LMFDB - Embedded newform 525.2.n.d.211.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.8
Character	$\chi$	$=$	525.211
Dual form			525.2.n.d.316.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19514 - 1.59486i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.65701 - 5.09975i) q^{4} +(-2.20491 + 0.371995i) q^{5} +(-0.838467 - 2.58054i) q^{6} -1.00000 q^{7} +(-2.81909 - 8.67626i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(2.19514 - 1.59486i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.65701 - 5.09975i) q^{4} +(-2.20491 + 0.371995i) q^{5} +(-0.838467 - 2.58054i) q^{6} -1.00000 q^{7} +(-2.81909 - 8.67626i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-4.24679 + 4.33310i) q^{10} +(0.985033 - 0.715668i) q^{11} +(-4.33811 - 3.15182i) q^{12} +(4.49327 + 3.26455i) q^{13} +(-2.19514 + 1.59486i) q^{14} +(-0.327566 + 2.21195i) q^{15} +(-11.3495 - 8.24588i) q^{16} +(-1.41203 - 4.34579i) q^{17} -2.71334 q^{18} +(2.38542 + 7.34155i) q^{19} +(-1.75647 + 11.8609i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.02089 - 3.14198i) q^{22} +(1.86639 - 1.35601i) q^{23} -9.12276 q^{24} +(4.72324 - 1.64043i) q^{25} +15.0698 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.65701 + 5.09975i) q^{28} +(0.367371 - 1.13065i) q^{29} +(2.80869 + 5.37794i) q^{30} +(-2.67188 - 8.22321i) q^{31} -19.8191 q^{32} +(-0.376249 - 1.15798i) q^{33} +(-10.0305 - 7.28761i) q^{34} +(2.20491 - 0.371995i) q^{35} +(-4.33811 + 3.15182i) q^{36} +(-1.29316 - 0.939538i) q^{37} +(16.9451 + 12.3113i) q^{38} +(4.49327 - 3.26455i) q^{39} +(9.44336 + 18.0817i) q^{40} +(6.56804 + 4.77196i) q^{41} +(0.838467 + 2.58054i) q^{42} +1.77088 q^{43} +(-2.01752 - 6.20929i) q^{44} +(2.00246 + 0.995062i) q^{45} +(1.93434 - 5.95327i) q^{46} +(-0.210110 + 0.646651i) q^{47} +(-11.3495 + 8.24588i) q^{48} +1.00000 q^{49} +(7.75189 - 11.1339i) q^{50} -4.56944 q^{51} +(24.0938 - 17.5052i) q^{52} +(-1.39383 + 4.28978i) q^{53} +(-0.838467 + 2.58054i) q^{54} +(-1.90568 + 1.94441i) q^{55} +(2.81909 + 8.67626i) q^{56} +7.71937 q^{57} +(-0.996800 - 3.06783i) q^{58} +(6.93628 + 5.03950i) q^{59} +(10.7376 + 5.33572i) q^{60} +(-5.12782 + 3.72558i) q^{61} +(-18.9800 - 13.7898i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-20.8067 + 15.1170i) q^{64} +(-11.1216 - 5.52656i) q^{65} +(-2.67273 - 1.94185i) q^{66} +(2.90592 + 8.94350i) q^{67} -24.5022 q^{68} +(-0.712899 - 2.19408i) q^{69} +(4.24679 - 4.33310i) q^{70} +(2.63054 - 8.09596i) q^{71} +(-2.81909 + 8.67626i) q^{72} +(-6.20475 + 4.50801i) q^{73} -4.33710 q^{74} +(-0.100580 - 4.99899i) q^{75} +41.3927 q^{76} +(-0.985033 + 0.715668i) q^{77} +(4.65684 - 14.3323i) q^{78} +(-4.37560 + 13.4667i) q^{79} +(28.0920 + 13.9595i) q^{80} +(0.309017 + 0.951057i) q^{81} +22.0283 q^{82} +(-2.47979 - 7.63200i) q^{83} +(4.33811 + 3.15182i) q^{84} +(4.73002 + 9.05681i) q^{85} +(3.88733 - 2.82431i) q^{86} +(-0.961789 - 0.698780i) q^{87} +(-8.98622 - 6.52887i) q^{88} +(-5.86179 + 4.25884i) q^{89} +(5.98266 - 1.00935i) q^{90} +(-4.49327 - 3.26455i) q^{91} +(-3.82270 - 11.7651i) q^{92} -8.64640 q^{93} +(0.570098 + 1.75458i) q^{94} +(-7.99064 - 15.3001i) q^{95} +(-6.12445 + 18.8491i) q^{96} +(1.34446 - 4.13782i) q^{97} +(2.19514 - 1.59486i) q^{98} -1.21757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	2.19514	−	1.59486i	1.55219	−	1.12774i	0.610132	−	0.792300i	$-0.291116\pi$
$2$	2.19514	−	1.59486i	1.55219	−	1.12774i	0.942063	−	0.335436i	$-0.108884\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.65701	−	5.09975i	0.828504	−	2.54987i
$5$	−2.20491	+	0.371995i	−0.986065	+	0.166361i
$5$	−2.20491	+	0.371995i	−0.986065	+	0.166361i
$6$	−0.838467	−	2.58054i	−0.342303	−	1.05350i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−2.81909	−	8.67626i	−0.996698	−	3.06752i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−4.24679	+	4.33310i	−1.34295	+	1.37025i
$11$	0.985033	−	0.715668i	0.296999	−	0.215782i	−0.429299	−	0.903162i	$-0.641239\pi$
$11$	0.985033	−	0.715668i	0.296999	−	0.215782i	0.726298	+	0.687380i	$0.241239\pi$
$12$	−4.33811	−	3.15182i	−1.25230	−	0.909852i
$13$	4.49327	+	3.26455i	1.24621	+	0.905424i	0.997996	−	0.0632815i	$-0.0201566\pi$
$13$	4.49327	+	3.26455i	1.24621	+	0.905424i	0.248213	+	0.968705i	$0.420157\pi$
$14$	−2.19514	+	1.59486i	−0.586675	+	0.426244i
$15$	−0.327566	+	2.21195i	−0.0845771	+	0.571122i
$16$	−11.3495	−	8.24588i	−2.83737	−	2.06147i
$17$	−1.41203	−	4.34579i	−0.342469	−	1.05401i	−0.962925	−	0.269769i	$-0.913053\pi$
$17$	−1.41203	−	4.34579i	−0.342469	−	1.05401i	0.620457	−	0.784241i	$-0.286947\pi$
$18$	−2.71334			−0.639539
$19$	2.38542	+	7.34155i	0.547252	+	1.68427i	0.715575	+	0.698536i	$0.246165\pi$
$19$	2.38542	+	7.34155i	0.547252	+	1.68427i	−0.168323	+	0.985732i	$0.553835\pi$
$20$	−1.75647	+	11.8609i	−0.392759	+	2.65217i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	1.02089	−	3.14198i	0.217655	−	0.669872i
$23$	1.86639	−	1.35601i	0.389170	−	0.282749i	−0.375945	−	0.926642i	$-0.622682\pi$
$23$	1.86639	−	1.35601i	0.389170	−	0.282749i	0.765115	+	0.643893i	$0.222682\pi$
$24$	−9.12276			−1.86218
$25$	4.72324	−	1.64043i	0.944648	−	0.328086i
$26$	15.0698			2.95544
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−1.65701	+	5.09975i	−0.313145	+	0.963762i
$29$	0.367371	−	1.13065i	0.0682190	−	0.209957i	−0.911135	−	0.412107i	$-0.864793\pi$
$29$	0.367371	−	1.13065i	0.0682190	−	0.209957i	0.979354	+	0.202150i	$0.0647930\pi$
$30$	2.80869	+	5.37794i	0.512794	+	0.981873i
$31$	−2.67188	−	8.22321i	−0.479885	−	1.47693i	−0.839255	−	0.543738i	$-0.817009\pi$
$31$	−2.67188	−	8.22321i	−0.479885	−	1.47693i	0.359370	−	0.933195i	$-0.382991\pi$
$32$	−19.8191			−3.50356
$33$	−0.376249	−	1.15798i	−0.0654966	−	0.201578i
$34$	−10.0305	−	7.28761i	−1.72022	−	1.24981i
$35$	2.20491	−	0.371995i	0.372697	−	0.0628786i
$36$	−4.33811	+	3.15182i	−0.723018	+	0.525303i
$37$	−1.29316	−	0.939538i	−0.212595	−	0.154459i	0.476392	−	0.879233i	$-0.341944\pi$
$37$	−1.29316	−	0.939538i	−0.212595	−	0.154459i	−0.688987	+	0.724774i	$0.741944\pi$
$38$	16.9451	+	12.3113i	2.74885	+	1.99716i
$39$	4.49327	−	3.26455i	0.719499	−	0.522747i
$40$	9.44336	+	18.0817i	1.49313	+	2.85896i
$41$	6.56804	+	4.77196i	1.02576	+	0.745255i	0.967455	−	0.253044i	$-0.0814317\pi$
$41$	6.56804	+	4.77196i	1.02576	+	0.745255i	0.0583009	+	0.998299i	$0.481432\pi$
$42$	0.838467	+	2.58054i	0.129378	+	0.398185i
$43$	1.77088			0.270057			0.135029	−	0.990842i	$-0.456887\pi$
$43$	1.77088			0.270057			0.135029	+	0.990842i	$0.456887\pi$
$44$	−2.01752	−	6.20929i	−0.304153	−	0.936086i
$45$	2.00246	+	0.995062i	0.298509	+	0.148335i
$46$	1.93434	−	5.95327i	0.285202	−	0.877762i
$47$	−0.210110	+	0.646651i	−0.0306476	+	0.0943237i	−0.965210	−	0.261475i	$-0.915791\pi$
$47$	−0.210110	+	0.646651i	−0.0306476	+	0.0943237i	0.934563	+	0.355799i	$0.115791\pi$
$48$	−11.3495	+	8.24588i	−1.63816	+	1.19019i
$49$	1.00000			0.142857
$50$	7.75189	−	11.1339i	1.09628	−	1.57457i
$51$	−4.56944			−0.639849
$52$	24.0938	−	17.5052i	3.34121	−	2.42753i
$53$	−1.39383	+	4.28978i	−0.191458	+	0.589246i	0.808542	+	0.588438i	$0.200257\pi$
$53$	−1.39383	+	4.28978i	−0.191458	+	0.589246i	−1.00000		0.000807602i	$0.999743\pi$
$54$	−0.838467	+	2.58054i	−0.114101	+	0.351166i
$55$	−1.90568	+	1.94441i	−0.256962	+	0.262184i
$56$	2.81909	+	8.67626i	0.376717	+	1.15941i
$57$	7.71937			1.02245
$58$	−0.996800	−	3.06783i	−0.130886	−	0.402826i
$59$	6.93628	+	5.03950i	0.903026	+	0.656087i	0.939242	−	0.343257i	$-0.111530\pi$
$59$	6.93628	+	5.03950i	0.903026	+	0.656087i	−0.0362152	+	0.999344i	$0.511530\pi$
$60$	10.7376	+	5.33572i	1.38622	+	0.688838i
$61$	−5.12782	+	3.72558i	−0.656550	+	0.477011i	−0.865496	−	0.500916i	$-0.832997\pi$
$61$	−5.12782	+	3.72558i	−0.656550	+	0.477011i	0.208946	+	0.977927i	$0.432997\pi$
$62$	−18.9800	−	13.7898i	−2.41046	−	1.75130i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	−20.8067	+	15.1170i	−2.60084	+	1.88962i
$65$	−11.1216	−	5.52656i	−1.37947	−	0.685486i
$66$	−2.67273	−	1.94185i	−0.328990	−	0.239025i
$67$	2.90592	+	8.94350i	0.355015	+	1.09262i	0.956001	+	0.293363i	$0.0947746\pi$
$67$	2.90592	+	8.94350i	0.355015	+	1.09262i	−0.600986	+	0.799259i	$0.705225\pi$
$68$	−24.5022			−2.97133
$69$	−0.712899	−	2.19408i	−0.0858230	−	0.264136i
$70$	4.24679	−	4.33310i	0.507589	−	0.517904i
$71$	2.63054	−	8.09596i	0.312187	−	0.960813i	−0.664710	−	0.747102i	$-0.731445\pi$
$71$	2.63054	−	8.09596i	0.312187	−	0.960813i	0.976897	−	0.213712i	$-0.0685553\pi$
$72$	−2.81909	+	8.67626i	−0.332233	+	1.02251i
$73$	−6.20475	+	4.50801i	−0.726211	+	0.527623i	−0.888362	−	0.459143i	$-0.848157\pi$
$73$	−6.20475	+	4.50801i	−0.726211	+	0.527623i	0.162152	+	0.986766i	$0.448157\pi$
$74$	−4.33710			−0.504178
$75$	−0.100580	−	4.99899i	−0.0116140	−	0.577233i
$76$	41.3927			4.74807
