LMFDB - Embedded newform 825.2.n.o.751.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.5
Character	$\chi$	$=$	825.751
Dual form			825.2.n.o.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.634375 - 0.460901i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.428031 + 1.31734i) q^{4} +(-0.634375 - 0.460901i) q^{6} +(0.469090 - 1.44371i) q^{7} +(0.820252 + 2.52448i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.634375 - 0.460901i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.428031 + 1.31734i) q^{4} +(-0.634375 - 0.460901i) q^{6} +(0.469090 - 1.44371i) q^{7} +(0.820252 + 2.52448i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.438933 + 3.28745i) q^{11} +1.38514 q^{12} +(-0.377416 + 0.274209i) q^{13} +(-0.367828 - 1.13206i) q^{14} +(-0.557320 - 0.404916i) q^{16} +(1.37234 + 0.997064i) q^{17} +(-0.242310 + 0.745753i) q^{18} +(1.73345 + 5.33501i) q^{19} -1.51801 q^{21} +(1.79364 + 1.88317i) q^{22} +7.68641 q^{23} +(2.14745 - 1.56021i) q^{24} +(-0.113040 + 0.347903i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.70108 + 1.23591i) q^{28} +(0.822307 - 2.53080i) q^{29} +(-3.20187 + 2.32629i) q^{31} -5.84896 q^{32} +(2.99091 - 1.43333i) q^{33} +1.33013 q^{34} +(-0.428031 - 1.31734i) q^{36} +(-0.945402 + 2.90965i) q^{37} +(3.55857 + 2.58545i) q^{38} +(0.377416 + 0.274209i) q^{39} +(-0.417266 - 1.28421i) q^{41} +(-0.962986 + 0.699650i) q^{42} +12.0864 q^{43} +(-4.51858 - 0.828906i) q^{44} +(4.87607 - 3.54267i) q^{46} +(0.790480 + 2.43285i) q^{47} +(-0.212877 + 0.655168i) q^{48} +(3.79887 + 2.76004i) q^{49} +(0.524187 - 1.61328i) q^{51} +(-0.199682 - 0.614557i) q^{52} +(-6.48598 + 4.71234i) q^{53} +0.784131 q^{54} +4.02938 q^{56} +(4.53823 - 3.29722i) q^{57} +(-0.644797 - 1.98448i) q^{58} +(2.33267 - 7.17923i) q^{59} +(8.99446 + 6.53486i) q^{61} +(-0.958996 + 2.95149i) q^{62} +(0.469090 + 1.44371i) q^{63} +(-2.59580 + 1.88596i) q^{64} +(1.23674 - 2.28778i) q^{66} +6.89959 q^{67} +(-1.90088 + 1.38107i) q^{68} +(-2.37523 - 7.31021i) q^{69} +(-11.8018 - 8.57452i) q^{71} +(-2.14745 - 1.56021i) q^{72} +(-0.700618 + 2.15628i) q^{73} +(0.741319 + 2.28155i) q^{74} -7.77002 q^{76} +(4.95202 + 0.908418i) q^{77} +0.365807 q^{78} +(-9.85457 + 7.15977i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.856598 - 0.622355i) q^{82} +(-9.53087 - 6.92458i) q^{83} +(0.649754 - 1.99974i) q^{84} +(7.66735 - 5.57065i) q^{86} -2.66104 q^{87} +(-7.93906 + 3.80462i) q^{88} +1.47962 q^{89} +(0.218836 + 0.673508i) q^{91} +(-3.29002 + 10.1257i) q^{92} +(3.20187 + 2.32629i) q^{93} +(1.62276 + 1.17901i) q^{94} +(1.80743 + 5.56269i) q^{96} +(11.4893 - 8.34744i) q^{97} +3.68201 q^{98} +(-2.28742 - 2.40161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.634375	−	0.460901i	0.448571	−	0.325906i	−0.340460	−	0.940259i	$-0.610583\pi$
$2$	0.634375	−	0.460901i	0.448571	−	0.325906i	0.789031	+	0.614353i	$0.210583\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.428031	+	1.31734i	−0.214016	+	0.658672i
$5$		0			0
$5$		0			0
$6$	−0.634375	−	0.460901i	−0.258983	−	0.188162i
$7$	0.469090	−	1.44371i	0.177299	−	0.545671i	−0.822432	−	0.568864i	$-0.807383\pi$
$7$	0.469090	−	1.44371i	0.177299	−	0.545671i	0.999731	+	0.0231928i	$0.00738316\pi$
$8$	0.820252	+	2.52448i	0.290003	+	0.892537i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	0.438933	+	3.28745i	0.132343	+	0.991204i
$11$	0.438933	+	3.28745i	0.132343	+	0.991204i
$12$	1.38514			0.399855
$13$	−0.377416	+	0.274209i	−0.104676	+	0.0760519i	−0.638892	−	0.769296i	$-0.720607\pi$
$13$	−0.377416	+	0.274209i	−0.104676	+	0.0760519i	0.534216	+	0.845348i	$0.320607\pi$
$14$	−0.367828	−	1.13206i	−0.0983061	−	0.302555i
$15$		0			0
$16$	−0.557320	−	0.404916i	−0.139330	−	0.101229i
$17$	1.37234	+	0.997064i	0.332841	+	0.241823i	0.741635	−	0.670803i	$-0.234051\pi$
$17$	1.37234	+	0.997064i	0.332841	+	0.241823i	−0.408794	+	0.912627i	$0.634051\pi$
$18$	−0.242310	+	0.745753i	−0.0571130	+	0.175776i
$19$	1.73345	+	5.33501i	0.397681	+	1.22394i	0.926854	+	0.375422i	$0.122502\pi$
$19$	1.73345	+	5.33501i	0.397681	+	1.22394i	−0.529174	+	0.848514i	$0.677498\pi$
$20$		0			0
$21$	−1.51801			−0.331256
$22$	1.79364	+	1.88317i	0.382405	+	0.401494i
$23$	7.68641			1.60273			0.801364	−	0.598177i	$-0.204108\pi$
$23$	7.68641			1.60273			0.801364	+	0.598177i	$0.204108\pi$
$24$	2.14745	−	1.56021i	0.438346	−	0.318477i
$25$		0			0
$26$	−0.113040	+	0.347903i	−0.0221691	+	0.0682294i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	1.70108	+	1.23591i	0.321474	+	0.233564i
$29$	0.822307	−	2.53080i	0.152699	−	0.469958i	−0.845222	−	0.534416i	$-0.820532\pi$
$29$	0.822307	−	2.53080i	0.152699	−	0.469958i	0.997920	+	0.0644576i	$0.0205317\pi$
$30$		0			0
$31$	−3.20187	+	2.32629i	−0.575072	+	0.417814i	−0.836944	−	0.547288i	$-0.815660\pi$
$31$	−3.20187	+	2.32629i	−0.575072	+	0.417814i	0.261872	+	0.965103i	$0.415660\pi$
$32$	−5.84896			−1.03396
$33$	2.99091	−	1.43333i	0.520651	−	0.249510i
$34$	1.33013			0.228115
$35$		0			0
$36$	−0.428031	−	1.31734i	−0.0713385	−	0.219557i
$37$	−0.945402	+	2.90965i	−0.155423	+	0.478343i	−0.998204	−	0.0599143i	$-0.980917\pi$
$37$	−0.945402	+	2.90965i	−0.155423	+	0.478343i	0.842780	+	0.538258i	$0.180917\pi$
$38$	3.55857	+	2.58545i	0.577276	+	0.419416i
$39$	0.377416	+	0.274209i	0.0604350	+	0.0439086i
$40$		0			0
$41$	−0.417266	−	1.28421i	−0.0651660	−	0.200560i	0.913172	−	0.407575i	$-0.133625\pi$
$41$	−0.417266	−	1.28421i	−0.0651660	−	0.200560i	−0.978338	+	0.207014i	$0.933625\pi$
$42$	−0.962986	+	0.699650i	−0.148592	+	0.107958i
$43$	12.0864			1.84317			0.921583	−	0.388181i	$-0.126896\pi$
