	1.15186i
$889$			25.8401i			0.866648i
$890$	−36.2400	−	15.4098i	−1.21477	−	0.516538i
$891$			45.9912i			1.54076i
$892$	−19.8776	−	4.93594i	−0.665551	−	0.165267i
$893$	−3.74512	+	3.74512i	−0.125326	+	0.125326i
$894$	9.61519	+	5.43397i	0.321580	+	0.181739i
$895$	−0.806565	−	0.643026i	−0.0269605	−	0.0214940i
$896$	−13.7834	+	27.8775i	−0.460471	+	0.931323i
$897$	36.8122	+	36.8122i	1.22912	+	1.22912i
$898$	42.6731	−	11.8562i	1.42402	−	0.395646i
$899$	−2.76580			−0.0922446
$900$	14.4014	−	13.8724i	0.480047	−	0.462413i
$901$	−30.7285			−1.02371
$902$	−29.2530	+	8.12758i	−0.974018	+	0.270619i
$903$	47.6900	+	47.6900i	1.58702	+	1.58702i
$904$	−42.5069	+	1.17386i	−1.41376	+	0.0390419i
$905$	−12.8796	−	10.2681i	−0.428133	−	0.341325i
$906$	0.0777665	+	0.0439493i	0.00258362	+	0.00146012i
$907$	17.1103	−	17.1103i	0.568138	−	0.568138i	−0.363468	−	0.931607i	$-0.618408\pi$
$907$	17.1103	−	17.1103i	0.568138	−	0.568138i	0.931607	+	0.363468i	$0.118408\pi$
$908$	−0.238424	+	0.960161i	−0.00791237	+	0.0318641i
$909$		−	13.1835i		−	0.437268i
$910$	−35.5892	−	15.1331i	−1.17977	−	0.501657i
$911$			28.2126i			0.934726i	0.884065	+	0.467363i	$0.154796\pi$
$911$			28.2126i			0.934726i	−0.884065	+	0.467363i	$0.845204\pi$
$912$	−8.54812	+	2.63124i	−0.283057	+	0.0871290i
$913$	17.6283	−	17.6283i	0.583410	−	0.583410i
$914$	−19.4182	+	34.3597i	−0.642296	+	1.13652i
$915$	−3.60338	−	31.9399i	−0.119124	−	1.05590i
$916$	−11.0257	−	18.3103i	−0.364300	−	0.604991i
$917$	21.8575	+	21.8575i	0.721799	+	0.721799i
$918$	−3.04186	−	10.9483i	−0.100396	−	0.361349i
$919$	−46.4579			−1.53251			−0.766253	−	0.642539i	$-0.777881\pi$
$919$	−46.4579			−1.53251			−0.766253	+	0.642539i	$0.777881\pi$
$920$	−19.9102	+	26.4397i	−0.656421	+	0.871689i
$921$	51.3758			1.69289
$922$	5.16072	+	18.5746i	0.169959	+	0.611722i
$923$	−10.0784	−	10.0784i	−0.331735	−	0.331735i
$924$	−26.5113	−	44.0272i	−0.872158	−	1.44839i
$925$	−19.8680	+	31.6398i	−0.653256	+	1.04031i
$926$	25.8556	−	45.7505i	0.849668	−	1.50345i
$927$	14.1285	−	14.1285i	0.464040	−	0.464040i
$928$	12.1338	−	55.3555i	0.398312	−	1.81713i
$929$		−	43.5988i		−	1.43043i	−0.698904	−	0.715216i	$-0.746328\pi$
$929$		−	43.5988i		−	1.43043i	0.698904	−	0.715216i	$-0.253672\pi$
$930$	0.730151	+	1.81046i	0.0239426	+	0.0593672i
$931$		−	0.555776i		−	0.0182148i
$932$	14.0155	−	56.4420i	0.459092	−	1.84882i
$933$	−44.5863	+	44.5863i	−1.45969	+	1.45969i
$934$	−6.17962	−	3.49238i	−0.202203	−	0.114274i
$935$	−33.3694	+	3.76465i	−1.09130	+	0.123117i
$936$	0.694621	+	25.1532i	0.0227044	+	0.822158i
$937$	−29.5459	−	29.5459i	−0.965223	−	0.965223i	0.0341921	−	0.999415i	$-0.489114\pi$
$937$	−29.5459	−	29.5459i	−0.965223	−	0.965223i	−0.999415	+	0.0341921i	$0.989114\pi$
$938$	−27.4179	+	7.61771i	−0.895225	+	0.248727i
$939$	15.2724			0.498396
$940$	−18.7937	+	14.4164i	−0.612984	+	0.470212i
$941$	−40.3487			−1.31533			−0.657665	−	0.753311i	$-0.728456\pi$
$941$	−40.3487			−1.31533			−0.657665	+	0.753311i	$0.728456\pi$