$77$	−0.985033	+	0.715668i	−0.112255	+	0.0815580i
$78$	4.65684	−	14.3323i	0.527283	−	1.62281i
$79$	−4.37560	+	13.4667i	−0.492293	+	1.51512i	0.328840	+	0.944386i	$0.393342\pi$
$79$	−4.37560	+	13.4667i	−0.492293	+	1.51512i	−0.821133	+	0.570737i	$0.806658\pi$
$80$	28.0920	+	13.9595i	3.14078	+	1.56072i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	22.0283			2.43262
$83$	−2.47979	−	7.63200i	−0.272192	−	0.837721i	−0.989949	−	0.141427i	$-0.954831\pi$
$83$	−2.47979	−	7.63200i	−0.272192	−	0.837721i	0.717757	−	0.696294i	$-0.245169\pi$
$84$	4.33811	+	3.15182i	0.473326	+	0.343892i
$85$	4.73002	+	9.05681i	0.513043	+	0.982348i
$86$	3.88733	−	2.82431i	0.419182	−	0.304553i
$87$	−0.961789	−	0.698780i	−0.103115	−	0.0749171i
$88$	−8.98622	−	6.52887i	−0.957934	−	0.695980i
$89$	−5.86179	+	4.25884i	−0.621349	+	0.451436i	−0.853392	−	0.521269i	$-0.825459\pi$
$89$	−5.86179	+	4.25884i	−0.621349	+	0.451436i	0.232044	+	0.972705i	$0.425459\pi$
$90$	5.98266	−	1.00935i	0.630627	−	0.106395i
$91$	−4.49327	−	3.26455i	−0.471023	−	0.342218i
$92$	−3.82270	−	11.7651i	−0.398544	−	1.22659i
$93$	−8.64640			−0.896590
$94$	0.570098	+	1.75458i	0.0588011	+	0.180971i
$95$	−7.99064	−	15.3001i	−0.819823	−	1.56976i
$96$	−6.12445	+	18.8491i	−0.625074	+	1.92378i
$97$	1.34446	−	4.13782i	0.136509	−	0.420132i	−0.859313	−	0.511451i	$-0.829108\pi$
$97$	1.34446	−	4.13782i	0.136509	−	0.420132i	0.995822	+	0.0913189i	$0.0291083\pi$
$98$	2.19514	−	1.59486i	0.221742	−	0.161105i
$99$	−1.21757			−0.122370
$100$	−0.539332	−	26.8055i	−0.0539332	−	2.68055i
$101$	−9.21751			−0.917177			−0.458588	−	0.888649i	$-0.651645\pi$
$101$	−9.21751			−0.917177			−0.458588	+	0.888649i	$0.651645\pi$
$102$	−10.0305	+	7.28761i	−0.993171	+	0.721581i
$103$	−3.16861	+	9.75197i	−0.312212	+	0.960890i	0.664675	+	0.747133i	$0.268570\pi$
$103$	−3.16861	+	9.75197i	−0.312212	+	0.960890i	−0.976887	+	0.213757i	$0.931430\pi$
$104$	15.6572	−	48.1879i	1.53531	−	4.72521i
$105$	0.327566	−	2.21195i	0.0319671	−	0.215864i
$106$	3.78194	+	11.6396i	0.367334	+	1.13054i
$107$	15.3360			1.48259			0.741295	−	0.671179i	$-0.234212\pi$
$107$	15.3360			1.48259			0.741295	+	0.671179i	$0.234212\pi$
$108$	1.65701	+	5.09975i	0.159446	+	0.490724i
$109$	7.85684	+	5.70833i	0.752549	+	0.546759i	0.896616	−	0.442809i	$-0.146018\pi$
$109$	7.85684	+	5.70833i	0.752549	+	0.546759i	−0.144067	+	0.989568i	$0.546018\pi$
$110$	−1.08217	+	7.30754i	−0.103181	+	0.696746i
$111$	−1.29316	+	0.939538i	−0.122742	+	0.0891770i
$112$	11.3495	+	8.24588i	1.07243	+	0.779163i
$113$	−9.91343	−	7.20253i	−0.932577	−	0.677557i	0.0140452	−	0.999901i	$-0.495529\pi$
$113$	−9.91343	−	7.20253i	−0.932577	−	0.677557i	−0.946623	+	0.322344i	$0.895529\pi$
$114$	16.9451	−	12.3113i	1.58705	−	1.15306i
$115$	−3.61080	+	3.68418i	−0.336709	+	0.343551i
$116$	−5.15730	−	3.74700i	−0.478843	−	0.347900i
$117$	−1.71628	−	5.28216i	−0.158670	−	0.488336i
$118$	23.2634			2.14157
$119$	1.41203	+	4.34579i	0.129441	+	0.398378i
$120$	20.1149	−	3.39362i	1.83623	−	0.309794i
$121$	−2.94108	+	9.05171i	−0.267371	+	0.822883i
$122$	−5.31448	+	16.3563i	−0.481150	+	1.48083i
$123$	6.56804	−	4.77196i	0.592220	−	0.430273i
$124$	−46.3637			−4.16358
$125$	−9.80408	+	5.37402i	−0.876903	+	0.480667i
$126$	2.71334			0.241723
$127$	15.4431	−	11.2201i	1.37035	−	0.995620i	0.372644	−	0.927974i	$-0.378451\pi$
$127$	15.4431	−	11.2201i	1.37035	−	0.995620i	0.997709	−	0.0676458i	$-0.0215488\pi$
$128$	−9.31524	+	28.6694i	−0.823359	+	2.53404i
$129$	0.547233	−	1.68421i	0.0481812	−	0.148287i
$130$	−33.2276	+	5.60591i	−2.91425	+	0.491670i
$131$	3.23027	+	9.94176i	0.282230	+	0.868616i	0.987215	+	0.159393i	$0.0509538\pi$
$131$	3.23027	+	9.94176i	0.282230	+	0.868616i	−0.704985	+	0.709223i	$0.749046\pi$
$132$	−6.52883			−0.568262
$133$	−2.38542	−	7.34155i	−0.206842	−	0.636593i
$134$	20.6425	+	14.9977i	1.78324	+	1.29560i
$135$	1.56515	−	1.59696i	0.134707	−	0.137445i
$136$	−33.7246	+	24.5024i	−2.89186	+	2.10106i
$137$	−4.62967	−	3.36365i	−0.395539	−	0.287376i	0.372182	−	0.928160i	$-0.378610\pi$
$137$	−4.62967	−	3.36365i	−0.395539	−	0.287376i	−0.767722	+	0.640784i	$0.778610\pi$
$138$	−5.06416	−	3.67932i	−0.431090	−	0.313205i
$139$	−13.8643	+	10.0730i	−1.17596	+	0.854384i	−0.991710	−	0.128496i	$-0.958985\pi$
$139$	−13.8643	+	10.0730i	−1.17596	+	0.854384i	−0.184248	+	0.982880i	$0.558985\pi$
$140$	1.75647	−	11.8609i	0.148449	−	1.00243i
$141$	0.550074	+	0.399652i	0.0463246	+	0.0336568i
$142$	−7.13753	−	21.9671i	−0.598968	−	1.84343i
$143$	6.76236			0.565497
$144$	4.33512	+	13.3421i	0.361260	+	1.11184i
$145$	−0.389422	+	2.62964i	−0.0323397	+	0.218380i
$146$	−6.43061	+	19.7914i	−0.532201	+	1.63795i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−6.93419	+	5.03799i	−0.569987	+	0.414120i
$149$	−10.5738			−0.866241			−0.433121	−	0.901336i	$-0.642588\pi$
$149$	−10.5738			−0.866241			−0.433121	+	0.901336i	$0.642588\pi$
$150$	−8.19347	−	10.8130i	−0.668994	−	0.882881i
$151$	−2.68558			−0.218549			−0.109275	−	0.994012i	$-0.534853\pi$
$151$	−2.68558			−0.218549			−0.109275	+	0.994012i	$0.534853\pi$
$152$	56.9725	−	41.3930i	4.62108	−	3.35741i
$153$	−1.41203	+	4.34579i	−0.114156	+	0.351337i
$154$	−1.02089	+	3.14198i	−0.0822657	+	0.253188i
$155$	8.95026	+	17.1375i	0.718902	+	1.37652i
$156$	−9.20301	−	28.3239i	−0.736830	−	2.26773i
$157$	−4.22013			−0.336803			−0.168401	−	0.985719i	$-0.553860\pi$
$157$	−4.22013			−0.336803			−0.168401	+	0.985719i	$0.553860\pi$
$158$	11.8725	+	36.5397i	0.944523	+	2.90694i
$159$	3.64910	+	2.65123i	0.289393	+	0.210256i
$160$	43.6994	−	7.37262i	3.45474	−	0.582857i
$161$	−1.86639	+	1.35601i	−0.147092	+	0.106869i
$162$	2.19514	+	1.59486i	0.172466	+	0.125304i
$163$	−8.09486	−	5.88126i	−0.634038	−	0.460656i	0.223759	−	0.974645i	$-0.428167\pi$
$163$	−8.09486	−	5.88126i	−0.634038	−	0.460656i	−0.857797	+	0.513989i	$0.828167\pi$
$164$	35.2191	−	25.5882i	2.75015	−	1.99810i
$165$	1.26036	+	2.41327i	0.0981186	+	0.187873i
$166$	−17.6154	−	12.7984i	−1.36722	−	0.993345i
$167$	−6.43702	−	19.8111i	−0.498112	−	1.53303i	−0.812050	−	0.583587i	$-0.801649\pi$
$167$	−6.43702	−	19.8111i	−0.498112	−	1.53303i	0.313938	−	0.949443i	$-0.398351\pi$
$168$	9.12276			0.703836
$169$	5.51496	+	16.9733i	0.424228	+	1.30564i
$170$	24.8274	+	12.3372i	1.90417	+	0.946220i
$171$	2.38542	−	7.34155i	0.182417	−	0.561423i
$172$	2.93437	−	9.03107i	0.223744	−	0.688612i
$173$	9.44604	−	6.86295i	0.718169	−	0.521780i	−0.167630	−	0.985850i	$-0.553611\pi$
$173$	9.44604	−	6.86295i	0.718169	−	0.521780i	0.885799	+	0.464070i	$0.153611\pi$
$174$	−3.22571			−0.244541
$175$	−4.72324	+	1.64043i	−0.357043	+	0.124005i
$176$	−17.0809			−1.28752
$177$	6.93628	−	5.03950i	0.521363	−	0.378792i
$178$	−6.07518	+	18.6975i	−0.455354	+	1.40143i
$179$	−5.21531	+	16.0511i	−0.389810	+	1.19971i	0.543120	+	0.839655i	$0.317243\pi$
$179$	−5.21531	+	16.0511i	−0.389810	+	1.19971i	−0.932930	+	0.360058i	$0.882757\pi$
$180$	8.39266	−	8.56322i	0.625552	−	0.638265i
$181$	−3.65451	−	11.2474i	−0.271638	−	0.836015i	−0.990089	−	0.140438i	$-0.955149\pi$
$181$	−3.65451	−	11.2474i	−0.271638	−	0.836015i	0.718452	−	0.695577i	$-0.244851\pi$
$182$	−15.0698			−1.11705
$183$	1.95865	+	6.02811i	0.144788	+	0.445611i
$184$	−17.0267	−	12.3706i	−1.25522	−	0.911973i
$185$	3.20081	+	1.59055i	0.235328	+	0.116939i
$186$	−18.9800	+	13.7898i	−1.39168	+	1.01112i
$187$	−4.50105	−	3.27020i	−0.329149	−	0.239141i
$188$	2.94960	+	2.14301i	0.215122	+	0.156295i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−41.9420	−	20.8418i	−3.04279	−	1.51202i
$191$	−11.7141	−	8.51078i	−0.847602	−	0.615819i	0.0768821	−	0.997040i	$-0.475504\pi$
$191$	−11.7141	−	8.51078i	−0.847602	−	0.615819i	−0.924484	+	0.381222i	$0.875504\pi$
$192$	7.94747	+	24.4598i	0.573559	+	1.76523i
$193$	24.9611			1.79674			0.898371	−	0.439237i	$-0.144751\pi$
$193$	24.9611			1.79674			0.898371	+	0.439237i	$0.144751\pi$
$194$	−3.64797	−	11.2273i	−0.261909	−	0.806073i
$195$	−8.69285	+	8.86951i	−0.622508	+	0.635159i
$196$	1.65701	−	5.09975i	0.118358	−	0.364268i
$197$	0.422324	−	1.29978i	0.0300893	−	0.0926055i	−0.934884	−	0.354953i	$-0.884497\pi$
$197$	0.422324	−	1.29978i	0.0300893	−	0.0926055i	0.964973	+	0.262348i	$0.0844968\pi$
$198$	−2.67273	+	1.94185i	−0.189942	+	0.138001i
$199$	13.4182			0.951190			0.475595	−	0.879664i	$-0.342233\pi$
$199$	13.4182			0.951190			0.475595	+	0.879664i	$0.342233\pi$
$200$	−27.5480	−	36.3555i	−1.94794	−	2.57073i
$201$	9.40376			0.663290
$202$	−20.2337	+	14.7006i	−1.42364	+	1.03433i
$203$	−0.367371	+	1.13065i	−0.0257844	+	0.0793561i
$204$	−7.57160	+	23.3030i	−0.530118	+	1.63154i
$205$	−16.2571	−	8.07846i	−1.13544	−	0.564224i
$206$	8.59750	+	26.4604i	0.599016	+	1.84358i
$207$	−2.30699			−0.160347
$208$	−24.0772	−	74.1020i	−1.66945	−	5.13805i
$209$	7.60383	+	5.52450i	0.525968	+	0.382138i
$210$	−2.80869	−	5.37794i	−0.193818	−	0.371113i