$43$	12.0864			1.84317			0.921583	+	0.388181i	$0.126896\pi$
$44$	−4.51858	−	0.828906i	−0.681202	−	0.124962i
$45$		0			0
$46$	4.87607	−	3.54267i	0.718937	−	0.522339i
$47$	0.790480	+	2.43285i	0.115303	+	0.354867i	0.992010	−	0.126158i	$-0.0402646\pi$
$47$	0.790480	+	2.43285i	0.115303	+	0.354867i	−0.876707	+	0.481025i	$0.840265\pi$
$48$	−0.212877	+	0.655168i	−0.0307262	+	0.0945654i
$49$	3.79887	+	2.76004i	0.542695	+	0.394291i
$50$		0			0
$51$	0.524187	−	1.61328i	0.0734009	−	0.225905i
$52$	−0.199682	−	0.614557i	−0.0276909	−	0.0852238i
$53$	−6.48598	+	4.71234i	−0.890918	+	0.647290i	−0.936117	−	0.351688i	$-0.885608\pi$
$53$	−6.48598	+	4.71234i	−0.890918	+	0.647290i	0.0451995	+	0.998978i	$0.485608\pi$
$54$	0.784131			0.106707
$55$		0			0
$56$	4.02938			0.538449
$57$	4.53823	−	3.29722i	0.601103	−	0.436727i
$58$	−0.644797	−	1.98448i	−0.0846659	−	0.260575i
$59$	2.33267	−	7.17923i	0.303688	−	0.934656i	−0.676475	−	0.736465i	$-0.736493\pi$
$59$	2.33267	−	7.17923i	0.303688	−	0.934656i	0.980163	−	0.198191i	$-0.0635065\pi$
$60$		0			0
$61$	8.99446	+	6.53486i	1.15162	+	0.836703i	0.988696	−	0.149935i	$-0.0479065\pi$
$61$	8.99446	+	6.53486i	1.15162	+	0.836703i	0.162927	+	0.986638i	$0.447907\pi$
$62$	−0.958996	+	2.95149i	−0.121793	+	0.374839i
$63$	0.469090	+	1.44371i	0.0590997	+	0.181890i
$64$	−2.59580	+	1.88596i	−0.324475	+	0.235745i
$65$		0			0
$66$	1.23674	−	2.28778i	0.152232	−	0.281607i
$67$	6.89959			0.842919			0.421460	−	0.906847i	$-0.361518\pi$
$67$	6.89959			0.842919			0.421460	+	0.906847i	$0.361518\pi$
$68$	−1.90088	+	1.38107i	−0.230516	+	0.167479i
$69$	−2.37523	−	7.31021i	−0.285944	−	0.880046i
$70$		0			0
$71$	−11.8018	−	8.57452i	−1.40062	−	1.01761i	−0.994604	−	0.103741i	$-0.966919\pi$
$71$	−11.8018	−	8.57452i	−1.40062	−	1.01761i	−0.406013	−	0.913867i	$-0.633081\pi$
$72$	−2.14745	−	1.56021i	−0.253079	−	0.183873i
$73$	−0.700618	+	2.15628i	−0.0820011	+	0.252373i	−0.983649	−	0.180098i	$-0.942358\pi$
$73$	−0.700618	+	2.15628i	−0.0820011	+	0.252373i	0.901648	+	0.432472i	$0.142358\pi$
$74$	0.741319	+	2.28155i	0.0861766	+	0.265224i
$75$		0			0
$76$	−7.77002			−0.891282
$77$	4.95202	+	0.908418i	0.564336	+	0.103524i
$78$	0.365807			0.0414195
$79$	−9.85457	+	7.15977i	−1.10873	+	0.805537i	−0.982463	−	0.186460i	$-0.940298\pi$
$79$	−9.85457	+	7.15977i	−1.10873	+	0.805537i	−0.126264	+	0.991997i	$0.540298\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.856598	−	0.622355i	−0.0945955	−	0.0687276i
$83$	−9.53087	−	6.92458i	−1.04615	−	0.760071i	−0.0746722	−	0.997208i	$-0.523791\pi$
$83$	−9.53087	−	6.92458i	−1.04615	−	0.760071i	−0.971476	+	0.237137i	$0.923791\pi$
$84$	0.649754	−	1.99974i	0.0708940	−	0.218189i
$85$		0			0
$86$	7.66735	−	5.57065i	0.826791	−	0.600699i
$87$	−2.66104			−0.285294
$88$	−7.93906	+	3.80462i	−0.846307	+	0.405573i
$89$	1.47962			0.156840			0.0784199	−	0.996920i	$-0.475013\pi$
$89$	1.47962			0.156840			0.0784199	+	0.996920i	$0.475013\pi$
$90$		0			0
$91$	0.218836	+	0.673508i	0.0229402	+	0.0706028i
$92$	−3.29002	+	10.1257i	−0.343009	+	1.05567i
$93$	3.20187	+	2.32629i	0.332018	+	0.241225i
$94$	1.62276	+	1.17901i	0.167375	+	0.121605i
$95$		0			0
$96$	1.80743	+	5.56269i	0.184470	+	0.567740i
$97$	11.4893	−	8.34744i	1.16656	−	0.847555i	0.175966	−	0.984396i	$-0.443695\pi$
$97$	11.4893	−	8.34744i	1.16656	−	0.847555i	0.990593	+	0.136842i	$0.0436952\pi$
$98$	3.68201			0.371939
$99$	−2.28742	−	2.40161i	−0.229894	−	0.241370i
$100$		0			0
$101$	2.12294	−	1.54241i	0.211240	−	0.153475i	−0.477134	−	0.878830i	$-0.658325\pi$
$101$	2.12294	−	1.54241i	0.211240	−	0.153475i	0.688375	+	0.725355i	$0.258325\pi$
$102$	−0.411032	−	1.26503i	−0.0406982	−	0.125256i
$103$	−0.00558722	+	0.0171957i	−0.000550525	+	0.00169434i	−0.951331	−	0.308170i	$-0.900284\pi$
$103$	−0.00558722	+	0.0171957i	−0.000550525	+	0.00169434i	0.950781	+	0.309864i	$0.100284\pi$
$104$	−1.00181	−	0.727858i	−0.0982356	−	0.0713724i
$105$		0			0
$106$	−1.94262	+	5.97878i	−0.188684	+	0.580711i
$107$	−4.54194	−	13.9786i	−0.439086	−	1.35137i	−0.888841	−	0.458215i	$-0.848489\pi$
$107$	−4.54194	−	13.9786i	−0.439086	−	1.35137i	0.449755	−	0.893152i	$-0.351511\pi$
$108$	−1.12060	+	0.814164i	−0.107830	+	0.0783430i
$109$	−5.31791			−0.509364			−0.254682	−	0.967025i	$-0.581971\pi$
$109$	−5.31791			−0.509364			−0.254682	+	0.967025i	$0.581971\pi$
$110$		0			0
$111$	3.05939			0.290384
$112$	−0.846014	+	0.614665i	−0.0799409	+	0.0580804i
$113$	−2.95942	−	9.10816i	−0.278399	−	0.856824i	−0.988300	−	0.152523i	$-0.951260\pi$
$113$	−2.95942	−	9.10816i	−0.278399	−	0.856824i	0.709901	−	0.704301i	$-0.248740\pi$
$114$	1.35925	−	4.18335i	0.127306	−	0.391806i
$115$		0			0
$116$	2.98196	+	2.16652i	0.276868	+	0.201157i
$117$	0.144160	−	0.443679i	0.0133276	−	0.0410182i
$118$	−1.82912	−	5.62946i	−0.168384	−	0.518233i
$119$	2.08322	−	1.51355i	0.190969	−	0.138747i
$120$		0			0
$121$	−10.6147	+	2.88594i	−0.964971	+	0.262358i
$122$	8.71779			0.789271
$123$	−1.09242	+	0.793688i	−0.0984999	+	0.0715644i
$124$	−1.69403	−	5.21369i	−0.152128	−	0.468203i
$125$		0			0
$126$	0.962986	+	0.699650i	0.0857896	+	0.0623298i
$127$	−14.6707	−	10.6589i	−1.30181	−	0.945823i	−0.301842	−	0.953358i	$-0.597602\pi$
$127$	−14.6707	−	10.6589i	−1.30181	−	0.945823i	−0.999972	+	0.00753504i	$0.997602\pi$
$128$	2.83739	−	8.73257i	0.250792	−	0.771858i
$129$	−3.73492	−	11.4949i	−0.328841	−	1.01207i
$130$		0			0
$131$	−8.67183			−0.757661			−0.378831	−	0.925466i	$-0.623674\pi$
$131$	−8.67183			−0.757661			−0.378831	+	0.925466i	$0.623674\pi$
$132$	0.607982	+	4.55358i	0.0529181	+	0.396338i
$133$	8.51535			0.738374
$134$	4.37693	−	3.18003i	0.378109	−	0.274712i