$942$	−25.1155	+	6.97802i	−0.818306	+	0.227356i
$943$	19.0016	+	19.0016i	0.618779	+	0.618779i
$944$	−4.10588	+	7.75765i	−0.133635	+	0.252490i
$945$	−8.57064	+	10.7504i	−0.278803	+	0.349710i
$946$	56.4846	+	31.9220i	1.83647	+	1.03787i
$947$	−31.7758	+	31.7758i	−1.03257	+	1.03257i	−0.0331227	+	0.999451i	$0.510545\pi$
$947$	−31.7758	+	31.7758i	−1.03257	+	1.03257i	−0.999451	+	0.0331227i	$0.989455\pi$
$948$	−14.6607	−	3.64050i	−0.476158	−	0.118238i
$949$			43.0339i			1.39694i
$950$	6.22001	−	3.36326i	0.201804	−	0.109119i
$951$			44.3574i			1.43839i
$952$	20.2851	+	19.1948i	0.657444	+	0.622108i
$953$	8.09221	−	8.09221i	0.262132	−	0.262132i	−0.563788	−	0.825920i	$-0.690656\pi$
$953$	8.09221	−	8.09221i	0.262132	−	0.262132i	0.825920	+	0.563788i	$0.190656\pi$
$954$	11.9023	−	21.0607i	0.385352	−	0.681864i
$955$	−10.8971	+	13.6686i	−0.352623	+	0.442305i
$956$	−18.3038	+	11.0218i	−0.591987	+	0.356470i
$957$	66.2211	+	66.2211i	2.14062	+	2.14062i
$958$	−10.8453	−	39.0349i	−0.350397	−	1.26116i
$959$	12.0821			0.390152
$960$	−39.4382	+	6.67082i	−1.27286	+	0.215300i
$961$	30.9238			0.997541
$962$	−12.5855	−	45.2981i	−0.405773	−	1.46047i
$963$	−7.22111	−	7.22111i	−0.232697	−	0.232697i
$964$	−20.1533	+	12.1355i	−0.649094	+	0.390857i
$965$	55.9295	−	6.30984i	1.80043	−	0.203121i
$966$	−22.3803	+	39.6011i	−0.720075	+	1.27414i
$967$	3.82211	−	3.82211i	0.122911	−	0.122911i	−0.642976	−	0.765886i	$-0.722300\pi$
$967$	3.82211	−	3.82211i	0.122911	−	0.122911i	0.765886	+	0.642976i	$0.222300\pi$
$968$	−13.3122	−	12.5967i	−0.427869	−	0.404872i
$969$			8.03176i			0.258017i
$970$	35.2452	−	14.2143i	1.13166	−	0.456393i
$971$			25.4719i			0.817434i	0.912661	+	0.408717i	$0.134024\pi$
$971$			25.4719i			0.817434i	−0.912661	+	0.408717i	$0.865976\pi$
$972$	34.7178	+	8.62102i	1.11358	+	0.276519i
$973$	−6.75399	+	6.75399i	−0.216523	+	0.216523i
$974$	−52.4495	−	29.6416i	−1.68059	−	0.949777i
$975$	−11.0821	−	48.4898i	−0.354910	−	1.55292i
$976$	−12.0292	+	22.7279i	−0.385045	+	0.727504i
$977$	3.31534	+	3.31534i	0.106067	+	0.106067i	0.758149	−	0.652082i	$-0.226104\pi$
$977$	3.31534	+	3.31534i	0.106067	+	0.106067i	−0.652082	+	0.758149i	$0.726104\pi$
$978$	49.7431	−	13.8205i	1.59061	−	0.441930i
$979$	−52.0648			−1.66400
$980$	0.324796	−	2.46419i	0.0103752	−	0.0787157i
$981$	−0.793602			−0.0253378
$982$	−16.2056	+	4.50253i	−0.517142	+	0.143682i
$983$	41.9720	+	41.9720i	1.33870	+	1.33870i	0.897322	+	0.441377i	$0.145510\pi$
$983$	41.9720	+	41.9720i	1.33870	+	1.33870i	0.441377	+	0.897322i	$0.354490\pi$
$984$	0.896475	+	32.4626i	0.0285786	+	1.03487i
$985$	−0.473441	−	4.19651i	−0.0150851	−	0.133712i
$986$	−44.3045	−	25.0384i	−1.41094	−	0.797387i
$987$	−23.0183	+	23.0183i	−0.732681	+	0.732681i
$988$	−2.14443	+	8.63585i	−0.0682233	+	0.274743i
$989$		−	57.4256i		−	1.82603i
$990$	10.3450	−	24.3289i	0.328786	−	0.773223i
$991$		−	9.67622i		−	0.307375i	−0.988119	−	0.153688i	$-0.950885\pi$