$211$	−2.65178	+	1.92663i	−0.182556	+	0.132635i	−0.675310	−	0.737534i	$-0.735990\pi$
$211$	−2.65178	+	1.92663i	−0.182556	+	0.132635i	0.492754	+	0.870169i	$0.335990\pi$
$212$	19.5672	+	14.2164i	1.34388	+	0.976386i
$213$	−6.88683	−	5.00358i	−0.471878	−	0.342839i
$214$	33.6647	−	24.4588i	2.30127	−	1.67197i
$215$	−3.90464	+	0.658760i	−0.266294	+	0.0449271i
$216$	7.38047	+	5.36222i	0.502177	+	0.364853i
$217$	2.67188	+	8.22321i	0.181379	+	0.558228i
$218$	26.3508			1.78470
$219$	2.37000	+	7.29412i	0.160150	+	0.492891i
$220$	6.75827	+	12.9404i	0.455643	+	0.872442i
$221$	7.84242	−	24.1365i	0.527538	−	1.62360i
$222$	−1.34024	+	4.12483i	−0.0899509	+	0.276840i
$223$	−3.02786	+	2.19987i	−0.202760	+	0.147314i	−0.684532	−	0.728983i	$-0.739993\pi$
$223$	−3.02786	+	2.19987i	−0.202760	+	0.147314i	0.481772	+	0.876297i	$0.339993\pi$
$224$	19.8191			1.32422
$225$	−4.78540	−	1.44911i	−0.319027	−	0.0966076i
$226$	−33.2483			−2.21165
$227$	11.7052	−	8.50433i	0.776902	−	0.564452i	−0.127146	−	0.991884i	$-0.540582\pi$
$227$	11.7052	−	8.50433i	0.776902	−	0.564452i	0.904048	+	0.427432i	$0.140582\pi$
$228$	12.7911	−	39.3668i	0.847108	−	2.60713i
$229$	3.84851	−	11.8445i	0.254317	−	0.782707i	−0.739647	−	0.672995i	$-0.765007\pi$
$229$	3.84851	−	11.8445i	0.254317	−	0.782707i	0.993964	−	0.109711i	$-0.0349926\pi$
$230$	−2.05044	+	13.8460i	−0.135202	+	0.912977i
$231$	0.376249	+	1.15798i	0.0247554	+	0.0761892i
$232$	−10.8455			−0.712040
$233$	1.95528	+	6.01774i	0.128095	+	0.394235i	0.994452	−	0.105189i	$-0.0335448\pi$
$233$	1.95528	+	6.01774i	0.128095	+	0.394235i	−0.866357	+	0.499424i	$0.833545\pi$
$234$	−12.1918	−	8.85783i	−0.797000	−	0.579054i
$235$	0.222721	−	1.50397i	0.0145287	−	0.0981079i
$236$	37.1937	−	27.0228i	2.42110	−	1.75903i
$237$	11.4555	+	8.32288i	0.744112	+	0.540629i
$238$	10.0305	+	7.28761i	0.650183	+	0.472386i
$239$	−13.2200	+	9.60489i	−0.855130	+	0.621289i	−0.926556	−	0.376157i	$-0.877245\pi$
$239$	−13.2200	+	9.60489i	−0.855130	+	0.621289i	0.0714253	+	0.997446i	$0.477245\pi$
$240$	21.9571	−	22.4034i	1.41733	−	1.44613i
$241$	−1.61269	−	1.17169i	−0.103882	−	0.0754749i	0.534631	−	0.845085i	$-0.320450\pi$
$241$	−1.61269	−	1.17169i	−0.103882	−	0.0754749i	−0.638514	+	0.769610i	$0.720450\pi$
$242$	7.98013	+	24.5603i	0.512982	+	1.57880i
$243$	1.00000			0.0641500
$244$	10.5027	+	32.3239i	0.672364	+	2.06932i
$245$	−2.20491	+	0.371995i	−0.140866	+	0.0237659i
$246$	6.80713	−	20.9502i	0.434007	−	1.33574i
$247$	−13.2486	+	40.7749i	−0.842986	+	2.59444i
$248$	−63.8145	+	46.3639i	−4.05222	+	2.94411i
$249$	−8.02476			−0.508548
$250$	−12.9505	+	27.4328i	−0.819060	+	1.73500i
$251$	−7.57995			−0.478442			−0.239221	−	0.970965i	$-0.576892\pi$
$251$	−7.57995			−0.478442			−0.239221	+	0.970965i	$0.576892\pi$
$252$	4.33811	−	3.15182i	0.273275	−	0.198546i
$253$	0.868003	−	2.67144i	0.0545709	−	0.167952i
$254$	16.0053	−	49.2591i	1.00426	−	3.09079i
$255$	10.0752	−	1.69981i	0.630933	−	0.106446i
$256$	9.38045	+	28.8701i	0.586278	+	1.80438i
$257$	−21.7469			−1.35653			−0.678266	−	0.734816i	$-0.737268\pi$
$257$	−21.7469			−1.35653			−0.678266	+	0.734816i	$0.737268\pi$
$258$	−1.48483	−	4.56983i	−0.0924414	−	0.284505i
$259$	1.29316	+	0.939538i	0.0803533	+	0.0583801i
$260$	−46.6128	+	47.5600i	−2.89080	+	2.94955i
$261$	−0.961789	+	0.698780i	−0.0595332	+	0.0432534i
$262$	22.9466	+	16.6717i	1.41765	+	1.02998i
$263$	14.7339	+	10.7048i	0.908532	+	0.660087i	0.940643	−	0.339397i	$-0.110223\pi$
$263$	14.7339	+	10.7048i	0.908532	+	0.660087i	−0.0321110	+	0.999484i	$0.510223\pi$
$264$	−8.98622	+	6.52887i	−0.553064	+	0.401824i
$265$	1.47750	−	9.97706i	0.0907619	−	0.612886i
$266$	−16.9451	−	12.3113i	−1.03897	−	0.754854i
$267$	2.23901	+	6.89095i	0.137025	+	0.421719i
$268$	50.4248			3.08018
$269$	−6.11424	−	18.8177i	−0.372792	−	1.14733i	−0.944956	−	0.327196i	$-0.893896\pi$
$269$	−6.11424	−	18.8177i	−0.372792	−	1.14733i	0.572165	−	0.820139i	$-0.306104\pi$
$270$	0.888796	−	6.00175i	0.0540904	−	0.365255i
$271$	1.24488	−	3.83135i	0.0756211	−	0.232738i	−0.906100	−	0.423064i	$-0.860955\pi$
$271$	1.24488	−	3.83135i	0.0756211	−	0.232738i	0.981721	+	0.190326i	$0.0609545\pi$
$272$	−19.8090	+	60.9660i	−1.20110	+	3.69661i
$273$	−4.49327	+	3.26455i	−0.271945	+	0.197580i
$274$	−15.5273			−0.938038
$275$	3.47854	−	4.99615i	0.209764	−	0.301279i
$276$	−12.3705			−0.744618
$277$	−2.34940	+	1.70694i	−0.141161	+	0.102560i	−0.656125	−	0.754652i	$-0.727806\pi$
$277$	−2.34940	+	1.70694i	−0.141161	+	0.102560i	0.514963	+	0.857212i	$0.327806\pi$
$278$	−14.3690	+	44.2233i	−0.861797	+	2.65234i
$279$	−2.67188	+	8.22321i	−0.159962	+	0.492311i
$280$	−9.44336	−	18.0817i	−0.564349	−	1.08059i
$281$	3.18882	+	9.81417i	0.190229	+	0.585464i	0.999999	−	0.00128287i	$-0.000408349\pi$
$281$	3.18882	+	9.81417i	0.190229	+	0.585464i	−0.809770	+	0.586747i	$0.800408\pi$
$282$	1.84488			0.109861
$283$	6.16320	+	18.9684i	0.366364	+	1.12755i	0.949122	+	0.314907i	$0.101973\pi$
$283$	6.16320	+	18.9684i	0.366364	+	1.12755i	−0.582758	+	0.812645i	$0.698027\pi$
$284$	−36.9285	−	26.8301i	−2.19130	−	1.59208i
$285$	−17.0205	+	2.87157i	−1.00821	+	0.170097i
$286$	14.8443	−	10.7850i	0.877761	−	0.637731i
$287$	−6.56804	−	4.77196i	−0.387699	−	0.281680i
$288$	16.0340	+	11.6494i	0.944814	+	0.686448i
$289$	−3.13879	+	2.28047i	−0.184635	+	0.134145i
$290$	3.33907	+	6.39349i	0.196077	+	0.375439i
$291$	−3.51984	−	2.55731i	−0.206337	−	0.149912i
$292$	12.7084	+	39.1125i	0.743704	+	2.28888i
$293$	−25.0562			−1.46380			−0.731898	−	0.681414i	$-0.761365\pi$
$293$	−25.0562			−1.46380			−0.731898	+	0.681414i	$0.761365\pi$
$294$	−0.838467	−	2.58054i	−0.0489004	−	0.150500i
$295$	−17.1685	−	8.53137i	−0.999590	−	0.496716i
$296$	−4.50614	+	13.8685i	−0.261914	+	0.806088i
$297$	−0.376249	+	1.15798i	−0.0218322	+	0.0671926i
$298$	−23.2110	+	16.8638i	−1.34457	+	0.976891i
$299$	12.8130			0.740995
$300$	−25.6602	−	7.77043i	−1.48150	−	0.448626i
$301$	−1.77088			−0.102072
$302$	−5.89521	+	4.28312i	−0.339231	+	0.246466i
$303$	−2.84837	+	8.76638i	−0.163634	+	0.503615i
$304$	33.4643	−	102.993i	1.91931	−	5.90704i
$305$	9.92047	−	10.1221i	0.568044	−	0.579588i
$306$	3.83132	+	11.7916i	0.219022	+	0.674081i
$307$	12.1248			0.691996			0.345998	−	0.938235i	$-0.387540\pi$
$307$	12.1248			0.691996			0.345998	+	0.938235i	$0.387540\pi$
$308$	2.01752	+	6.20929i	0.114959	+	0.353807i
$309$	8.29552	+	6.02705i	0.471916	+	0.342867i
$310$	46.9789	+	23.3447i	2.66822	+	1.32589i
$311$	−11.3874	+	8.27345i	−0.645722	+	0.469144i	−0.861811	−	0.507229i	$-0.830670\pi$
$311$	−11.3874	+	8.27345i	−0.645722	+	0.469144i	0.216089	+	0.976374i	$0.430670\pi$
$312$	−40.9910	−	29.7817i	−2.32066	−	1.68606i
$313$	−17.8264	−	12.9517i	−1.00761	−	0.732071i	−0.0439035	−	0.999036i	$-0.513979\pi$
$313$	−17.8264	−	12.9517i	−1.00761	−	0.732071i	−0.963706	+	0.266964i	$0.913979\pi$
$314$	−9.26375	+	6.73051i	−0.522784	+	0.379824i
$315$	−2.00246	−	0.995062i	−0.112826	−	0.0560654i
$316$	61.4264	+	44.6289i	3.45550	+	2.51057i
$317$	−3.79705	−	11.6861i	−0.213263	−	0.656357i	−0.999272	−	0.0381422i	$-0.987856\pi$
$317$	−3.79705	−	11.6861i	−0.213263	−	0.656357i	0.786009	−	0.618215i	$-0.212144\pi$
$318$	12.2386			0.686307
$319$	−0.447299	−	1.37664i	−0.0250439	−	0.0770772i
$320$	40.2535	−	41.0715i	2.25024	−	2.29597i
$321$	4.73910	−	14.5854i	0.264510	−	0.814080i
$322$	−1.93434	+	5.95327i	−0.107796	+	0.331763i
$323$	28.5366	−	20.7330i	1.58782	−	1.15362i
$324$	5.36219			0.297900
$325$	26.5781	+	8.04837i	1.47429	+	0.446443i
$326$	−27.1491			−1.50365
$327$	7.85684	−	5.70833i	0.434484	−	0.315671i
$328$	22.8869	−	70.4386i	1.26372	−	3.88932i
$329$	0.210110	−	0.646651i	0.0115837	−	0.0356510i
$330$	6.61547	+	3.28736i	0.364170	+	0.180963i
$331$	1.49465	+	4.60006i	0.0821534	+	0.252842i	0.983693	−	0.179854i	$-0.0575624\pi$
$331$	1.49465	+	4.60006i	0.0821534	+	0.252842i	−0.901540	+	0.432696i	$0.857562\pi$
$332$	−43.0303			−2.36160
$333$	0.493945	+	1.52021i	0.0270680	+	0.0833067i
$334$	−45.7261	−	33.2219i	−2.50202	−	1.81782i
$335$	−9.73423	−	18.6386i	−0.531838	−	1.01834i
$336$	11.3495	−	8.24588i	0.619165	−	0.449850i
$337$	−9.23188	−	6.70735i	−0.502892	−	0.365373i	0.307228	−	0.951636i	$-0.400598\pi$
$337$	−9.23188	−	6.70735i	−0.502892	−	0.365373i	−0.810121	+	0.586263i	$0.800598\pi$
$338$	39.1761	+	28.4631i	2.13090	+	1.54819i
$339$	−9.91343	+	7.20253i	−0.538424	+	0.391188i
$340$	54.0251	−	9.11470i	2.92992	−	0.494314i
$341$	−8.51699	−	6.18795i	−0.461221	−	0.335096i
$342$	−6.47243	−	19.9201i	−0.349989	−	1.07716i
$343$	−1.00000			−0.0539949
$344$	−4.99228	−	15.3647i	−0.269166	−	0.828407i
$345$	2.38806	+	4.57255i	0.128569	+	0.246178i
$346$	9.78989	−	30.1302i	0.526308	−	1.61981i
$347$	2.75595	−	8.48194i	0.147947	−	0.455334i	−0.849431	−	0.527699i	$-0.823055\pi$
$347$	2.75595	−	8.48194i	0.147947	−	0.455334i	0.997378	+	0.0723652i	$0.0230547\pi$