$135$		0			0
$136$	−1.39140	+	4.28229i	−0.119311	+	0.367203i
$137$	1.26268	+	0.917391i	0.107878	+	0.0783780i	0.640416	−	0.768028i	$-0.278762\pi$
$137$	1.26268	+	0.917391i	0.107878	+	0.0783780i	−0.532538	+	0.846406i	$0.678762\pi$
$138$	−4.87607	−	3.54267i	−0.415079	−	0.301572i
$139$	−4.41533	+	13.5890i	−0.374503	+	1.15260i	0.569310	+	0.822123i	$0.307211\pi$
$139$	−4.41533	+	13.5890i	−0.374503	+	1.15260i	−0.943813	+	0.330480i	$0.892789\pi$
$140$		0			0
$141$	2.06950	−	1.50358i	0.174284	−	0.126624i
$142$	−11.4388			−0.959921
$143$	−1.06711	−	1.12038i	−0.0892361	−	0.0936907i
$144$	0.688885			0.0574071
$145$		0			0
$146$	0.549376	+	1.69081i	0.0454667	+	0.139932i
$147$	1.45104	−	4.46584i	0.119680	−	0.368336i
$148$	−3.42835	−	2.49084i	−0.281809	−	0.204746i
$149$	8.91107	+	6.47427i	0.730023	+	0.530393i	0.889571	−	0.456797i	$-0.151004\pi$
$149$	8.91107	+	6.47427i	0.730023	+	0.530393i	−0.159548	+	0.987190i	$0.551004\pi$
$150$		0			0
$151$	−1.33557	−	4.11048i	−0.108688	−	0.334506i	0.881891	−	0.471454i	$-0.156271\pi$
$151$	−1.33557	−	4.11048i	−0.108688	−	0.334506i	−0.990578	+	0.136948i	$0.956271\pi$
$152$	−12.0462	+	8.75211i	−0.977079	+	0.709890i
$153$	−1.69631			−0.137138
$154$	3.56013	−	1.70611i	0.286884	−	0.137483i
$155$		0			0
$156$	−0.522774	+	0.379817i	−0.0418554	+	0.0304097i
$157$	−0.287846	−	0.885900i	−0.0229727	−	0.0707025i	0.938913	−	0.344155i	$-0.111834\pi$
$157$	−0.287846	−	0.885900i	−0.0229727	−	0.0707025i	−0.961886	+	0.273452i	$0.911834\pi$
$158$	−2.95156	+	9.08396i	−0.234813	+	0.722681i
$159$	6.48598	+	4.71234i	0.514372	+	0.373713i
$160$		0			0
$161$	3.60562	−	11.0969i	0.284162	−	0.874562i
$162$	−0.242310	−	0.745753i	−0.0190377	−	0.0585919i
$163$	−13.7196	+	9.96788i	−1.07460	+	0.780744i	−0.976734	−	0.214455i	$-0.931202\pi$
$163$	−13.7196	+	9.96788i	−1.07460	+	0.780744i	−0.0978685	+	0.995199i	$0.531202\pi$
$164$	1.87035			0.146050
$165$		0			0
$166$	−9.23769			−0.716984
$167$	−2.02297	+	1.46977i	−0.156542	+	0.113735i	−0.663299	−	0.748355i	$-0.730844\pi$
$167$	−2.02297	+	1.46977i	−0.156542	+	0.113735i	0.506757	+	0.862089i	$0.330844\pi$
$168$	−1.24515	−	3.83217i	−0.0960653	−	0.295658i
$169$	−3.94997	+	12.1568i	−0.303844	+	0.935135i
$170$		0			0
$171$	−4.53823	−	3.29722i	−0.347047	−	0.252145i
$172$	−5.17338	+	15.9220i	−0.394466	+	1.21404i
$173$	1.73592	+	5.34260i	0.131979	+	0.406191i	0.995108	−	0.0987935i	$-0.0314983\pi$
$173$	1.73592	+	5.34260i	0.131979	+	0.406191i	−0.863129	+	0.504984i	$0.831498\pi$
$174$	−1.68810	+	1.22648i	−0.127974	+	0.0929789i
$175$		0			0
$176$	1.08652	−	2.00989i	0.0818993	−	0.151501i
$177$	−7.54869			−0.567394
$178$	0.938636	−	0.681959i	0.0703538	−	0.0511150i
$179$	−2.46257	−	7.57901i	−0.184061	−	0.566481i	0.815870	−	0.578235i	$-0.196259\pi$
$179$	−2.46257	−	7.57901i	−0.184061	−	0.566481i	−0.999931	+	0.0117540i	$0.996259\pi$
$180$		0			0
$181$	14.0342	+	10.1964i	1.04315	+	0.757896i	0.970899	−	0.239491i	$-0.0769804\pi$
$181$	14.0342	+	10.1964i	1.04315	+	0.757896i	0.0722551	+	0.997386i	$0.476980\pi$
$182$	0.449245	+	0.326395i	0.0333002	+	0.0241940i
$183$	3.43558	−	10.5736i	0.253965	−	0.781625i
$184$	6.30480	+	19.4042i	0.464796	+	1.43049i
$185$		0			0
$186$	3.10338			0.227551
$187$	−2.67543	+	4.94915i	−0.195647	+	0.361917i
$188$	−3.54325			−0.258418
$189$	1.22809	−	0.892262i	0.0893306	−	0.0649025i
$190$		0			0
$191$	−6.85624	+	21.1013i	−0.496100	+	1.52684i	0.319134	+	0.947709i	$0.396608\pi$
$191$	−6.85624	+	21.1013i	−0.496100	+	1.52684i	−0.815235	+	0.579131i	$0.803392\pi$
$192$	2.59580	+	1.88596i	0.187336	+	0.136107i
$193$	−21.2734	−	15.4560i	−1.53129	−	1.11255i	−0.955515	−	0.294942i	$-0.904700\pi$
$193$	−21.2734	−	15.4560i	−1.53129	−	1.11255i	−0.575777	−	0.817607i	$-0.695300\pi$
$194$	3.44117	−	10.5908i	0.247061	−	0.760377i
$195$		0			0
$196$	−5.26196	+	3.82303i	−0.375854	+	0.273074i
$197$	11.5966			0.826227			0.413113	−	0.910680i	$-0.364441\pi$
$197$	11.5966			0.826227			0.413113	+	0.910680i	$0.364441\pi$
$198$	−2.55798	−	0.469247i	−0.181788	−	0.0333479i
$199$	14.4208			1.02226			0.511131	−	0.859503i	$-0.329227\pi$
$199$	14.4208			1.02226			0.511131	+	0.859503i	$0.329227\pi$
$200$		0			0
$201$	−2.13209	−	6.56190i	−0.150386	−	0.462841i
$202$	0.635844	−	1.95693i	0.0447379	−	0.137689i
$203$	−3.26801	−	2.37435i	−0.229369	−	0.166646i
$204$	1.90088	+	1.38107i	0.133088	+	0.0966943i
$205$		0			0
$206$	0.00438111	+	0.0134837i	0.000305247	+	0.000939453i
$207$	−6.21844	+	4.51796i	−0.432211	+	0.314020i
$208$	0.321373			0.0222832
$209$	−16.7777	+	8.04034i	−1.16054	+	0.556162i
$210$		0			0
$211$	2.64311	−	1.92033i	0.181959	−	0.132201i	−0.493077	−	0.869986i	$-0.664128\pi$
$211$	2.64311	−	1.92033i	0.181959	−	0.132201i	0.675036	+	0.737785i	$0.264128\pi$
$212$	−3.43157	−	10.5613i	−0.235681	−	0.725353i
$213$	−4.50789	+	13.8739i	−0.308876	+	0.950621i
$214$	−9.32406	−	6.77433i	−0.637380	−	0.463084i
$215$		0			0
$216$	−0.820252	+	2.52448i	−0.0558111	+	0.171769i
$217$	1.85653	+	5.71381i	0.126029	+	0.387878i
$218$	−3.37355	+	2.45103i	−0.228486	+	0.166005i
$219$	2.26725			0.153206
$220$		0			0
$221$	−0.791347			−0.0532318
$222$	1.94080	−	1.41007i	0.130258	−	0.0946379i
$223$	−5.60199	−	17.2412i	−0.375137	−	1.15455i	−0.943386	−	0.331696i	$-0.892379\pi$
$223$	−5.60199	−	17.2412i	−0.375137	−	1.15455i	0.568249	−	0.822857i	$-0.307621\pi$
$224$	−2.74369	+	8.44420i	−0.183320	+	0.564202i
$225$		0			0
$226$	−6.07534	−	4.41400i	−0.404126	−	0.293615i
$227$	8.69831	−	26.7707i	0.577327	−	1.77683i	−0.0507872	−	0.998709i	$-0.516173\pi$
$227$	8.69831	−	26.7707i	0.577327	−	1.77683i	0.628114	−	0.778121i	$-0.283827\pi$