$991$		−	9.67622i		−	0.307375i	0.988119	−	0.153688i	$-0.0491149\pi$
$992$	0.334399	−	1.52556i	0.0106172	−	0.0484365i
$993$	−29.4333	+	29.4333i	−0.934037	+	0.934037i
$994$	6.12727	−	10.8420i	0.194345	−	0.343886i
$995$	−27.2008	−	21.6855i	−0.862322	−	0.687477i
$996$	−13.7557	−	22.8440i	−0.435866	−	0.723841i
$997$	14.1267	+	14.1267i	0.447397	+	0.447397i	0.894488	−	0.447091i	$-0.147540\pi$
$997$	14.1267	+	14.1267i	0.447397	+	0.447397i	−0.447091	+	0.894488i	$0.647540\pi$
$998$	−6.85371	−	24.6681i	−0.216950	−	0.780854i
$999$	−16.7140			−0.528808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.267.12	✓	52
4.3	odd	2		380.2.k.d.267.2	yes	52
5.3	odd	4		380.2.k.d.343.2	yes	52
20.3	even	4	inner	380.2.k.c.343.12	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.12	✓	52	1.1	even	1	trivial
380.2.k.c.343.12	yes	52	20.3	even	4	inner
380.2.k.d.267.2	yes	52	4.3	odd	2
380.2.k.d.343.2	yes	52	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.378581 - 1.36260i) q^{2} +(-1.58108 - 1.58108i) q^{3} +(-1.71335 + 1.03171i) q^{4} +(-1.74843 - 1.39392i) q^{5} +(-1.55581 + 2.75294i) q^{6} +(-1.94368 + 1.94368i) q^{7} +(2.05445 + 1.94403i) q^{8} +1.99961i q^{9} +O(q^{10})\)	\(q+(-0.378581 - 1.36260i) 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} +(2.05445 + 1.94403i) q^{8} +1.99961i q^{9} +(-1.23743 + 2.91012i) q^{10} +4.18087i q^{11} +(4.34015 + 1.07773i) 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} +(2.72467 - 0.757015i) q^{18} +1.00000 q^{19} +(4.43379 + 0.584402i) q^{20} +6.14621 q^{21} +(5.69685 - 1.58280i) 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} +(1.32490 - 5.33552i) q^{28} +10.0179i q^{29} +(6.55759 - 2.64465i) q^{30} +0.276086i q^{31} +(-5.52566 - 1.21121i) 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} +(-0.378581 - 1.36260i) q^{38} -9.94801 q^{39} +(-0.882243 - 6.26272i) q^{40} -5.13494 q^{41} +(-2.32684 - 8.37482i) 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} +(-8.54812 + 2.63124i) q^{48} -0.555776i q^{49} +(6.22001 - 3.36326i) q^{50} +8.03176i q^{51} +(-2.14443 + 8.63585i) 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} +(13.6504 - 3.79259i) q^{58} -2.19430 q^{59} +(-6.08618 - 7.93415i) q^{60} -6.42875 q^{61} +(0.376195 - 0.104521i) 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} +(6.97236 + 1.73135i) q^{68} +11.7014i q^{69} +(-3.25117 - 8.06149i) q^{70} -3.20361i q^{71} +(-3.88730 + 4.10810i) 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} +(3.76613 + 13.5552i) q^{78} -3.37793 q^{79} +(-8.19957 + 3.57309i) q^{80} +11.0004 q^{81} +(1.94399 + 6.99687i) 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} +(-8.12773 + 8.58938i) q^{88} +12.4531i q^{89} +(-5.81910 - 2.47437i) q^{90} +12.2295i q^{91} +(10.1580 + 2.52240i) 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} +(-0.757299 + 0.210406i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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