$348$	−5.15730	+	3.74700i	−0.276460	+	0.200860i
$349$	−13.7985			−0.738617			−0.369309	−	0.929307i	$-0.620405\pi$
$349$	−13.7985			−0.738617			−0.369309	+	0.929307i	$0.620405\pi$
$350$	−7.75189	+	11.1339i	−0.414356	+	0.595130i
$351$	−5.55399			−0.296450
$352$	−19.5225	+	14.1839i	−1.04055	+	0.756006i
$353$	8.60094	−	26.4710i	0.457782	−	1.40891i	−0.410056	−	0.912060i	$-0.634491\pi$
$353$	8.60094	−	26.4710i	0.457782	−	1.40891i	0.867838	−	0.496847i	$-0.165509\pi$
$354$	7.18877	−	22.1248i	0.382079	−	1.17592i
$355$	−2.78843	+	18.8294i	−0.147995	+	0.999360i
$356$	12.0060	+	36.9506i	0.636316	+	1.95838i
$357$	4.56944			0.241840
$358$	14.1509	+	43.5519i	0.747897	+	2.30179i
$359$	0.563645	+	0.409512i	0.0297481	+	0.0216132i	0.602560	−	0.798074i	$-0.294147\pi$
$359$	0.563645	+	0.409512i	0.0297481	+	0.0216132i	−0.572812	+	0.819687i	$0.694147\pi$
$360$	2.98830	−	20.1790i	0.157497	−	1.06353i
$361$	−32.8369	+	23.8574i	−1.72826	+	1.25565i
$362$	−25.9602	−	18.8612i	−1.36444	−	0.991322i
$363$	7.69984	+	5.59426i	0.404137	+	0.293623i
$364$	−24.0938	+	17.5052i	−1.26286	+	0.917520i
$365$	12.0039	−	12.2479i	0.628315	−	0.641084i
$366$	13.9135	+	10.1087i	0.727270	+	0.528392i
$367$	1.78709	+	5.50010i	0.0932854	+	0.287103i	0.986803	−	0.161925i	$-0.0517703\pi$
$367$	1.78709	+	5.50010i	0.0932854	+	0.287103i	−0.893518	+	0.449028i	$0.851770\pi$
$368$	−32.3641			−1.68710
$369$	−2.50877	−	7.72120i	−0.130601	−	0.401949i
$370$	9.56291	−	1.61338i	0.497152	−	0.0838756i
$371$	1.39383	−	4.28978i	0.0723642	−	0.222714i
$372$	−14.3272	+	44.0945i	−0.742829	+	2.28619i
$373$	−9.22509	+	6.70242i	−0.477657	+	0.347038i	−0.800418	−	0.599442i	$-0.795389\pi$
$373$	−9.22509	+	6.70242i	−0.477657	+	0.347038i	0.322761	+	0.946481i	$0.395389\pi$
$374$	−15.0959			−0.780591
$375$	2.08137	+	10.9849i	0.107481	+	0.567257i
$376$	6.20283			0.319886
$377$	5.34176	−	3.88102i	0.275115	−	0.199883i
$378$	0.838467	−	2.58054i	0.0431261	−	0.132728i
$379$	7.79142	−	23.9795i	0.400218	−	1.23175i	−0.524604	−	0.851346i	$-0.675787\pi$
$379$	7.79142	−	23.9795i	0.400218	−	1.23175i	0.924822	−	0.380399i	$-0.124213\pi$
$380$	−91.2672	+	15.3979i	−4.68191	+	0.789895i
$381$	−5.89874	−	18.1545i	−0.302202	−	0.930081i
$382$	−39.2875			−2.01012
$383$	2.80576	+	8.63525i	0.143368	+	0.441241i	0.996797	−	0.0799674i	$-0.0254816\pi$
$383$	2.80576	+	8.63525i	0.143368	+	0.441241i	−0.853430	+	0.521208i	$0.825482\pi$
$384$	24.3876	+	17.7186i	1.24453	+	0.904201i
$385$	1.90568	−	1.94441i	0.0971225	−	0.0990963i
$386$	54.7931	−	39.8095i	2.78889	−	2.02625i
$387$	−1.43268	−	1.04090i	−0.0728270	−	0.0529119i
$388$	−18.8741	−	13.7128i	−0.958185	−	0.696162i
$389$	−8.76708	+	6.36966i	−0.444509	+	0.322954i	−0.787424	−	0.616412i	$-0.788586\pi$
$389$	−8.76708	+	6.36966i	−0.444509	+	0.322954i	0.342915	+	0.939366i	$0.388586\pi$
$390$	−4.93636	+	33.3336i	−0.249962	+	1.68791i
$391$	−8.52837	−	6.19623i	−0.431298	−	0.313357i
$392$	−2.81909	−	8.67626i	−0.142385	−	0.438217i
$393$	10.4534			0.527304
$394$	−1.14591	−	3.52674i	−0.0577300	−	0.177675i
$395$	4.63824	−	31.3205i	0.233375	−	1.57591i
$396$	−2.01752	+	6.20929i	−0.101384	+	0.312029i
$397$	11.1606	−	34.3486i	0.560132	−	1.72391i	−0.121858	−	0.992548i	$-0.538885\pi$
$397$	11.1606	−	34.3486i	0.560132	−	1.72391i	0.681990	−	0.731361i	$-0.261115\pi$
$398$	29.4547	−	21.4001i	1.47643	−	1.07269i
$399$	−7.71937			−0.386452
$400$	−67.1331	−	20.3292i	−3.35666	−	1.01646i
$401$	−11.5543			−0.576994			−0.288497	−	0.957481i	$-0.593156\pi$
$401$	−11.5543			−0.576994			−0.288497	+	0.957481i	$0.593156\pi$
$402$	20.6425	−	14.9977i	1.02956	−	0.748016i
$403$	14.8396	−	45.6716i	0.739214	−	2.27507i
$404$	−15.2735	+	47.0070i	−0.759885	+	2.33869i
$405$	−1.03514	−	1.98204i	−0.0514366	−	0.0984883i
$406$	0.996800	+	3.06783i	0.0494704	+	0.152254i
$407$	−1.94621			−0.0964699
$408$	12.8816	+	39.6456i	0.637737	+	1.96275i
$409$	15.9235	+	11.5691i	0.787365	+	0.572054i	0.907180	−	0.420742i	$-0.138230\pi$
$409$	15.9235	+	11.5691i	0.787365	+	0.572054i	−0.119815	+	0.992796i	$0.538230\pi$
$410$	−48.5705	+	8.19444i	−2.39872	+	0.404694i
$411$	−4.62967	+	3.36365i	−0.228365	+	0.165917i
$412$	44.4822	+	32.3182i	2.19148	+	1.59220i
$413$	−6.93628	−	5.03950i	−0.341312	−	0.247978i
$414$	−5.06416	+	3.67932i	−0.248890	+	0.180829i
$415$	8.30677	+	15.9054i	0.407763	+	0.780765i
$416$	−89.0528	−	64.7006i	−4.36617	−	3.17221i
$417$	5.29571	+	16.2985i	0.259332	+	0.798141i
$418$	25.5022			1.24736
$419$	9.30936	+	28.6513i	0.454792	+	1.39971i	0.871379	+	0.490610i	$0.163226\pi$
$419$	9.30936	+	28.6513i	0.454792	+	1.39971i	−0.416587	+	0.909096i	$0.636774\pi$
$420$	−10.7376	−	5.33572i	−0.523941	−	0.260356i
$421$	7.91586	−	24.3625i	0.385795	−	1.18736i	−0.550106	−	0.835095i	$-0.685413\pi$
$421$	7.91586	−	24.3625i	0.385795	−	1.18736i	0.935902	−	0.352261i	$-0.114587\pi$
$422$	−2.74831	+	8.45842i	−0.133786	+	0.411750i
$423$	0.550074	−	0.399652i	0.0267455	−	0.0194318i
$424$	41.1486			1.99835
$425$	−13.7983	−	18.2099i	−0.669318	−	0.883309i
$426$	−23.0975			−1.11908
$427$	5.12782	−	3.72558i	0.248152	−	0.180293i
$428$	25.4119	−	78.2099i	1.22833	−	3.78042i
$429$	2.08968	−	6.43138i	0.100891	−	0.310510i
$430$	−7.52058	+	7.67342i	−0.362674	+	0.370045i
$431$	7.46330	+	22.9697i	0.359495	+	1.10641i	0.953357	+	0.301844i	$0.0976023\pi$
$431$	7.46330	+	22.9697i	0.359495	+	1.10641i	−0.593862	+	0.804567i	$0.702398\pi$
$432$	14.0287			0.674958
$433$	−0.156625	−	0.482041i	−0.00752690	−	0.0231654i	0.947223	−	0.320577i	$-0.103877\pi$
$433$	−0.156625	−	0.482041i	−0.00752690	−	0.0231654i	−0.954749	+	0.297411i	$0.903877\pi$
$434$	18.9800	+	13.7898i	0.911070	+	0.661931i
$435$	2.38060	+	1.18297i	0.114141	+	0.0567189i
$436$	42.1299	−	30.6092i	2.01766	−	1.46591i
$437$	14.4074	+	10.4676i	0.689198	+	0.500732i
$438$	16.8356	+	12.2318i	0.804434	+	0.584456i
$439$	3.15125	−	2.28952i	0.150401	−	0.109273i	−0.510040	−	0.860151i	$-0.670369\pi$
$439$	3.15125	−	2.28952i	0.150401	−	0.109273i	0.660441	+	0.750878i	$0.270369\pi$
$440$	22.2425	+	11.0527i	1.06037	+	0.526918i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−21.2791	−	65.4904i	−1.01214	−	3.11506i
$443$	27.2601			1.29517			0.647583	−	0.761995i	$-0.275780\pi$
$443$	27.2601			1.29517			0.647583	+	0.761995i	$0.275780\pi$
$444$	2.64863	+	8.15163i	0.125698	+	0.386859i
$445$	11.3404	−	11.5709i	0.537589	−	0.548514i
$446$	−3.13808	+	9.65801i	−0.148592	+	0.457320i
$447$	−3.26749	+	10.0563i	−0.154547	+	0.475647i
$448$	20.8067	−	15.1170i	0.983026	−	0.714210i
$449$	−19.8847			−0.938416			−0.469208	−	0.883088i	$-0.655461\pi$
$449$	−19.8847			−0.938416			−0.469208	+	0.883088i	$0.655461\pi$
$450$	−12.8157	+	4.45104i	−0.604140	+	0.209824i
$451$	9.88488			0.465461
$452$	−53.1577	+	38.6214i	−2.50033	+	1.81660i
$453$	−0.829890	+	2.55414i	−0.0389916	+	0.120004i
$454$	12.1313	−	37.3363i	0.569350	−	1.75228i
$455$	11.1216	+	5.52656i	0.521391	+	0.259089i
$456$	−21.7616	−	66.9752i	−1.01908	−	3.13640i
$457$	12.8102			0.599235			0.299618	−	0.954059i	$-0.403141\pi$
$457$	12.8102			0.599235			0.299618	+	0.954059i	$0.403141\pi$
$458$	−10.4423	−	32.1381i	−0.487937	−	1.50172i
$459$	3.69675	+	2.68585i	0.172550	+	0.125365i
$460$	12.8053	+	24.5189i	0.597048	+	1.14320i
$461$	−10.5519	+	7.66642i	−0.491452	+	0.357061i	−0.805742	−	0.592266i	$-0.798233\pi$
$461$	−10.5519	+	7.66642i	−0.491452	+	0.357061i	0.314290	+	0.949327i	$0.398233\pi$
$462$	2.67273	+	1.94185i	0.124346	+	0.0903430i
$463$	−2.26872	−	1.64832i	−0.105436	−	0.0766040i	0.533818	−	0.845600i	$-0.320757\pi$
$463$	−2.26872	−	1.64832i	−0.105436	−	0.0766040i	−0.639254	+	0.768995i	$0.720757\pi$
$464$	−13.4927	+	9.80300i	−0.626382	+	0.455093i
$465$	19.0645	−	3.21642i	0.884096	−	0.149158i
$466$	13.8896	+	10.0913i	0.643421	+	0.467473i
$467$	0.314836	+	0.968966i	0.0145689	+	0.0448384i	0.958077	−	0.286512i	$-0.0924958\pi$
$467$	0.314836	+	0.968966i	0.0145689	+	0.0448384i	−0.943508	+	0.331350i	$0.892496\pi$
$468$	−29.7816			−1.37665
$469$	−2.90592	−	8.94350i	−0.134183	−	0.412973i
$470$	−1.90971	−	3.65662i	−0.0880883	−	0.168667i
$471$	−1.30409	+	4.01358i	−0.0600893	+	0.184936i
$472$	24.1700	−	74.3878i	1.11252	−	3.42397i
$473$	1.74438	−	1.26737i	0.0802067	−	0.0582735i
$474$	38.4201			1.76469
$475$	23.3102	+	30.7628i	1.06954	+	1.41149i
$476$	24.5022			1.12306
$477$	3.64910	−	2.65123i	0.167081	−	0.121391i
$478$	−13.7012	+	42.1681i	−0.626680	+	1.92872i
$479$	−6.74573	+	20.7612i	−0.308220	+	0.948604i	0.670236	+	0.742148i	$0.266193\pi$
$479$	−6.74573	+	20.7612i	−0.308220	+	0.948604i	−0.978456	+	0.206456i	$0.933807\pi$
$480$	6.49207	−	43.8389i	0.296321	−	2.00096i
$481$	−2.74336	−	8.44320i	−0.125087	−	0.384977i
$482$	−5.40874			−0.246361
$483$	0.712899	+	2.19408i	0.0324380	+	0.0998340i
$484$	41.2880	+	29.9975i	1.87673	+	1.36352i
$485$	−1.42516	+	9.62364i	−0.0647132	+	0.436987i