$228$	2.40107	+	7.38973i	0.159015	+	0.489397i
$229$	14.8547	−	10.7926i	0.981624	−	0.713192i	0.0235534	−	0.999723i	$-0.492502\pi$
$229$	14.8547	−	10.7926i	0.981624	−	0.713192i	0.958071	+	0.286531i	$0.0925020\pi$
$230$		0			0
$231$	−0.666303	−	4.99037i	−0.0438395	−	0.328342i
$232$	7.06345			0.463738
$233$	7.31279	−	5.31305i	0.479077	−	0.348070i	−0.321891	−	0.946777i	$-0.604319\pi$
$233$	7.31279	−	5.31305i	0.479077	−	0.348070i	0.800968	+	0.598707i	$0.204319\pi$
$234$	−0.113040	−	0.347903i	−0.00738969	−	0.0227431i
$235$		0			0
$236$	8.45906	+	6.14587i	0.550638	+	0.400062i
$237$	9.85457	+	7.15977i	0.640123	+	0.465077i
$238$	0.623949	−	1.92032i	0.0404446	−	0.124476i
$239$	−3.68464	−	11.3402i	−0.238340	−	0.733534i	−0.996661	−	0.0816530i	$-0.973980\pi$
$239$	−3.68464	−	11.3402i	−0.238340	−	0.733534i	0.758321	−	0.651881i	$-0.226020\pi$
$240$		0			0
$241$	25.4155			1.63715			0.818577	−	0.574396i	$-0.194763\pi$
$241$	25.4155			1.63715			0.818577	+	0.574396i	$0.194763\pi$
$242$	−5.40356	+	6.72308i	−0.347354	+	0.432176i
$243$	−1.00000			−0.0641500
$244$	−12.4586	+	9.05168i	−0.797578	+	0.579475i
$245$		0			0
$246$	−0.327191	+	1.00699i	−0.0208610	+	0.0642035i
$247$	−2.11714	−	1.53819i	−0.134710	−	0.0978728i
$248$	−8.49901	−	6.17489i	−0.539688	−	0.392106i
$249$	−3.64047	+	11.2042i	−0.230705	+	0.710038i
$250$		0			0
$251$	11.9719	−	8.69810i	0.755660	−	0.549019i	−0.141916	−	0.989879i	$-0.545326\pi$
$251$	11.9719	−	8.69810i	0.755660	−	0.549019i	0.897576	+	0.440859i	$0.145326\pi$
$252$	−2.10265			−0.132454
$253$	3.37382	+	25.2687i	0.212110	+	1.58863i
$254$	−14.2194			−0.892205
$255$		0			0
$256$	−4.20790	−	12.9506i	−0.262993	−	0.809411i
$257$	2.52453	−	7.76969i	0.157476	−	0.484660i	−0.840928	−	0.541147i	$-0.817990\pi$
$257$	2.52453	−	7.76969i	0.157476	−	0.484660i	0.998403	+	0.0564874i	$0.0179901\pi$
$258$	−7.66735	−	5.57065i	−0.477348	−	0.346814i
$259$	3.75721	+	2.72977i	0.233462	+	0.169620i
$260$		0			0
$261$	0.822307	+	2.53080i	0.0508995	+	0.156653i
$262$	−5.50119	+	3.99685i	−0.339865	+	0.246926i
$263$	−9.66161			−0.595761			−0.297880	−	0.954603i	$-0.596280\pi$
$263$	−9.66161			−0.595761			−0.297880	+	0.954603i	$0.596280\pi$
$264$	6.07171	+	6.37480i	0.373688	+	0.392342i
$265$		0			0
$266$	5.40193	−	3.92473i	0.331213	−	0.240641i
$267$	−0.457229	−	1.40721i	−0.0279819	−	0.0861196i
$268$	−2.95324	+	9.08914i	−0.180398	+	0.555208i
$269$	−0.307325	−	0.223285i	−0.0187379	−	0.0136139i	0.578377	−	0.815770i	$-0.303686\pi$
$269$	−0.307325	−	0.223285i	−0.0187379	−	0.0136139i	−0.597115	+	0.802156i	$0.703686\pi$
$270$		0			0
$271$	−2.77138	+	8.52943i	−0.168349	+	0.518126i	−0.999267	−	0.0382687i	$-0.987816\pi$
$271$	−2.77138	+	8.52943i	−0.168349	+	0.518126i	0.830918	+	0.556395i	$0.187816\pi$
$272$	−0.361105	−	1.11137i	−0.0218952	−	0.0673865i
$273$	0.572920	−	0.416251i	0.0346747	−	0.0251926i
$274$	1.22384			0.0739349
$275$		0			0
$276$	10.6467			0.640859
$277$	−2.73375	+	1.98618i	−0.164255	+	0.119338i	−0.666876	−	0.745168i	$-0.732369\pi$
$277$	−2.73375	+	1.98618i	−0.164255	+	0.119338i	0.502621	+	0.864507i	$0.332369\pi$
$278$	3.46220	+	10.6556i	0.207649	+	0.639077i
$279$	1.22300	−	3.76402i	0.0732193	−	0.225346i
$280$		0			0
$281$	4.10617	+	2.98331i	0.244953	+	0.177969i	0.703487	−	0.710708i	$-0.251625\pi$
$281$	4.10617	+	2.98331i	0.244953	+	0.177969i	−0.458534	+	0.888677i	$0.651625\pi$
$282$	0.619840	−	1.90767i	0.0369109	−	0.113600i
$283$	−6.89047	−	21.2067i	−0.409596	−	1.26061i	−0.916996	−	0.398897i	$-0.869393\pi$
$283$	−6.89047	−	21.2067i	−0.409596	−	1.26061i	0.507400	−	0.861711i	$-0.330607\pi$
$284$	16.3471	−	11.8769i	0.970024	−	0.704764i
$285$		0			0
$286$	−1.19333	−	0.218909i	−0.0705631	−	0.0129444i
$287$	−2.04977			−0.120994
$288$	4.73191	−	3.43793i	0.278830	−	0.202582i
$289$	−4.36411	−	13.4313i	−0.256712	−	0.790079i
$290$		0			0
$291$	−11.4893	−	8.34744i	−0.673513	−	0.489336i
$292$	−2.54068	−	1.84591i	−0.148682	−	0.108024i
$293$	5.01120	−	15.4229i	0.292757	−	0.901014i	−0.691208	−	0.722655i	$-0.742921\pi$
$293$	5.01120	−	15.4229i	0.292757	−	0.901014i	0.983966	−	0.178358i	$-0.0570787\pi$
$294$	−1.13780	−	3.50180i	−0.0663581	−	0.204229i
$295$		0			0
$296$	−8.12081			−0.472012
$297$	−1.57721	+	2.91760i	−0.0915191	+	0.169296i
$298$	8.63696			0.500325
$299$	−2.90098	+	2.10768i	−0.167768	+	0.121890i
$300$		0			0
$301$	5.66963	−	17.4493i	0.326792	−	1.00576i
$302$	−2.74178	−	1.99202i	−0.157772	−	0.114628i
$303$	−2.12294	−	1.54241i	−0.121960	−	0.0886089i
$304$	1.19415	−	3.67521i	0.0684890	−	0.210788i
$305$		0			0
$306$	−1.07609	+	0.781829i	−0.0615162	+	0.0446942i
$307$	29.9543			1.70958			0.854791	−	0.518973i	$-0.173686\pi$
$307$	29.9543			1.70958			0.854791	+	0.518973i	$0.173686\pi$
$308$	−3.31632	+	6.13469i	−0.188965	+	0.349557i
$309$	0.0180806			0.00102857
$310$		0			0
$311$	1.57914	+	4.86011i	0.0895451	+	0.275591i	0.985794	−	0.167961i	$-0.0537182\pi$
$311$	1.57914	+	4.86011i	0.0895451	+	0.275591i	−0.896249	+	0.443552i	$0.853718\pi$
$312$	−0.382658	+	1.17770i	−0.0216637	+	0.0666741i
$313$	20.3149	+	14.7596i	1.14826	+	0.834262i	0.988249	−	0.152852i	$-0.0488459\pi$
$313$	20.3149	+	14.7596i	1.14826	+	0.834262i	0.160014	+	0.987115i	$0.448846\pi$
$314$	−0.590915	−	0.429325i	−0.0333473	−	0.0242282i
$315$		0			0
$316$	−5.21382	−	16.0465i	−0.293300	−	0.902685i
$317$	−10.0471	+	7.29966i	−0.564302	+	0.409989i	−0.833031	−	0.553226i	$-0.813396\pi$
$317$	−10.0471	+	7.29966i	−0.564302	+	0.409989i	0.268729	+	0.963216i	$0.413396\pi$
$318$	6.28647			0.352528
$319$	8.68082	+	1.59244i	0.486033	+	0.0891597i
$320$		0			0
$321$	−11.8909	+	8.63928i	−0.663688	+	0.482198i