$486$	2.19514	−	1.59486i	0.0995734	−	0.0723443i
$487$	10.0474	+	7.29990i	0.455293	+	0.330790i	0.791682	−	0.610933i	$-0.209206\pi$
$487$	10.0474	+	7.29990i	0.455293	+	0.330790i	−0.336389	+	0.941723i	$0.609206\pi$
$488$	46.7798	+	33.9875i	2.11762	+	1.53854i
$489$	−8.09486	+	5.88126i	−0.366062	+	0.265960i
$490$	−4.24679	+	4.33310i	−0.191850	+	0.195749i
$491$	33.6945	+	24.4805i	1.52061	+	1.10479i	0.961184	+	0.275909i	$0.0889787\pi$
$491$	33.6945	+	24.4805i	1.52061	+	1.10479i	0.559427	+	0.828880i	$0.311021\pi$
$492$	−13.4525	−	41.4025i	−0.606486	−	1.86657i
$493$	−5.43231			−0.244659
$494$	35.9478	+	110.636i	1.61737	+	4.97775i
$495$	2.68462	−	0.452929i	0.120665	−	0.0203577i
$496$	−37.4832	+	115.361i	−1.68304	+	5.17987i
$497$	−2.63054	+	8.09596i	−0.117996	+	0.363153i
$498$	−17.6154	+	12.7984i	−0.789366	+	0.573508i
$499$	18.5655			0.831106			0.415553	−	0.909569i	$-0.363588\pi$
$499$	18.5655			0.831106			0.415553	+	0.909569i	$0.363588\pi$
$500$	11.1607	+	58.9031i	0.499122	+	2.63423i
$501$	−20.8306			−0.930645
$502$	−16.6390	+	12.0890i	−0.742636	+	0.539556i
$503$	−4.51980	+	13.9105i	−0.201528	+	0.620239i	0.798310	+	0.602246i	$0.205728\pi$
$503$	−4.51980	+	13.9105i	−0.201528	+	0.620239i	−0.999838	+	0.0179925i	$0.994272\pi$
$504$	2.81909	−	8.67626i	0.125572	−	0.386471i
$505$	20.3238	−	3.42887i	0.904396	−	0.152583i
$506$	−2.35518	−	7.24851i	−0.104701	−	0.322236i
$507$	17.8468			0.792603
$508$	−31.6302	−	97.3477i	−1.40336	−	4.31911i
$509$	−19.7695	−	14.3634i	−0.876269	−	0.636647i	0.0559928	−	0.998431i	$-0.482168\pi$
$509$	−19.7695	−	14.3634i	−0.876269	−	0.636647i	−0.932262	+	0.361784i	$0.882168\pi$
$510$	19.4054	−	19.7998i	0.859288	−	0.876751i
$511$	6.20475	−	4.50801i	0.274482	−	0.199423i
$512$	17.8598	+	12.9759i	0.789299	+	0.573459i
$513$	−6.24510	−	4.53733i	−0.275728	−	0.200328i
$514$	−47.7373	+	34.6832i	−2.10560	+	1.52981i
$515$	3.35880	−	22.6809i	0.148006	−	0.999440i
$516$	−7.68229	−	5.58151i	−0.338194	−	0.245712i
$517$	0.255823	+	0.787341i	0.0112511	+	0.0346272i
$518$	4.33710			0.190561
$519$	−3.60806	−	11.1045i	−0.158376	−	0.487433i
$520$	−16.5970	+	112.074i	−0.727827	+	4.91478i
$521$	13.4308	−	41.3357i	0.588413	−	1.81095i	0.00330227	−	0.999995i	$-0.498949\pi$
$521$	13.4308	−	41.3357i	0.588413	−	1.81095i	0.585110	−	0.810954i	$-0.301051\pi$
$522$	−0.996800	+	3.06783i	−0.0436288	+	0.134275i
$523$	0.216622	−	0.157385i	0.00947223	−	0.00688198i	−0.583039	−	0.812444i	$-0.698137\pi$
$523$	0.216622	−	0.157385i	0.00947223	−	0.00688198i	0.592511	+	0.805562i	$0.298137\pi$
$524$	56.0531			2.44869
$525$	0.100580	+	4.99899i	0.00438969	+	0.218174i
$526$	49.4156			2.15462
$527$	−31.9636	+	23.2229i	−1.39236	+	1.01161i
$528$	−5.27830	+	16.2449i	−0.229708	+	0.706970i
$529$	−5.46274	+	16.8126i	−0.237510	+	0.730982i
$530$	−12.6687	−	24.2574i	−0.550293	−	1.05367i
$531$	−2.64942	−	8.15408i	−0.114975	−	0.353857i
$532$	−41.3927			−1.79460
$533$	13.9337	+	42.8834i	0.603534	+	1.85749i
$534$	15.9050	+	11.5557i	0.688277	+	0.500063i
$535$	−33.8145	+	5.70493i	−1.46193	+	0.246646i
$536$	69.4041	−	50.4250i	2.99780	−	2.17803i
$537$	13.6539	+	9.92010i	0.589207	+	0.428084i
$538$	−43.4331	−	31.5560i	−1.87254	−	1.36048i
$539$	0.985033	−	0.715668i	0.0424284	−	0.0308260i
$540$	−5.55063	−	10.6281i	−0.238861	−	0.457360i
$541$	−23.6706	−	17.1977i	−1.01768	−	0.739386i	−0.0518725	−	0.998654i	$-0.516519\pi$
$541$	−23.6706	−	17.1977i	−1.01768	−	0.739386i	−0.965806	+	0.259267i	$0.916519\pi$
$542$	−3.37778	−	10.3957i	−0.145088	−	0.446535i
$543$	−11.8262			−0.507513
$544$	27.9853	+	86.1299i	1.19986	+	3.69279i
$545$	−19.4471	−	9.66363i	−0.833021	−	0.413944i
$546$	−4.65684	+	14.3323i	−0.199294	+	0.613364i
$547$	6.32579	−	19.4688i	0.270471	−	0.832425i	−0.719911	−	0.694066i	$-0.755817\pi$
$547$	6.32579	−	19.4688i	0.270471	−	0.832425i	0.990382	−	0.138358i	$-0.0441826\pi$
$548$	−24.8252	+	18.0365i	−1.06048	+	0.770483i
$549$	6.33833			0.270513
$550$	−0.332285	−	16.5150i	−0.0141687	−	0.704202i
$551$	9.17706			0.390956
$552$	−17.0267	+	12.3706i	−0.724703	+	0.526528i
$553$	4.37560	−	13.4667i	0.186069	−	0.572662i
$554$	−2.43492	+	7.49391i	−0.103450	+	0.318386i
$555$	2.50180	−	2.55265i	0.106196	−	0.108354i
$556$	28.3966	+	87.3958i	1.20428	+	3.70641i
$557$	38.7246			1.64081			0.820406	−	0.571781i	$-0.193747\pi$
$557$	38.7246			1.64081			0.820406	+	0.571781i	$0.193747\pi$
$558$	7.24972	+	22.3123i	0.306905	+	0.944557i
$559$	7.95706	+	5.78115i	0.336548	+	0.244516i
$560$	−28.0920	−	13.9595i	−1.18710	−	0.589895i
$561$	−4.50105	+	3.27020i	−0.190034	+	0.138068i
$562$	22.6521	+	16.4577i	0.955521	+	0.694227i
$563$	12.6288	+	9.17532i	0.532238	+	0.386694i	0.821194	−	0.570649i	$-0.193308\pi$
$563$	12.6288	+	9.17532i	0.532238	+	0.386694i	−0.288956	+	0.957342i	$0.593308\pi$
$564$	2.94960	−	2.14301i	0.124201	−	0.0902371i
$565$	24.5375	+	12.1932i	1.03230	+	0.512970i
$566$	43.7809	+	31.8087i	1.84025	+	1.33702i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	−77.6584			−3.25847
$569$	0.750778	+	2.31066i	0.0314743	+	0.0968678i	0.965560	−	0.260182i	$-0.0837826\pi$
$569$	0.750778	+	2.31066i	0.0314743	+	0.0968678i	−0.934085	+	0.357050i	$0.883783\pi$
$570$	−32.7825	+	33.4488i	−1.37311	+	1.40101i
$571$	−1.83195	+	5.63818i	−0.0766649	+	0.235950i	−0.982043	−	0.188655i	$-0.939587\pi$
$571$	−1.83195	+	5.63818i	−0.0766649	+	0.235950i	0.905379	+	0.424605i	$0.139587\pi$
$572$	11.2053	−	34.4863i	0.468516	−	1.44195i
$573$	−11.7141	+	8.51078i	−0.489363	+	0.355543i
$574$	−22.0283			−0.919445
$575$	6.59098	−	9.46647i	0.274863	−	0.394779i
$576$	25.7185			1.07161
$577$	24.1243	−	17.5273i	1.00431	−	0.729672i	0.0413004	−	0.999147i	$-0.486850\pi$
$577$	24.1243	−	17.5273i	1.00431	−	0.729672i	0.963008	+	0.269474i	$0.0868499\pi$
$578$	−3.25305	+	10.0119i	−0.135309	+	0.416439i
$579$	7.71342	−	23.7395i	0.320559	−	0.986578i
$580$	12.7652	+	6.34329i	0.530047	+	0.263391i
$581$	2.47979	+	7.63200i	0.102879	+	0.316629i
$582$	−11.8051			−0.489336
$583$	1.69709	+	5.22309i	0.0702861	+	0.216318i
$584$	56.6044	+	41.1255i	2.34231	+	1.70179i
$585$	5.74917	+	11.0082i	0.237699	+	0.455134i
$586$	−55.0017	+	39.9611i	−2.27210	+	1.65078i
$587$	−0.808981	−	0.587759i	−0.0333902	−	0.0242594i	0.570965	−	0.820974i	$-0.306569\pi$
$587$	−0.808981	−	0.587759i	−0.0333902	−	0.0242594i	−0.604355	+	0.796715i	$0.706569\pi$
$588$	−4.33811	−	3.15182i	−0.178900	−	0.129979i
$589$	53.9976	−	39.2316i	2.22493	−	1.61651i
$590$	−51.2936	+	8.65386i	−2.11172	+	0.356274i
$591$	−1.10566	−	0.803308i	−0.0454807	−	0.0330437i
$592$	6.92942	+	21.3265i	0.284797	+	0.876516i
$593$	25.5633			1.04976			0.524880	−	0.851176i	$-0.324110\pi$
$593$	25.5633			1.04976			0.524880	+	0.851176i	$0.324110\pi$
$594$	1.02089	+	3.14198i	0.0418876	+	0.128917i
$595$	−4.73002	−	9.05681i	−0.193912	−	0.371293i
$596$	−17.5209	+	53.9238i	−0.717685	+	2.20881i
$597$	4.14645	−	12.7615i	0.169703	−	0.522291i
$598$	28.1263	−	20.4349i	1.15017	−	0.835646i
$599$	3.30978			0.135234			0.0676169	−	0.997711i	$-0.478460\pi$
$599$	3.30978			0.135234			0.0676169	+	0.997711i	$0.478460\pi$
$600$	−43.0890	+	14.9653i	−1.75910	+	0.610954i
$601$	−8.35563			−0.340833			−0.170417	−	0.985372i	$-0.554511\pi$
$601$	−8.35563			−0.340833			−0.170417	+	0.985372i	$0.554511\pi$
$602$	−3.88733	+	2.82431i	−0.158436	+	0.115110i
$603$	2.90592	−	8.94350i	0.118338	−	0.364208i
$604$	−4.45003	+	13.6958i	−0.181069	+	0.557273i
$605$	3.11762	−	21.0523i	0.126749	−	0.855896i
$606$	7.72858	+	23.7861i	0.313952	+	0.966245i
$607$	−29.5573			−1.19969			−0.599847	−	0.800115i	$-0.704772\pi$
$607$	−29.5573			−1.19969			−0.599847	+	0.800115i	$0.704772\pi$
$608$	−47.2769	−	145.503i	−1.91733	−	5.90094i
$609$	0.961789	+	0.698780i	0.0389736	+	0.0283160i
$610$	5.63348	−	38.0411i	0.228093	−	1.54024i
$611$	−3.05510	+	2.21966i	−0.123596	+	0.0897980i
$612$	19.8227	+	14.4020i	0.801285	+	0.582168i
$613$	2.39507	+	1.74012i	0.0967359	+	0.0702827i	0.635102	−	0.772428i	$-0.280958\pi$
$613$	2.39507	+	1.74012i	0.0967359	+	0.0702827i	−0.538366	+	0.842711i	$0.680958\pi$
$614$	26.6155	−	19.3373i	1.07411	−	0.780389i
$615$	−12.7068	+	12.9650i	−0.512387	+	0.522800i
$616$	8.98622	+	6.52887i	0.362065	+	0.263056i
$617$	5.08520	+	15.6506i	0.204722	+	0.630071i	0.999725	+	0.0234643i	$0.00746960\pi$
$617$	5.08520	+	15.6506i	0.204722	+	0.630071i	−0.795002	+	0.606606i	$0.792530\pi$
$618$	27.8221			1.11917
$619$	−6.35228	−	19.5503i	−0.255320	−	0.785794i	−0.993766	−	0.111482i	$-0.964440\pi$
$619$	−6.35228	−	19.5503i	−0.255320	−	0.785794i	0.738447	−	0.674312i	$-0.235560\pi$
$620$	102.228	−	17.2471i	4.10556	−	0.692658i
$621$	−0.712899	+	2.19408i	−0.0286077	+	0.0880453i
$622$	−11.8020	+	36.3227i	−0.473215	+	1.45641i
$623$	5.86179	−	4.25884i	0.234848	−	0.170627i
$624$	−77.9154			−3.11911
$625$	19.6180	−	15.4963i	0.784719	−	0.619851i
$626$	−59.7875			−2.38959
$627$	7.60383	−	5.52450i	0.303668	−	0.220627i
$628$	−6.99279	+	21.5216i	−0.279043	+	0.858805i
$629$	−2.25705	+	6.94648i	−0.0899944	+	0.276974i
$630$	−5.98266	+	1.00935i	−0.238355	+	0.0402134i
$631$	6.78231	+	20.8738i	0.269999	+	0.830973i	0.990499	+	0.137518i	$0.0439124\pi$
$631$	6.78231	+	20.8738i	0.269999	+	0.830973i	−0.720500	+	0.693455i	$0.756088\pi$
$632$	129.176			5.13834
$633$	1.01289	+	3.11735i	0.0402587	+	0.123904i
$634$	−26.9727	−	19.5968i	−1.07122	−	0.778290i
$635$	−29.8768	+	30.4840i	−1.18562	+	1.20972i
$636$	19.5672	−	14.2164i	0.775889	−	0.563717i
$637$	4.49327	+	3.26455i	0.178030	+	0.129346i
$638$	−3.17743	−	2.30854i	−0.125796	−	0.0913960i
$639$	−6.88683	+	5.00358i	−0.272439	+	0.197938i
$640$	9.87439	−	66.6785i	0.390319	−	2.63570i
$641$	−0.802685	−	0.583184i	−0.0317041	−	0.0230344i	0.571820	−	0.820379i	$-0.306237\pi$
$641$	−0.802685	−	0.583184i	−0.0317041	−	0.0230344i	−0.603524	+	0.797344i	$0.706237\pi$
$642$	−12.8588	−	39.5752i	−0.507495	−	1.56191i
$643$	−18.1538			−0.715915			−0.357957	−	0.933738i	$-0.616527\pi$
$643$	−18.1538			−0.715915			−0.357957	+	0.933738i	$0.616527\pi$
$644$	3.82270	+	11.7651i	0.150636	+	0.463609i
$645$	−0.580081	+	3.91710i	−0.0228407	+	0.154236i
$646$	29.5754	−	91.0237i	1.16363	−	3.58128i
$647$	4.57380	−	14.0767i	0.179815	−	0.553413i	−0.820006	−	0.572355i	$-0.806030\pi$
$647$	4.57380	−	14.0767i	0.179815	−	0.553413i	0.999821	+	0.0189423i	$0.00602989\pi$
$648$	7.38047	−	5.36222i	0.289932	−	0.210648i
$649$	10.4391			0.409769
$650$	71.1784	−	24.7210i	2.79185	−	0.969638i
$651$	8.64640			0.338879
$652$	−43.4062	+	31.5364i	−1.69992	+	1.23506i
$653$	6.91161	−	21.2718i	0.270472	−	0.832428i	−0.719910	−	0.694068i	$-0.755817\pi$
$653$	6.91161	−	21.2718i	0.270472	−	0.832428i	0.990382	−	0.138360i	$-0.0441832\pi$
$654$	8.14284	−	25.0611i	0.318410	−	0.979967i
$655$	−10.8207	−	20.7190i	−0.422802	−	0.809559i
$656$	−35.1948	−	108.319i	−1.37413	−	4.22913i
$657$	7.66949			0.299215
$658$	−0.570098	−	1.75458i	−0.0222247	−	0.0684007i
$659$	−8.55784	−	6.21763i	−0.333366	−	0.242205i	0.408492	−	0.912762i	$-0.366055\pi$
$659$	−8.55784	−	6.21763i	−0.333366	−	0.242205i	−0.741858	+	0.670558i	$0.766055\pi$
$660$	14.3955	−	2.42869i	0.560343	−	0.0945368i
$661$	−21.0402	+	15.2866i	−0.818370	+	0.594580i	−0.916245	−	0.400618i	$-0.868795\pi$
$661$	−21.0402	+	15.2866i	−0.818370	+	0.594580i	0.0978753	+	0.995199i	$0.468795\pi$
$662$	10.6174	+	7.71400i	0.412657	+	0.299813i
$663$	−20.5317	−	14.9172i	−0.797386	−	0.579335i
$664$	−59.2265	+	43.0306i	−2.29843	+	1.66991i
$665$	7.99064	+	15.3001i	0.309864	+	0.593312i
$666$	3.50879	+	2.54928i	0.135963	+	0.0987827i
$667$	−0.847520	−	2.60840i	−0.0328161	−	0.100998i
$668$	−111.698			−4.32172
$669$	1.15654	+	3.55946i	0.0447144	+	0.137617i
$670$	−51.0939	−	25.3896i	−1.97393	−	0.980884i
$671$	−2.38479	+	7.33963i	−0.0920638	+	0.283343i
$672$	6.12445	−	18.8491i	0.236256	−	0.727121i
$673$	−24.0333	+	17.4612i	−0.926417	+	0.673081i	−0.945113	−	0.326744i	$-0.894049\pi$
$673$	−24.0333	+	17.4612i	−0.926417	+	0.673081i	0.0186958	+	0.999825i	$0.494049\pi$
$674$	−30.9625			−1.19263
$675$	−2.85696	+	4.10339i	−0.109964	+	0.157939i
$676$	95.6979			3.68069
$677$	17.0775	−	12.4075i	0.656342	−	0.476860i	−0.209084	−	0.977898i	$-0.567048\pi$
$677$	17.0775	−	12.4075i	0.656342	−	0.476860i	0.865426	+	0.501038i	$0.167048\pi$
$678$	−10.2743	+	31.6211i	−0.394582	+	1.21440i
$679$	−1.34446	+	4.13782i	−0.0515956	+	0.158795i
$680$	65.2449	−	66.5708i	2.50203	−	2.55287i
$681$	−4.47099	−	13.7603i	−0.171329	−	0.527296i
$682$	−28.5649			−1.09380
$683$	−14.3339	−	44.1153i	−0.548473	−	1.68803i	−0.712587	−	0.701584i	$-0.752476\pi$
$683$	−14.3339	−	44.1153i	−0.548473	−	1.68803i	0.164114	−	0.986441i	$-0.447524\pi$
$684$	−33.4874	−	24.3300i	−1.28042	−	0.930282i
$685$	11.4592	+	5.69432i	0.437835	+	0.217569i
$686$	−2.19514	+	1.59486i	−0.0838106	+	0.0608920i
$687$	−10.0755	−	7.32030i	−0.384406	−	0.279287i
$688$	−20.0986	−	14.6025i	−0.766253	−	0.556715i
$689$	−20.2671	+	14.7249i	−0.772114	+	0.560973i
$690$	12.5347	+	6.22873i	0.477187	+	0.237124i
$691$	23.7679	+	17.2684i	0.904175	+	0.656922i	0.939535	−	0.342453i	$-0.111258\pi$
$691$	23.7679	+	17.2684i	0.904175	+	0.656922i	−0.0353600	+	0.999375i	$0.511258\pi$
$692$	−19.3471	−	59.5444i	−0.735468	−	2.26354i
$693$	1.21757			0.0462516
$694$	−7.47781	−	23.0143i	−0.283854	−	0.873613i
$695$	26.8225	−	27.3676i	1.01743	−	1.03811i
$696$	−3.35143	+	10.3147i	−0.127036	+	0.390976i
$697$	11.4637	−	35.2815i	0.434217	−	1.33638i
$698$	−30.2896	+	22.0067i	−1.14648	+	0.832965i
$699$	6.32742			0.239325
$700$	0.539332	+	26.8055i	0.0203848	+	1.01315i
$701$	8.97223			0.338876			0.169438	−	0.985541i	$-0.445805\pi$
$701$	8.97223			0.338876			0.169438	+	0.985541i	$0.445805\pi$
$702$	−12.1918	+	8.85783i	−0.460148	+	0.334317i
$703$	3.81294	−	11.7350i	0.143808	−	0.442595i
$704$	−9.67658	+	29.7814i	−0.364700	+	1.12243i
$705$	−1.36153	−	0.676571i	−0.0512782	−	0.0254812i
$706$	−23.3372	−	71.8246i	−0.878309	−	2.70316i
$707$	9.21751			0.346660
$708$	−14.2067	−	43.7238i	−0.533921	−	1.64324i
$709$	5.98459	+	4.34806i	0.224756	+	0.163295i	0.694465	−	0.719527i	$-0.255641\pi$
$709$	5.98459	+	4.34806i	0.224756	+	0.163295i	−0.469709	+	0.882821i	$0.655641\pi$
$710$	23.9092	+	45.7802i	0.897297	+	1.71810i
$711$	11.4555	−	8.32288i	0.429613	−	0.312132i
$712$	53.4757	+	38.8524i	2.00409	+	1.45606i
$713$	−16.1376	−	11.7246i	−0.604358	−	0.439091i
$714$	10.0305	−	7.28761i	0.375383	−	0.272732i
$715$	−14.9104	+	2.51556i	−0.557616	+	0.0940767i
$716$	73.2146	+	53.1935i	2.73616	+	1.98794i
$717$	5.04959	+	15.5410i	0.188580	+	0.580391i
$718$	1.89039			0.0705488
$719$	6.70045	+	20.6219i	0.249884	+	0.769065i	0.994795	+	0.101900i	$0.0324923\pi$
$719$	6.70045	+	20.6219i	0.249884	+	0.769065i	−0.744910	+	0.667165i	$0.767508\pi$
$720$	−14.5217	−	27.8055i	−0.541193	−	1.03625i
$721$	3.16861	−	9.75197i	0.118005	−	0.363182i
$722$	−34.0322	+	104.740i	−1.26655	+	3.89803i
$723$	−1.61269	+	1.17169i	−0.0599765	+	0.0435755i
$724$	−63.4146			−2.35679
$725$	−0.119574	−	5.94298i	−0.00444085	−	0.220717i
$726$	25.8243			0.958428
$727$	−12.2324	+	8.88738i	−0.453676	+	0.329615i	−0.791045	−	0.611758i	$-0.790463\pi$
$727$	−12.2324	+	8.88738i	−0.453676	+	0.329615i	0.337370	+	0.941372i	$0.390463\pi$
$728$	−15.6572	+	48.1879i	−0.580294	+	1.78596i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	6.81661	−	46.0304i	0.252294	−	1.70366i
$731$	−2.50055	−	7.69590i	−0.0924862	−	0.284643i
$732$	33.9873			1.25621
$733$	6.41142	+	19.7323i	0.236811	+	0.728830i	0.996876	+	0.0789829i	$0.0251672\pi$
$733$	6.41142	+	19.7323i	0.236811	+	0.728830i	−0.760065	+	0.649847i	$0.774833\pi$
$734$	12.6948	+	9.22331i	0.468574	+	0.340439i
$735$	−0.327566	+	2.21195i	−0.0120824	+	0.0815888i
$736$	−36.9903	+	26.8751i	−1.36348	+	0.990628i
$737$	9.26301	+	6.72997i	0.341207	+	0.247902i
$738$	−17.8213	−	12.9479i	−0.656011	−	0.476620i
$739$	38.9749	−	28.3170i	1.43372	−	1.04166i	0.444407	−	0.895825i	$-0.353414\pi$
$739$	38.9749	−	28.3170i	1.43372	−	1.04166i	0.989309	−	0.145831i	$-0.0465856\pi$
$740$	13.4152	−	13.6878i	0.493151	−	0.503173i
$741$	34.6852	+	25.2003i	1.27419	+	0.925755i
$742$	−3.78194	−	11.6396i	−0.138839	−	0.427303i
$743$	−11.9694			−0.439113			−0.219557	−	0.975600i	$-0.570461\pi$
$743$	−11.9694			−0.439113			−0.219557	+	0.975600i	$0.570461\pi$
$744$	24.3750	+	75.0184i	0.893630	+	2.75031i
$745$	23.3143	−	3.93341i	0.854170	−	0.144109i
$746$	−9.56091	+	29.4254i	−0.350050	+	1.07734i
$747$	−2.47979	+	7.63200i	−0.0907307	+	0.279240i
$748$	−24.1355	+	17.5355i	−0.882481	+	0.641160i
$749$	−15.3360			−0.560366
$750$	22.0882	+	20.7938i	0.806549	+	0.759284i
$751$	−26.4821			−0.966346			−0.483173	−	0.875525i	$-0.660516\pi$
$751$	−26.4821			−0.966346			−0.483173	+	0.875525i	$0.660516\pi$
$752$	7.71684	−	5.60661i	0.281404	−	0.204452i
$753$	−2.34233	+	7.20896i	−0.0853594	+	0.262709i
$754$	5.53621	−	17.0387i	0.201617	−	0.620514i
$755$	5.92145	−	0.999022i	0.215504	−	0.0363581i
$756$	−1.65701	−	5.09975i	−0.0602648	−	0.185476i
$757$	−4.26160			−0.154890			−0.0774452	−	0.996997i	$-0.524676\pi$
$757$	−4.26160			−0.154890			−0.0774452	+	0.996997i	$0.524676\pi$
$758$	−21.1407	−	65.0645i	−0.767866	−	2.36325i
$759$	−2.27246	−	1.65104i	−0.0824851	−	0.0599289i
$760$	−110.221	+	112.461i	−3.99814	+	4.07940i
$761$	7.86304	−	5.71283i	0.285035	−	0.207090i	−0.436076	−	0.899910i	$-0.643632\pi$
$761$	7.86304	−	5.71283i	0.285035	−	0.207090i	0.721111	+	0.692820i	$0.243632\pi$
$762$	−41.9023	−	30.4438i	−1.51796	−	1.10286i
$763$	−7.85684	−	5.70833i	−0.284437	−	0.206655i
$764$	−62.8132	+	45.6365i	−2.27250	+	1.65107i
$765$	1.49679	−	10.1073i	0.0541166	−	0.365432i
$766$	19.9310	+	14.4807i	0.720137	+	0.523210i
$767$	14.7149	+	45.2877i	0.531323	+	1.63524i
$768$	30.3558			1.09537