$322$	−2.82728	−	8.70146i	−0.157558	−	0.484914i
$323$	−2.94046	+	9.04981i	−0.163612	+	0.503545i
$324$	1.12060	+	0.814164i	0.0622556	+	0.0452313i
$325$		0			0
$326$	−4.10918	+	12.6468i	−0.227586	+	0.700439i
$327$	1.64333	+	5.05764i	0.0908761	+	0.279688i
$328$	2.89970	−	2.10676i	0.160109	−	0.116326i
$329$	3.88313			0.214084
$330$		0			0
$331$	8.35534			0.459251			0.229626	−	0.973279i	$-0.426250\pi$
$331$	8.35534			0.459251			0.229626	+	0.973279i	$0.426250\pi$
$332$	13.2016	−	9.59150i	0.724530	−	0.526402i
$333$	−0.945402	−	2.90965i	−0.0518077	−	0.159448i
$334$	−0.605903	+	1.86478i	−0.0331535	+	0.102036i
$335$		0			0
$336$	0.846014	+	0.614665i	0.0461539	+	0.0335328i
$337$	1.21555	−	3.74107i	0.0662150	−	0.203789i	−0.912475	−	0.409133i	$-0.865831\pi$
$337$	1.21555	−	3.74107i	0.0662150	−	0.203789i	0.978690	+	0.205344i	$0.0658313\pi$
$338$	3.09729	+	9.53249i	0.168471	+	0.518499i
$339$	−7.74787	+	5.62916i	−0.420806	+	0.305734i
$340$		0			0
$341$	−9.05298	−	9.50490i	−0.490246	−	0.514719i
$342$	−4.39863			−0.237851
$343$	14.3634	−	10.4356i	0.775548	−	0.563469i
$344$	9.91394	+	30.5120i	0.534524	+	1.64509i
$345$		0			0
$346$	3.56363	+	2.58913i	0.191582	+	0.139193i
$347$	−7.44241	−	5.40723i	−0.399529	−	0.290275i	0.369820	−	0.929103i	$-0.379419\pi$
$347$	−7.44241	−	5.40723i	−0.399529	−	0.290275i	−0.769349	+	0.638828i	$0.779419\pi$
$348$	1.13901	−	3.50551i	0.0610573	−	0.187915i
$349$	−6.24065	−	19.2067i	−0.334054	−	1.02811i	−0.967186	−	0.254069i	$-0.918231\pi$
$349$	−6.24065	−	19.2067i	−0.334054	−	1.02811i	0.633132	−	0.774044i	$-0.281769\pi$
$350$		0			0
$351$	−0.466512			−0.0249006
$352$	−2.56730	−	19.2282i	−0.136838	−	1.02487i
$353$	34.8561			1.85520			0.927601	−	0.373572i	$-0.121867\pi$
$353$	34.8561			1.85520			0.927601	+	0.373572i	$0.121867\pi$
$354$	−4.78870	+	3.47920i	−0.254517	+	0.184917i
$355$		0			0
$356$	−0.633325	+	1.94917i	−0.0335662	+	0.103306i
$357$	−2.08322	−	1.51355i	−0.110256	−	0.0801055i
$358$	−5.05536	−	3.67294i	−0.267184	−	0.194121i
$359$	8.78520	−	27.0381i	0.463665	−	1.42701i	−0.396988	−	0.917824i	$-0.629945\pi$
$359$	8.78520	−	27.0381i	0.463665	−	1.42701i	0.860654	−	0.509191i	$-0.170055\pi$
$360$		0			0
$361$	−10.0862	+	7.32802i	−0.530850	+	0.385685i
$362$	13.6025			0.714931
$363$	6.02481	+	9.20335i	0.316220	+	0.483051i
$364$	−0.980911			−0.0514137
$365$		0			0
$366$	−2.69394	−	8.29111i	−0.140815	−	0.433383i
$367$	−8.21286	+	25.2766i	−0.428708	+	1.31943i	0.470692	+	0.882298i	$0.344004\pi$
$367$	−8.21286	+	25.2766i	−0.428708	+	1.31943i	−0.899399	+	0.437128i	$0.855996\pi$
$368$	−4.28379	−	3.11235i	−0.223308	−	0.162243i
$369$	1.09242	+	0.793688i	0.0568690	+	0.0413177i
$370$		0			0
$371$	3.76074	+	11.5744i	0.195248	+	0.600912i
$372$	−4.43503	+	3.22224i	−0.229945	+	0.167065i
$373$	19.1900			0.993621			0.496811	−	0.867859i	$-0.334504\pi$
$373$	19.1900			0.993621			0.496811	+	0.867859i	$0.334504\pi$
$374$	0.583836	+	4.37273i	0.0301894	+	0.226108i
$375$		0			0
$376$	−5.49327	+	3.99110i	−0.283294	+	0.205825i
$377$	0.383616	+	1.18065i	0.0197572	+	0.0608065i
$378$	0.367828	−	1.13206i	0.0189190	−	0.0582268i
$379$	2.46014	+	1.78739i	0.126369	+	0.0918122i	0.649174	−	0.760640i	$-0.275115\pi$
$379$	2.46014	+	1.78739i	0.126369	+	0.0918122i	−0.522806	+	0.852452i	$0.675115\pi$
$380$		0			0
$381$	−5.60371	+	17.2464i	−0.287087	+	0.883562i
$382$	5.37619	+	16.5462i	0.275070	+	0.846579i
$383$	7.03315	−	5.10988i	0.359377	−	0.261103i	−0.393415	−	0.919361i	$-0.628706\pi$
$383$	7.03315	−	5.10988i	0.359377	−	0.261103i	0.752792	+	0.658258i	$0.228706\pi$
$384$	−9.18197			−0.468566
$385$		0			0
$386$	−20.6190			−1.04948
$387$	−9.77814	+	7.10424i	−0.497051	+	0.361129i
$388$	6.07869	+	18.7083i	0.308599	+	0.949770i
$389$	−4.23102	+	13.0218i	−0.214521	+	0.660229i	0.784666	+	0.619919i	$0.212835\pi$
$389$	−4.23102	+	13.0218i	−0.214521	+	0.660229i	−0.999187	+	0.0403101i	$0.987165\pi$
$390$		0			0
$391$	10.5484	+	7.66384i	0.533454	+	0.387577i
$392$	−3.85162	+	11.8541i	−0.194536	+	0.598721i
$393$	2.67974	+	8.24740i	0.135175	+	0.416026i
$394$	7.35663	−	5.34490i	0.370621	−	0.269272i
$395$		0			0
$396$	4.14283	−	1.98536i	0.208185	−	0.0997680i
$397$	−8.96241			−0.449811			−0.224905	−	0.974381i	$-0.572207\pi$
$397$	−8.96241			−0.449811			−0.224905	+	0.974381i	$0.572207\pi$
$398$	9.14818	−	6.64654i	0.458557	−	0.333161i
$399$	−2.63139	−	8.09858i	−0.131734	−	0.405436i
$400$		0			0
$401$	−5.98370	−	4.34742i	−0.298812	−	0.217100i	0.428269	−	0.903651i	$-0.359124\pi$
$401$	−5.98370	−	4.34742i	−0.298812	−	0.217100i	−0.727081	+	0.686552i	$0.759124\pi$
$402$	−4.37693	−	3.18003i	−0.218301	−	0.158605i
$403$	0.570546	−	1.75596i	0.0284209	−	0.0874706i
$404$	1.12320	+	3.45684i	0.0558811	+	0.171984i
$405$		0			0
$406$	−3.16748			−0.157199
$407$	−9.98030	−	1.83082i	−0.494705	−	0.0907506i
$408$	4.50266			0.222915
$409$	22.5760	−	16.4024i	1.11631	−	0.811047i	0.132665	−	0.991161i	$-0.457647\pi$
$409$	22.5760	−	16.4024i	1.11631	−	0.811047i	0.983646	+	0.180114i	$0.0576467\pi$
$410$		0			0
$411$	0.482301	−	1.48437i	0.0237902	−	0.0732186i
$412$	−0.0202612	−	0.0147206i	−0.000998196	−	0.000725232i
$413$	−9.27049	−	6.73540i	−0.456171	−	0.331428i
$414$	−1.86249	+	5.73217i	−0.0915366	+	0.281721i
$415$		0			0
$416$	2.20749	−	1.60384i	0.108231	−	0.0786346i
$417$	14.2883			0.699702
$418$	−6.93757	+	12.8335i	−0.339328	+	0.627705i
$419$	−25.4267			−1.24218			−0.621088	−	0.783741i	$-0.713309\pi$
$419$	−25.4267			−1.24218			−0.621088	+	0.783741i	$0.713309\pi$
$420$		0			0
$421$	−1.03694	−	3.19137i	−0.0505373	−	0.155538i	0.922603	−	0.385751i	$-0.126058\pi$
$421$	−1.03694	−	3.19137i	−0.0505373	−	0.155538i	−0.973140	+	0.230213i	$0.926058\pi$
$422$	0.791641	−	2.43642i	0.0385365	−	0.118603i
$423$	−2.06950	−	1.50358i	−0.100623	−	0.0731066i
$424$	−17.2163	−	12.5084i	−0.836099	−	0.607461i
$425$		0			0
$426$	3.53478	+	10.8789i	0.171261	+	0.527086i
$427$	13.6536	−	9.91995i	0.660746	−	0.480060i
$428$	20.3588			0.984079
$429$	−0.735788	+	1.36110i	−0.0355242	+	0.0657144i
$430$		0			0
$431$	−8.39488	+	6.09924i	−0.404367	+	0.293790i	−0.771317	−	0.636451i	$-0.780402\pi$
$431$	−8.39488	+	6.09924i	−0.404367	+	0.293790i	0.366950	+	0.930241i	$0.380402\pi$
$432$	−0.212877	−	0.655168i	−0.0102421	−	0.0315218i
$433$	−8.39497	+	25.8371i	−0.403437	+	1.24165i	0.518757	+	0.854922i	$0.326395\pi$
$433$	−8.39497	+	25.8371i	−0.403437	+	1.24165i	−0.922194	+	0.386728i	$0.873605\pi$
$434$	3.81123	+	2.76902i	0.182945	+	0.132917i
$435$		0			0
$436$	2.27623	−	7.00553i	0.109012	−	0.335504i
$437$	13.3240	+	41.0071i	0.637374	+	1.96163i
$438$	1.43829	−	1.04498i	0.0687239	−	0.0499309i
$439$	−30.5785			−1.45943			−0.729715	−	0.683751i	$-0.760347\pi$
$439$	−30.5785			−1.45943			−0.729715	+	0.683751i	$0.760347\pi$
$440$		0			0
$441$	−4.69566			−0.223603
$442$	−0.502011	+	0.364733i	−0.0238782	+	0.0173486i
$443$	−1.26231	−	3.88499i	−0.0599741	−	0.184581i	0.916581	−	0.399849i	$-0.130938\pi$
$443$	−1.26231	−	3.88499i	−0.0599741	−	0.184581i	−0.976555	+	0.215268i	$0.930938\pi$
$444$	−1.30951	+	4.03027i	−0.0621467	+	0.191268i
$445$		0			0
$446$	−11.5002	−	8.35540i	−0.544551	−	0.395640i
$447$	3.40372	−	10.4756i	0.160991	−	0.495478i
$448$	1.50511	+	4.63226i	0.0711099	+	0.218854i
$449$	−16.4256	+	11.9339i	−0.775172	+	0.563195i	−0.903526	−	0.428533i	$-0.859031\pi$
$449$	−16.4256	+	11.9339i	−0.775172	+	0.563195i	0.128354	+	0.991728i	$0.459031\pi$
$450$		0			0
$451$	4.03864	−	1.93543i	0.190172	−	0.0911356i
$452$	13.2653			0.623948
$453$	−3.49658	+	2.54041i	−0.164284	+	0.119359i
$454$	−6.82062	−	20.9917i	−0.320107	−	0.985189i
$455$		0			0
$456$	12.0462	+	8.75211i	0.564117	+	0.409855i
$457$	−20.8841	−	15.1732i	−0.976917	−	0.709772i	−0.0198993	−	0.999802i	$-0.506335\pi$
$457$	−20.8841	−	15.1732i	−0.976917	−	0.709772i	−0.957017	+	0.290030i	$0.906335\pi$
$458$	4.44914	−	13.6931i	0.207895	−	0.639835i
$459$	0.524187	+	1.61328i	0.0244670	+	0.0753016i
$460$		0			0
$461$	2.54024			0.118311			0.0591553	−	0.998249i	$-0.481159\pi$
$461$	2.54024			0.118311			0.0591553	+	0.998249i	$0.481159\pi$
$462$	−2.72275	−	2.85867i	−0.126674	−	0.132997i
$463$	2.87598			0.133658			0.0668290	−	0.997764i	$-0.478712\pi$
$463$	2.87598			0.133658			0.0668290	+	0.997764i	$0.478712\pi$
$464$	−1.48305	+	1.07750i	−0.0688489	+	0.0500216i
$465$		0			0
$466$	2.19026	−	6.74094i	0.101462	−	0.312268i
$467$	18.4719	+	13.4207i	0.854780	+	0.621034i	0.926460	−	0.376394i	$-0.122836\pi$
$467$	18.4719	+	13.4207i	0.854780	+	0.621034i	−0.0716801	+	0.997428i	$0.522836\pi$
$468$	0.522774	+	0.379817i	0.0241652	+	0.0175571i
$469$	3.23653	−	9.96101i	0.149449	−	0.459957i
$470$		0			0
$471$	−0.753592	+	0.547517i	−0.0347237	+	0.0252282i
$472$	20.0372			0.922286
$473$	5.30514	+	39.7336i	0.243930	+	1.82695i
$474$	9.55144			0.438712
$475$		0			0
$476$	1.10218	+	3.39217i	0.0505184	+	0.155480i
$477$	2.47742	−	7.62473i	0.113433	−	0.349112i
$478$	−7.56414	−	5.49567i	−0.345976	−	0.251366i
$479$	19.3407	+	14.0519i	0.883701	+	0.642046i	0.934228	−	0.356677i	$-0.116090\pi$
$479$	19.3407	+	14.0519i	0.883701	+	0.642046i	−0.0505272	+	0.998723i	$0.516090\pi$
$480$		0			0
$481$	−0.441042	−	1.35739i	−0.0201098	−	0.0618915i
$482$	16.1230	−	11.7140i	0.734380	−	0.533559i
$483$	−11.6680			−0.530913
$484$	0.741635	−	15.2185i	0.0337107	−	0.691748i
$485$		0			0
$486$	−0.634375	+	0.460901i	−0.0287759	+	0.0209069i
$487$	4.21888	+	12.9844i	0.191176	+	0.588379i	1.00000		0.000328069i	$0.000104428\pi$
$487$	4.21888	+	12.9844i	0.191176	+	0.588379i	−0.808824	+	0.588051i	$0.799896\pi$
$488$	−9.11937	+	28.0665i	−0.412815	+	1.27051i
$489$	13.7196	+	9.96788i	0.620422	+	0.450763i
$490$		0			0
$491$	13.3256	−	41.0118i	0.601374	−	1.85084i	0.0813521	−	0.996685i	$-0.474076\pi$
$491$	13.3256	−	41.0118i	0.601374	−	1.85084i	0.520022	−	0.854153i	$-0.325924\pi$
$492$	−0.577971	−	1.77881i	−0.0260570	−	0.0801951i
$493$	3.65185	−	2.65323i	0.164471	−	0.119495i
$494$	−2.05202			−0.0923245
$495$		0			0
$496$	2.72642			0.122420
$497$	−17.9152	+	13.0162i	−0.803608	+	0.583855i
$498$	2.85460	+	8.78557i	0.127918	+	0.393691i
$499$	3.68917	−	11.3541i	0.165150	−	0.508279i	−0.833897	−	0.551919i	$-0.813896\pi$
$499$	3.68917	−	11.3541i	0.165150	−	0.508279i	0.999047	+	0.0436404i	$0.0138956\pi$
$500$		0			0
$501$	2.02297	+	1.46977i	0.0903797	+	0.0656647i
$502$	3.58572	−	11.0357i	0.160039	−	0.492548i
$503$	−5.41614	−	16.6692i	−0.241494	−	0.743241i	−0.996193	−	0.0871709i	$-0.972217\pi$
$503$	−5.41614	−	16.6692i	−0.241494	−	0.743241i	0.754700	−	0.656071i	$-0.227783\pi$
$504$	−3.25984	+	2.36841i	−0.145205	+	0.105497i
$505$		0			0
$506$	13.7866	+	14.4749i	0.612891	+	0.643486i
$507$	12.7824			0.567685
$508$	20.3209	−	14.7640i	0.901596	−	0.655048i
$509$	8.23324	+	25.3393i	0.364932	+	1.12315i	0.950024	+	0.312178i	$0.101059\pi$
$509$	8.23324	+	25.3393i	0.364932	+	1.12315i	−0.585092	+	0.810967i	$0.698941\pi$
$510$		0			0
$511$	2.78439	+	2.02298i	0.123174	+	0.0894912i
$512$	6.21843	+	4.51795i	0.274818	+	0.199667i
$513$	−1.73345	+	5.33501i	−0.0765337	+	0.235546i
$514$	−1.97956	−	6.09246i	−0.0873146	−	0.268727i
$515$		0			0
$516$	16.7414			0.736999
$517$	−7.65090	+	3.66652i	−0.336486	+	0.161253i
$518$	3.64164			0.160004
$519$	4.54469	−	3.30191i	0.199490	−	0.144938i