$769$	−10.6749	−	32.8540i	−0.384947	−	1.18474i	−0.936519	−	0.350617i	$-0.885972\pi$
$769$	−10.6749	−	32.8540i	−0.384947	−	1.18474i	0.551572	−	0.834127i	$-0.314028\pi$
$770$	1.08217	−	7.30754i	0.0389987	−	0.263345i
$771$	−6.72015	+	20.6825i	−0.242020	+	0.744862i
$772$	41.3608	−	127.296i	1.48861	−	4.58147i
$773$	−25.5250	+	18.5450i	−0.918072	+	0.667018i	−0.943043	−	0.332670i	$-0.892050\pi$
$773$	−25.5250	+	18.5450i	−0.918072	+	0.667018i	0.0249717	+	0.999688i	$0.492050\pi$
$774$	−4.80501			−0.172712
$775$	−26.1096	−	34.4572i	−0.937883	−	1.23774i
$776$	−39.6909			−1.42482
$777$	1.29316	−	0.939538i	0.0463920	−	0.0337058i
$778$	−9.08622	+	27.9645i	−0.325757	+	1.00258i
$779$	−19.3661	+	59.6027i	−0.693863	+	2.13549i
$780$	30.8282	+	59.0282i	1.10382	+	2.11355i
$781$	−3.20285	−	9.85737i	−0.114607	−	0.352725i
$782$	−28.6030			−1.02284
$783$	0.367371	+	1.13065i	0.0131288	+	0.0404062i
$784$	−11.3495	−	8.24588i	−0.405339	−	0.294496i
$785$	9.30499	−	1.56987i	0.332109	−	0.0560309i
$786$	22.9466	−	16.6717i	0.818478	−	0.594659i
$787$	12.7819	+	9.28660i	0.455626	+	0.331031i	0.791813	−	0.610764i	$-0.209137\pi$
$787$	12.7819	+	9.28660i	0.455626	+	0.331031i	−0.336187	+	0.941795i	$0.609137\pi$
$788$	−5.92876	−	4.30749i	−0.211203	−	0.153448i
$789$	14.7339	−	10.7048i	0.524541	−	0.381102i
$790$	−39.7703	−	76.1502i	−1.41496	−	2.70930i
$791$	9.91343	+	7.20253i	0.352481	+	0.256093i
$792$	3.43243	+	10.5639i	0.121966	+	0.375373i
$793$	−35.2030			−1.25010
$794$	−30.2823	−	93.1994i	−1.07468	−	3.30752i
$795$	−9.03218	−	4.48826i	−0.320338	−	0.159182i
$796$	22.2340	−	68.4294i	0.788065	−	2.42541i
$797$	1.20929	−	3.72180i	0.0428351	−	0.131833i	−0.927352	−	0.374190i	$-0.877921\pi$
$797$	1.20929	−	3.72180i	0.0428351	−	0.131833i	0.970187	+	0.242357i	$0.0779207\pi$
$798$	−16.9451	+	12.3113i	−0.599848	+	0.435815i
$799$	3.10689			0.109914
$800$	−93.6106	+	32.5119i	−3.30963	+	1.14947i
$801$	7.24557			0.256010
$802$	−25.3632	+	18.4275i	−0.895607	+	0.650697i
$803$	−2.88564	+	8.88108i	−0.101832	+	0.313407i
$804$	15.5821	−	47.9568i	0.549539	−	1.69131i
$805$	3.61080	−	3.68418i	0.127264	−	0.129850i
$806$	−40.2649	−	123.923i	−1.41827	−	4.36498i
$807$	−19.7861			−0.696503
$808$	25.9850	+	79.9736i	0.914149	+	2.81346i
$809$	−34.2784	−	24.9047i	−1.20516	−	0.875603i	−0.210381	−	0.977619i	$-0.567471\pi$
$809$	−34.2784	−	24.9047i	−1.20516	−	0.875603i	−0.994783	+	0.102017i	$0.967471\pi$
$810$	−5.43335	−	2.69994i	−0.190908	−	0.0948662i
$811$	5.19642	−	3.77542i	0.182471	−	0.132573i	−0.492800	−	0.870143i	$-0.664027\pi$
$811$	5.19642	−	3.77542i	0.182471	−	0.132573i	0.675271	+	0.737570i	$0.264027\pi$
$812$	5.15730	+	3.74700i	0.180986	+	0.131494i
$813$	−3.25914	−	2.36790i	−0.114303	−	0.0830460i
$814$	−4.27219	+	3.10392i	−0.149740	+	0.108793i
$815$	20.0362	+	9.95639i	0.701838	+	0.348757i
$816$	51.8608	+	37.6790i	1.81549	+	1.31903i
$817$	4.22430	+	13.0010i	0.147789	+	0.454849i
$818$	53.4052			1.86727
$819$	1.71628	+	5.28216i	0.0599716	+	0.184573i
$820$	−68.1362	+	69.5209i	−2.37942	+	2.42778i
$821$	−14.3676	+	44.2188i	−0.501431	+	1.54325i	0.305257	+	0.952270i	$0.401258\pi$
$821$	−14.3676	+	44.2188i	−0.501431	+	1.54325i	−0.806688	+	0.590977i	$0.798742\pi$
$822$	−4.79820	+	14.7673i	−0.167356	+	0.515070i
$823$	−18.6932	+	13.5814i	−0.651604	+	0.473418i	−0.863817	−	0.503805i	$-0.831933\pi$
$823$	−18.6932	+	13.5814i	−0.651604	+	0.473418i	0.212213	+	0.977223i	$0.431933\pi$
$824$	93.5432			3.25873
$825$	−3.67669	−	4.85219i	−0.128006	−	0.168931i
$826$	−23.2634			−0.809436
$827$	−5.64160	+	4.09886i	−0.196178	+	0.142531i	−0.681538	−	0.731783i	$-0.738688\pi$
$827$	−5.64160	+	4.09886i	−0.196178	+	0.142531i	0.485360	+	0.874314i	$0.338688\pi$
$828$	−3.82270	+	11.7651i	−0.132848	+	0.408865i
$829$	−8.22228	+	25.3056i	−0.285571	+	0.878898i	0.700655	+	0.713500i	$0.252891\pi$
$829$	−8.22228	+	25.3056i	−0.285571	+	0.878898i	−0.986227	+	0.165399i	$0.947109\pi$
$830$	43.6013	+	21.6664i	1.51342	+	0.752050i
$831$	0.897389	+	2.76188i	0.0311301	+	0.0958085i
$832$	−142.840			−4.95210
$833$	−1.41203	−	4.34579i	−0.0489241	−	0.150573i
$834$	37.6186	+	27.3315i	1.30263	+	0.946413i
$835$	21.5627	+	41.2872i	0.746208	+	1.42880i
$836$	40.7732	−	29.6235i	1.41017	−	1.02455i
$837$	6.99508	+	5.08223i	0.241785	+	0.175667i
$838$	66.1300	+	48.0463i	2.28442	+	1.65973i
$839$	−1.93811	+	1.40812i	−0.0669109	+	0.0486136i	−0.620738	−	0.784018i	$-0.713167\pi$
$839$	−1.93811	+	1.40812i	−0.0669109	+	0.0486136i	0.553827	+	0.832632i	$0.313167\pi$
$840$	−20.1149	+	3.39362i	−0.694028	+	0.117091i
$841$	22.3181	+	16.2150i	0.769589	+	0.559139i
$842$	−21.4784	−	66.1037i	−0.740194	−	2.27808i
$843$	10.3192			0.355413
$844$	5.43131	+	16.7158i	0.186953	+	0.575383i
$845$	−18.4740	−	35.3730i	−0.635524	−	1.21687i
$846$	0.570098	−	1.75458i	0.0196004	−	0.0603237i
$847$	2.94108	−	9.05171i	0.101057	−	0.311020i
$848$	51.1923	−	37.1934i	1.75795	−	1.27723i
$849$	19.9445			0.684494
$850$	−59.3314	−	17.9667i	−2.03505	−	0.616254i
$851$	−3.68758			−0.126409
$852$	−36.9285	+	26.8301i	−1.26515	+	0.919186i
$853$	12.0817	−	37.1836i	0.413669	−	1.27314i	−0.499766	−	0.866160i	$-0.666581\pi$
$853$	12.0817	−	37.1836i	0.413669	−	1.27314i	0.913436	−	0.406983i	$-0.133419\pi$
$854$	5.31448	−	16.3563i	0.181858	−	0.559701i
$855$	−2.52860	+	17.0748i	−0.0864763	+	0.583946i
$856$	−43.2336	−	133.059i	−1.47770	−	4.54788i
$857$	−15.6843			−0.535764			−0.267882	−	0.963452i	$-0.586324\pi$
$857$	−15.6843			−0.535764			−0.267882	+	0.963452i	$0.586324\pi$
$858$	−5.67001	−	17.4505i	−0.193571	−	0.595750i
$859$	33.5473	+	24.3735i	1.14462	+	0.831615i	0.987756	−	0.156006i	$-0.0498619\pi$
$859$	33.5473	+	24.3735i	1.14462	+	0.831615i	0.156863	+	0.987620i	$0.449862\pi$
$860$	−3.11051	+	21.0042i	−0.106067	+	0.716239i
$861$	−6.56804	+	4.77196i	−0.223838	+	0.162628i
$862$	53.0164	+	38.5187i	1.80575	+	1.31195i
$863$	−33.3680	−	24.2433i	−1.13586	−	0.825251i	−0.149324	−	0.988788i	$-0.547710\pi$
$863$	−33.3680	−	24.2433i	−1.13586	−	0.825251i	−0.986537	+	0.163537i	$0.947710\pi$
$864$	16.0340	−	11.6494i	0.545489	−	0.396321i
$865$	−18.2747	+	18.6460i	−0.621357	+	0.633985i
$866$	−1.11260	−	0.808351i	−0.0378077	−	0.0274689i
$867$	1.19891	+	3.68987i	0.0407172	+	0.125315i
$868$	46.3637			1.57369
$869$	5.32758	+	16.3966i	0.180726	+	0.556217i
$870$	7.11240	−	1.19995i	0.241133	−	0.0406821i
$871$	−16.1394	+	49.6721i	−0.546864	+	1.68308i
$872$	27.3778	−	84.2603i	0.927130	−	2.85341i
$873$	−3.51984	+	2.55731i	−0.119129	+	0.0865519i
$874$	48.3205			1.63446
$875$	9.80408	−	5.37402i	0.331438	−	0.181675i
$876$	41.1253			1.38949
$877$	−34.9015	+	25.3575i	−1.17854	+	0.856260i	−0.992006	−	0.126188i	$-0.959726\pi$
$877$	−34.9015	+	25.3575i	−1.17854	+	0.856260i	−0.186535	+	0.982448i	$0.559726\pi$
$878$	3.26597	−	10.0516i	0.110221	−	0.339225i
$879$	−7.74278	+	23.8298i	−0.261158	+	0.803760i
$880$	37.6619	−	6.35402i	1.26958	−	0.214194i
$881$	7.31225	+	22.5048i	0.246356	+	0.758205i	0.995410	+	0.0956972i	$0.0305080\pi$
$881$	7.31225	+	22.5048i	0.246356	+	0.758205i	−0.749055	+	0.662508i	$0.769492\pi$
$882$	−2.71334			−0.0913628
$883$	−13.7547	−	42.3327i	−0.462883	−	1.42461i	−0.861625	−	0.507545i	$-0.830553\pi$
$883$	−13.7547	−	42.3327i	−0.462883	−	1.42461i	0.398742	−	0.917063i	$-0.369447\pi$
$884$	−110.095	−	79.9887i	−3.70290	−	2.69031i
$885$	−13.4192	+	13.6919i	−0.451081	+	0.460248i
$886$	59.8395	−	43.4760i	2.01035	−	1.46060i
$887$	−36.8026	−	26.7386i	−1.23571	−	0.897795i	−0.238404	−	0.971166i	$-0.576624\pi$
$887$	−36.8026	−	26.7386i	−1.23571	−	0.897795i	−0.997305	+	0.0733709i	$0.976624\pi$
$888$	11.7972	+	8.57118i	0.395889	+	0.287630i
$889$	−15.4431	+	11.2201i	−0.517945	+	0.376309i
$890$	6.43984	−	43.4861i	0.215864	−	1.45766i
$891$	0.985033	+	0.715668i	0.0329998	+	0.0239758i
$892$	6.20159	+	19.0865i	0.207644	+	0.639064i
$893$	−5.24862			−0.175638
$894$	8.86580	+	27.2861i	0.296517	+	0.912584i
$895$	5.52836	−	37.3312i	0.184793	−	1.24784i
$896$	9.31524	−	28.6694i	0.311200	−	0.957776i
$897$	3.95943	−	12.1859i	0.132202	−	0.406875i
$898$	−43.6496	+	31.7133i	−1.45660	+	1.05829i
$899$	−10.2792			−0.342829
$900$	−15.3196	+	22.0032i	−0.510652	+	0.733438i
$901$	20.6106			0.686639
$902$	21.6986	−	15.7650i	0.722486	−	0.524917i
$903$	−0.547233	+	1.68421i	−0.0182108	+	0.0560470i
$904$	−34.5442	+	106.316i	−1.14892	+	3.53602i
$905$	12.2418	+	23.4401i	0.406933	+	0.779175i
$906$	2.25177	+	6.93023i	0.0748100	+	0.230242i
$907$	22.4538			0.745567			0.372784	−	0.927918i	$-0.378403\pi$
$907$	22.4538			0.745567			0.372784	+	0.927918i	$0.378403\pi$
$908$	−23.9743	−	73.7854i	−0.795616	−	2.44865i
$909$	7.45713	+	5.41792i	0.247337	+	0.179701i
$910$	33.2276	−	5.60591i	1.10148	−	0.185834i
$911$	−1.50867	+	1.09611i	−0.0499844	+	0.0363158i	−0.612497	−	0.790473i	$-0.709835\pi$
$911$	−1.50867	+	1.09611i	−0.0499844	+	0.0363158i	0.562513	+	0.826789i	$0.309835\pi$