$520$		0			0
$521$	8.18853	−	25.2017i	0.358746	−	1.10411i	−0.595060	−	0.803682i	$-0.702872\pi$
$521$	8.18853	−	25.2017i	0.358746	−	1.10411i	0.953805	−	0.300425i	$-0.0971285\pi$
$522$	1.68810	+	1.22648i	0.0738861	+	0.0536814i
$523$	−7.22278	−	5.24766i	−0.315830	−	0.229464i	0.418564	−	0.908187i	$-0.362534\pi$
$523$	−7.22278	−	5.24766i	−0.315830	−	0.229464i	−0.734394	+	0.678723i	$0.762534\pi$
$524$	3.71181	−	11.4238i	0.162151	−	0.499050i
$525$		0			0
$526$	−6.12909	+	4.45304i	−0.267241	+	0.194162i
$527$	−6.71351			−0.292445
$528$	−2.24727	−	0.412248i	−0.0978000	−	0.0179408i
$529$	36.0809			1.56874
$530$		0			0
$531$	2.33267	+	7.17923i	0.101229	+	0.311552i
$532$	−3.64484	+	11.2176i	−0.158024	+	0.486347i
$533$	0.509626	+	0.370265i	0.0220743	+	0.0160380i
$534$	−0.938636	−	0.681959i	−0.0406188	−	0.0295113i
$535$		0			0
$536$	5.65941	+	17.4179i	0.244449	+	0.752337i
$537$	−6.44709	+	4.68408i	−0.278212	+	0.202133i
$538$	−0.297872			−0.0128422
$539$	−7.40605	+	13.7001i	−0.319001	+	0.590103i
$540$		0			0
$541$	−14.3869	+	10.4527i	−0.618541	+	0.449396i	−0.852412	−	0.522871i	$-0.824861\pi$
$541$	−14.3869	+	10.4527i	−0.618541	+	0.449396i	0.233871	+	0.972268i	$0.424861\pi$
$542$	2.17312	+	6.68819i	0.0933437	+	0.287282i
$543$	5.36059	−	16.4982i	0.230045	−	0.708005i
$544$	−8.02676	−	5.83179i	−0.344145	−	0.250036i
$545$		0			0
$546$	0.171596	−	0.528119i	0.00734364	−	0.0226014i
$547$	−4.74315	−	14.5979i	−0.202803	−	0.624162i	−0.999796	−	0.0201748i	$-0.993578\pi$
$547$	−4.74315	−	14.5979i	−0.202803	−	0.624162i	0.796994	−	0.603987i	$-0.206422\pi$
$548$	−1.74899	+	1.27071i	−0.0747130	+	0.0542822i
$549$	−11.1178			−0.474495
$550$		0			0
$551$	14.9273			0.635923
$552$	16.5062	−	11.9924i	0.702549	−	0.510432i
$553$	5.71394	+	17.5857i	0.242982	+	0.747821i
$554$	−0.818789	+	2.51997i	−0.0347870	+	0.107063i
$555$		0			0
$556$	−16.0115	−	11.6330i	−0.679038	−	0.493350i
$557$	5.22462	−	16.0797i	0.221374	−	0.681320i	−0.777265	−	0.629173i	$-0.783394\pi$
$557$	5.22462	−	16.0797i	0.221374	−	0.681320i	0.998639	−	0.0521466i	$-0.0166063\pi$
$558$	−0.958996	−	2.95149i	−0.0405975	−	0.124946i
$559$	−4.56162	+	3.31421i	−0.192936	+	0.140176i
$560$		0			0
$561$	5.53367	+	1.01512i	0.233632	+	0.0428583i
$562$	3.97986			0.167880
$563$	−9.58106	+	6.96105i	−0.403793	+	0.293373i	−0.771084	−	0.636733i	$-0.780285\pi$
$563$	−9.58106	+	6.96105i	−0.403793	+	0.293373i	0.367291	+	0.930106i	$0.380285\pi$
$564$	1.09492	+	3.36983i	0.0461046	+	0.141895i
$565$		0			0
$566$	−14.1453	−	10.2772i	−0.594573	−	0.431982i
$567$	−1.22809	−	0.892262i	−0.0515750	−	0.0374715i
$568$	11.9657	−	36.8267i	0.502070	−	1.54521i
$569$	8.51586	+	26.2091i	0.357003	+	1.09874i	0.954839	+	0.297124i	$0.0960276\pi$
$569$	8.51586	+	26.2091i	0.357003	+	1.09874i	−0.597835	+	0.801619i	$0.703972\pi$
$570$		0			0
$571$	18.4594			0.772502			0.386251	−	0.922394i	$-0.373770\pi$
$571$	18.4594			0.772502			0.386251	+	0.922394i	$0.373770\pi$
$572$	1.93268	−	0.926194i	0.0808094	−	0.0387261i
$573$	22.1873			0.926887
$574$	−1.30032	+	0.944739i	−0.0542744	+	0.0394326i
$575$		0			0
$576$	0.991507	−	3.05154i	0.0413128	−	0.127148i
$577$	14.9374	+	10.8527i	0.621854	+	0.451803i	0.853569	−	0.520980i	$-0.174434\pi$
$577$	14.9374	+	10.8527i	0.621854	+	0.451803i	−0.231715	+	0.972784i	$0.574434\pi$
$578$	−8.95900	−	6.50909i	−0.372645	−	0.270743i
$579$	−8.12571	+	25.0084i	−0.337693	+	1.03931i
$580$		0			0
$581$	−14.4679	+	10.5116i	−0.600230	+	0.436093i
$582$	−11.1359			−0.461596
$583$	−18.3385	−	19.2539i	−0.759503	−	0.797417i
$584$	−6.01816			−0.249033
$585$		0			0
$586$	−3.92943	−	12.0936i	−0.162323	−	0.499580i
$587$	3.05610	−	9.40571i	0.126139	−	0.388215i	−0.867968	−	0.496620i	$-0.834574\pi$
$587$	3.05610	−	9.40571i	0.126139	−	0.388215i	0.994107	+	0.108405i	$0.0345743\pi$
$588$	5.26196	+	3.82303i	0.216999	+	0.157659i
$589$	−17.9611	−	13.0495i	−0.740073	−	0.537694i
$590$		0			0
$591$	−3.58356	−	11.0291i	−0.147408	−	0.453675i
$592$	1.70506	−	1.23880i	0.0700773	−	0.0509142i
$593$	20.5782			0.845047			0.422523	−	0.906352i	$-0.361144\pi$
$593$	20.5782			0.845047			0.422523	+	0.906352i	$0.361144\pi$
$594$	0.344181	+	2.57779i	0.0141219	+	0.105768i
$595$		0			0
$596$	−12.3431	+	8.96776i	−0.505591	+	0.367334i
$597$	−4.45626	−	13.7150i	−0.182383	−	0.561316i
$598$	−0.868876	+	2.67412i	−0.0355310	+	0.109353i
$599$	−16.5591	−	12.0309i	−0.676588	−	0.491570i	0.195636	−	0.980677i	$-0.437323\pi$
$599$	−16.5591	−	12.0309i	−0.676588	−	0.491570i	−0.872224	+	0.489107i	$0.837323\pi$
$600$		0			0
$601$	2.50993	−	7.72476i	0.102382	−	0.315100i	−0.886725	−	0.462297i	$-0.847025\pi$
$601$	2.50993	−	7.72476i	0.102382	−	0.315100i	0.989107	+	0.147198i	$0.0470253\pi$
$602$	−4.44573	−	13.6826i	−0.181195	−	0.557659i
$603$	−5.58189	+	4.05548i	−0.227312	+	0.165152i
$604$	5.98658			0.243591
$605$		0			0
$606$	−2.05764			−0.0835857
$607$	−14.7044	+	10.6834i	−0.596834	+	0.433625i	−0.844754	−	0.535155i	$-0.820253\pi$
$607$	−14.7044	+	10.6834i	−0.596834	+	0.433625i	0.247920	+	0.968781i	$0.420253\pi$
$608$	−10.1389	−	31.2043i	−0.411186	−	1.26550i
$609$	−1.24827	+	3.84177i	−0.0505823	+	0.155676i
$610$		0			0
$611$	−0.965448	−	0.701439i	−0.0390579	−	0.0283772i
$612$	0.726072	−	2.23462i	0.0293497	−	0.0903291i
$613$	9.35677	+	28.7972i	0.377916	+	1.16311i	0.941490	+	0.337041i	$0.109426\pi$
$613$	9.35677	+	28.7972i	0.377916	+	1.16311i	−0.563573	+	0.826066i	$0.690574\pi$
$614$	19.0023	−	13.8060i	0.766869	−	0.557163i
$615$		0			0
$616$	1.76863	+	13.2464i	0.0712601	+	0.533713i
$617$	−29.0856			−1.17094			−0.585471	−	0.810694i	$-0.699090\pi$