$912$	−87.6108	−	63.6530i	−2.90108	−	2.10776i
$913$	−7.90465	−	5.74307i	−0.261606	−	0.190068i
$914$	28.1201	−	20.4304i	0.930130	−	0.675779i
$915$	−6.56107	−	12.5628i	−0.216902	−	0.415314i
$916$	−54.0270	−	39.2529i	−1.78510	−	1.29695i
$917$	−3.23027	−	9.94176i	−0.106673	−	0.328306i
$918$	12.3984			0.409209
$919$	−6.33454	−	19.4957i	−0.208957	−	0.643104i	−0.999528	−	0.0307327i	$-0.990216\pi$
$919$	−6.33454	−	19.4957i	−0.208957	−	0.643104i	0.790571	−	0.612371i	$-0.209784\pi$
$920$	42.1440	+	20.9422i	1.38945	+	0.690444i
$921$	3.74675	−	11.5313i	0.123460	−	0.379970i
$922$	−10.9360	+	33.6576i	−0.360159	+	1.10846i
$923$	38.2494	−	27.7898i	1.25899	−	0.914712i
$924$	6.52883			0.214783
$925$	−7.64917	−	2.31632i	−0.251503	−	0.0761601i
$926$	−7.60899			−0.250047
$927$	8.29552	−	6.02705i	0.272461	−	0.197954i
$928$	−7.28097	+	22.4085i	−0.239010	+	0.735596i
$929$	13.2785	−	40.8669i	0.435653	−	1.34080i	−0.456764	−	0.889588i	$-0.650992\pi$
$929$	13.2785	−	40.8669i	0.435653	−	1.34080i	0.892416	−	0.451213i	$-0.149008\pi$
$930$	36.7195	−	37.4657i	1.20408	−	1.22855i
$931$	2.38542	+	7.34155i	0.0781788	+	0.240610i
$932$	33.9289			1.11138
$933$	4.34961	+	13.3867i	0.142400	+	0.438262i
$934$	2.23647	+	1.62489i	0.0731796	+	0.0531681i
$935$	11.1409	+	5.53613i	0.364346	+	0.181051i
$936$	−40.9910	+	29.7817i	−1.33983	+	0.973446i
$937$	−30.7278	−	22.3251i	−1.00383	−	0.729328i	−0.0409267	−	0.999162i	$-0.513031\pi$
$937$	−30.7278	−	22.3251i	−1.00383	−	0.729328i	−0.962907	+	0.269834i	$0.913031\pi$
$938$	−20.6425	−	14.9977i	−0.674002	−	0.489691i
$939$	−17.8264	+	12.9517i	−0.581744	+	0.422662i
$940$	−7.30079	−	3.62791i	−0.238126	−	0.118329i
$941$	−16.1943	−	11.7658i	−0.527919	−	0.383555i	0.291660	−	0.956522i	$-0.405792\pi$
$941$	−16.1943	−	11.7658i	−0.527919	−	0.383555i	−0.819579	+	0.572967i	$0.805792\pi$
$942$	3.53844	+	10.8902i	0.115288	+	0.354821i
$943$	18.7294			0.609913
$944$	−37.1680	−	114.391i	−1.20972	−	3.72312i
$945$	−1.56515	+	1.59696i	−0.0509145	+	0.0519492i
$946$	1.80788	−	5.56408i	0.0587792	−	0.180904i
$947$	−4.52567	+	13.9286i	−0.147064	+	0.452618i	−0.997271	−	0.0738320i	$-0.976477\pi$
$947$	−4.52567	+	13.9286i	−0.147064	+	0.452618i	0.850206	+	0.526450i	$0.176477\pi$
$948$	61.4264	−	44.6289i	1.99504	−	1.44948i
$949$	−42.5963			−1.38273
$950$	100.231	+	30.3520i	3.25193	+	0.984750i
$951$	−12.2875			−0.398450
$952$	33.7246	−	24.5024i	1.09302	−	0.794126i
$953$	−14.5228	+	44.6967i	−0.470441	+	1.44787i	0.381569	+	0.924341i	$0.375384\pi$
$953$	−14.5228	+	44.6967i	−0.470441	+	1.44787i	−0.852009	+	0.523527i	$0.824616\pi$
$954$	3.78194	−	11.6396i	0.122445	−	0.376846i
$955$	28.9945	+	14.4079i	0.938239	+	0.466229i
$956$	27.0769	+	83.3341i	0.875729	+	2.69522i
$957$	−1.44749			−0.0467907
$958$	18.3034	+	56.3322i	0.591357	+	1.82001i
$959$	4.62967	+	3.36365i	0.149500	+	0.108618i
$960$	−26.6224	−	50.9752i	−0.859233	−	1.64522i
$961$	−35.4028	+	25.7216i	−1.14202	+	0.829730i
$962$	−19.4878	−	14.1587i	−0.628311	−	0.456494i
$963$	−12.4071	−	9.01429i	−0.399814	−	0.290482i
$964$	−8.64754	+	6.28281i	−0.278519	+	0.202356i
$965$	−55.0370	+	9.28542i	−1.77170	+	0.298908i
$966$	5.06416	+	3.67932i	0.162937	+	0.118380i
$967$	−16.3882	−	50.4375i	−0.527007	−	1.62196i	−0.760312	−	0.649558i	$-0.774954\pi$
$967$	−16.3882	−	50.4375i	−0.527007	−	1.62196i	0.233304	−	0.972404i	$-0.425046\pi$
$968$	86.8261			2.79070
$969$	−10.9000	−	33.5468i	−0.350159	−	1.07768i
$970$	12.2199	+	23.3981i	0.392358	+	0.751269i
$971$	2.15039	−	6.61821i	0.0690092	−	0.212389i	−0.910605	−	0.413279i	$-0.864383\pi$
$971$	2.15039	−	6.61821i	0.0690092	−	0.212389i	0.979614	+	0.200890i	$0.0643835\pi$
$972$	1.65701	−	5.09975i	0.0531486	−	0.163575i
$973$	13.8643	−	10.0730i	0.444470	−	0.322927i
$974$	33.6978			1.07975
$975$	15.8675	−	22.7902i	0.508167	−	0.729869i
$976$	88.9187			2.84622
$977$	−43.1173	+	31.3265i	−1.37944	+	1.00223i	−0.382513	+	0.923950i	$0.624941\pi$
$977$	−43.1173	+	31.3265i	−1.37944	+	1.00223i	−0.996932	+	0.0782749i	$0.975059\pi$
$978$	−8.38953	+	25.8203i	−0.268268	+	0.825643i
$979$	−2.72614	+	8.39020i	−0.0871278	+	0.268152i
$980$	−1.75647	+	11.8609i	−0.0561084	+	0.378882i
$981$	−3.00105	−	9.23627i	−0.0958160	−	0.294891i
$982$	113.007			3.60619
$983$	−2.79860	−	8.61321i	−0.0892615	−	0.274719i	0.896454	−	0.443136i	$-0.146134\pi$
$983$	−2.79860	−	8.61321i	−0.0892615	−	0.274719i	−0.985716	+	0.168418i	$0.946134\pi$
$984$	−59.9187	−	43.5335i	−1.91014	−	1.38780i
$985$	−0.447674	+	3.02300i	−0.0142641	+	0.0963207i
$986$	−11.9247	+	8.66377i	−0.379759	+	0.275911i
$987$	−0.550074	−	0.399652i	−0.0175090	−	0.0127211i
$988$	185.989	+	135.129i	5.91709	+	4.29902i
$989$	3.30517	−	2.40135i	0.105098	−	0.0763584i
$990$	5.17076	−	5.27584i	0.164337	−	0.167677i
$991$	−9.88541	−	7.18217i	−0.314021	−	0.228149i	0.419599	−	0.907709i	$-0.362171\pi$
$991$	−9.88541	−	7.18217i	−0.314021	−	0.228149i	−0.733620	+	0.679560i	$0.762171\pi$
$992$	52.9545	+	162.977i	1.68131	+	5.17453i
$993$	4.83679			0.153491
$994$	7.13753	+	21.9671i	0.226389	+	0.696753i
$995$	−29.5859	+	4.99150i	−0.937935	+	0.158241i
$996$	−13.2971	+	40.9243i	−0.421335	+	1.29673i
$997$	−7.23973	+	22.2816i	−0.229284	+	0.705665i	0.768544	+	0.639797i	$0.220982\pi$
$997$	−7.23973	+	22.2816i	−0.229284	+	0.705665i	−0.997828	+	0.0658680i	$0.979018\pi$
$998$	40.7538	−	29.6094i	1.29004	−	0.937268i
$999$	1.59844			0.0505723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.211.8	✓	32
25.16	even	5	inner	525.2.n.d.316.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.211.8	✓	32	1.1	even	1	trivial
525.2.n.d.316.8	yes	32	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19514 - 1.59486i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.65701 - 5.09975i) q^{4} +(-2.20491 + 0.371995i) q^{5} +(-0.838467 - 2.58054i) q^{6} -1.00000 q^{7} +(-2.81909 - 8.67626i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.19514 - 1.59486i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.65701 - 5.09975i) q^{4} +(-2.20491 + 0.371995i) q^{5} +(-0.838467 - 2.58054i) q^{6} -1.00000 q^{7} +(-2.81909 - 8.67626i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-4.24679 + 4.33310i) q^{10} +(0.985033 - 0.715668i) q^{11} +(-4.33811 - 3.15182i) q^{12} +(4.49327 + 3.26455i) q^{13} +(-2.19514 + 1.59486i) q^{14} +(-0.327566 + 2.21195i) q^{15} +(-11.3495 - 8.24588i) q^{16} +(-1.41203 - 4.34579i) q^{17} -2.71334 q^{18} +(2.38542 + 7.34155i) q^{19} +(-1.75647 + 11.8609i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.02089 - 3.14198i) q^{22} +(1.86639 - 1.35601i) q^{23} -9.12276 q^{24} +(4.72324 - 1.64043i) q^{25} +15.0698 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-1.65701 + 5.09975i) q^{28} +(0.367371 - 1.13065i) q^{29} +(2.80869 + 5.37794i) q^{30} +(-2.67188 - 8.22321i) q^{31} -19.8191 q^{32} +(-0.376249 - 1.15798i) q^{33} +(-10.0305 - 7.28761i) q^{34} +(2.20491 - 0.371995i) q^{35} +(-4.33811 + 3.15182i) q^{36} +(-1.29316 - 0.939538i) q^{37} +(16.9451 + 12.3113i) q^{38} +(4.49327 - 3.26455i) q^{39} +(9.44336 + 18.0817i) q^{40} +(6.56804 + 4.77196i) q^{41} +(0.838467 + 2.58054i) q^{42} +1.77088 q^{43} +(-2.01752 - 6.20929i) q^{44} +(2.00246 + 0.995062i) q^{45} +(1.93434 - 5.95327i) q^{46} +(-0.210110 + 0.646651i) q^{47} +(-11.3495 + 8.24588i) q^{48} +1.00000 q^{49} +(7.75189 - 11.1339i) q^{50} -4.56944 q^{51} +(24.0938 - 17.5052i) q^{52} +(-1.39383 + 4.28978i) q^{53} +(-0.838467 + 2.58054i) q^{54} +(-1.90568 + 1.94441i) q^{55} +(2.81909 + 8.67626i) q^{56} +7.71937 q^{57} +(-0.996800 - 3.06783i) q^{58} +(6.93628 + 5.03950i) q^{59} +(10.7376 + 5.33572i) q^{60} +(-5.12782 + 3.72558i) q^{61} +(-18.9800 - 13.7898i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-20.8067 + 15.1170i) q^{64} +(-11.1216 - 5.52656i) q^{65} +(-2.67273 - 1.94185i) q^{66} +(2.90592 + 8.94350i) q^{67} -24.5022 q^{68} +(-0.712899 - 2.19408i) q^{69} +(4.24679 - 4.33310i) q^{70} +(2.63054 - 8.09596i) q^{71} +(-2.81909 + 8.67626i) q^{72} +(-6.20475 + 4.50801i) q^{73} -4.33710 q^{74} +(-0.100580 - 4.99899i) q^{75} +41.3927 q^{76} +(-0.985033 + 0.715668i) q^{77} +(4.65684 - 14.3323i) q^{78} +(-4.37560 + 13.4667i) q^{79} +(28.0920 + 13.9595i) q^{80} +(0.309017 + 0.951057i) q^{81} +22.0283 q^{82} +(-2.47979 - 7.63200i) q^{83} +(4.33811 + 3.15182i) q^{84} +(4.73002 + 9.05681i) q^{85} +(3.88733 - 2.82431i) q^{86} +(-0.961789 - 0.698780i) q^{87} +(-8.98622 - 6.52887i) q^{88} +(-5.86179 + 4.25884i) q^{89} +(5.98266 - 1.00935i) q^{90} +(-4.49327 - 3.26455i) q^{91} +(-3.82270 - 11.7651i) q^{92} -8.64640 q^{93} +(0.570098 + 1.75458i) q^{94} +(-7.99064 - 15.3001i) q^{95} +(-6.12445 + 18.8491i) q^{96} +(1.34446 - 4.13782i) q^{97} +(2.19514 - 1.59486i) q^{98} -1.21757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

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