$617$	−29.0856			−1.17094			−0.585471	+	0.810694i	$0.699090\pi$
$618$	0.0114699	−	0.00833338i	0.000461387	−	0.000335218i
$619$	4.55168	+	14.0086i	0.182948	+	0.563055i	0.999907	−	0.0136403i	$-0.00434198\pi$
$619$	4.55168	+	14.0086i	0.182948	+	0.563055i	−0.816959	+	0.576695i	$0.804342\pi$
$620$		0			0
$621$	6.21844	+	4.51796i	0.249537	+	0.181299i
$622$	3.24180	+	2.35530i	0.129984	+	0.0944391i
$623$	0.694076	−	2.13615i	0.0278076	−	0.0855829i
$624$	−0.0993098	−	0.305644i	−0.00397557	−	0.0122356i
$625$		0			0
$626$	19.6900			0.786969
$627$	12.8314	+	13.4720i	0.512438	+	0.538018i
$628$	1.29024			0.0514863
$629$	−4.19852	+	3.05040i	−0.167406	+	0.121627i
$630$		0			0
$631$	3.05624	−	9.40615i	0.121667	−	0.374453i	−0.871612	−	0.490196i	$-0.836925\pi$
$631$	3.05624	−	9.40615i	0.121667	−	0.374453i	0.993279	+	0.115744i	$0.0369251\pi$
$632$	−26.1579	−	19.0048i	−1.04051	−	0.755972i
$633$	−2.64311	−	1.92033i	−0.105054	−	0.0763262i
$634$	−3.00923	+	9.26144i	−0.119512	+	0.367819i
$635$		0			0
$636$	−8.98398	+	6.52724i	−0.356238	+	0.258822i
$637$	−2.19058			−0.0867940
$638$	6.24086	−	2.99079i	0.247078	−	0.118407i
$639$	14.5878			0.577086
$640$		0			0
$641$	13.6718	+	42.0775i	0.540004	+	1.66196i	0.732581	+	0.680680i	$0.238316\pi$
$641$	13.6718	+	42.0775i	0.540004	+	1.66196i	−0.192576	+	0.981282i	$0.561684\pi$
$642$	−3.56148	+	10.9611i	−0.140560	+	0.432600i
$643$	1.03153	+	0.749447i	0.0406794	+	0.0295553i	0.607939	−	0.793984i	$-0.291996\pi$
$643$	1.03153	+	0.749447i	0.0406794	+	0.0295553i	−0.567260	+	0.823539i	$0.691996\pi$
$644$	13.0752	+	9.49968i	0.515235	+	0.374340i
$645$		0			0
$646$	2.30571	+	7.09624i	0.0907168	+	0.279198i
$647$	−34.8647	+	25.3307i	−1.37067	+	0.995851i	−0.372986	+	0.927837i	$0.621666\pi$
$647$	−34.8647	+	25.3307i	−1.37067	+	0.995851i	−0.997684	+	0.0680139i	$0.978334\pi$
$648$	2.65439			0.104274
$649$	24.6253	+	4.51735i	0.966626	+	0.177322i
$650$		0			0
$651$	4.86045	−	3.53133i	0.190496	−	0.138404i
$652$	−7.25871	−	22.3400i	−0.284273	−	0.874902i
$653$	−5.96094	+	18.3459i	−0.233270	+	0.717930i	0.764077	+	0.645125i	$0.223195\pi$
$653$	−5.96094	+	18.3459i	−0.233270	+	0.717930i	−0.997346	+	0.0728045i	$0.976805\pi$
$654$	3.37355	+	2.45103i	0.131916	+	0.0958429i
$655$		0			0
$656$	−0.287448	+	0.884675i	−0.0112230	+	0.0345408i
$657$	−0.700618	−	2.15628i	−0.0273337	−	0.0841245i
$658$	2.46336	−	1.78974i	0.0960319	−	0.0697712i
$659$	33.4717			1.30387			0.651937	−	0.758273i	$-0.273957\pi$
$659$	33.4717			1.30387			0.651937	+	0.758273i	$0.273957\pi$
$660$		0			0
$661$	−6.94932			−0.270297			−0.135149	−	0.990825i	$-0.543151\pi$
$661$	−6.94932			−0.270297			−0.135149	+	0.990825i	$0.543151\pi$
$662$	5.30042	−	3.85098i	0.206007	−	0.149673i
$663$	0.244540	+	0.752616i	0.00949714	+	0.0292292i
$664$	9.66323	−	29.7404i	0.375006	−	1.15415i
$665$		0			0
$666$	−1.94080	−	1.41007i	−0.0752044	−	0.0546392i
$667$	6.32059	−	19.4528i	0.244734	−	0.753215i
$668$	−1.07030	−	3.29406i	−0.0414113	−	0.127451i
$669$	−14.6662	+	10.6556i	−0.567028	+	0.411970i
$670$		0			0
$671$	−17.5351	+	32.4372i	−0.676934	+	1.25222i
$672$	8.87876			0.342506
$673$	−17.6810	+	12.8460i	−0.681553	+	0.495177i	−0.873873	−	0.486155i	$-0.838399\pi$
$673$	−17.6810	+	12.8460i	−0.681553	+	0.495177i	0.192319	+	0.981332i	$0.438399\pi$
$674$	−0.953148	−	2.93349i	−0.0367139	−	0.112994i
$675$		0			0
$676$	−14.3239	−	10.4069i	−0.550920	−	0.400267i
$677$	1.01819	+	0.739757i	0.0391322	+	0.0284312i	0.607179	−	0.794565i	$-0.292301\pi$
$677$	1.01819	+	0.739757i	0.0391322	+	0.0284312i	−0.568047	+	0.822996i	$0.692301\pi$
$678$	−2.32058	+	7.14200i	−0.0891211	+	0.274287i
$679$	−6.66179	−	20.5029i	−0.255656	−	0.786828i
$680$		0			0
$681$	−28.1483			−1.07865
$682$	−10.1238	−	1.85715i	−0.387660	−	0.0711139i
$683$	−19.8677			−0.760215			−0.380108	−	0.924942i	$-0.624113\pi$
$683$	−19.8677			−0.760215			−0.380108	+	0.924942i	$0.624113\pi$
$684$	6.28608	−	4.56710i	0.240354	−	0.174628i
$685$		0			0
$686$	4.30199	−	13.2402i	0.164251	−	0.505512i
$687$	−14.8547	−	10.7926i	−0.566741	−	0.411762i
$688$	−6.73601	−	4.89400i	−0.256808	−	0.186582i
$689$	1.15575	−	3.55703i	0.0440305	−	0.135512i
$690$		0			0
$691$	−6.01690	+	4.37154i	−0.228894	+	0.166301i	−0.696321	−	0.717730i	$-0.745181\pi$
$691$	−6.01690	+	4.37154i	−0.228894	+	0.166301i	0.467427	+	0.884032i	$0.345181\pi$
$692$	−7.78108			−0.295792
$693$	−4.54023	+	2.17580i	−0.172469	+	0.0826518i
$694$	−7.21347			−0.273820
$695$		0			0
$696$	−2.18273	−	6.71774i	−0.0827360	−	0.254635i
$697$	0.707811	−	2.17842i	0.0268103	−	0.0825135i
$698$	−12.8113	−	9.30796i	−0.484915	−	0.352312i
$699$	−7.31279	−	5.31305i	−0.276595	−	0.200958i
$700$		0			0
$701$	−8.95068	−	27.5474i	−0.338063	−	1.04045i	−0.965194	−	0.261536i	$-0.915771\pi$
$701$	−8.95068	−	27.5474i	−0.338063	−	1.04045i	0.627131	−	0.778914i	$-0.284229\pi$
$702$	−0.295944	+	0.215016i	−0.0111697	+	0.00811525i
$703$	−17.1618			−0.647270
$704$	−7.33938	−	7.70575i	−0.276613	−	0.290421i
$705$		0			0
$706$	22.1118	−	16.0652i	0.832190	−	0.604622i
$707$	−1.23094	−	3.78843i	−0.0462941	−	0.142479i
$708$	3.23107	−	9.94422i	0.121431	−	0.373727i
$709$	21.5378	+	15.6481i	0.808870	+	0.587678i	0.913503	−	0.406833i	$-0.133367\pi$
$709$	21.5378	+	15.6481i	0.808870	+	0.587678i	−0.104633	+	0.994511i	$0.533367\pi$
$710$		0			0
$711$	3.76411	−	11.5847i	0.141165	−	0.434462i
$712$	1.21366	+	3.73527i	0.0454840	+	0.139985i
$713$	−24.6109	+	17.8808i	−0.921684	+	0.669643i
$714$	−2.01914			−0.0755644
$715$		0			0
$716$	11.0382			0.412518
$717$	−9.64652	+	7.00861i	−0.360256	+	0.261741i
$718$	−6.88875	−	21.2014i	−0.257086	−	0.791229i
$719$	3.89316	−	11.9819i	0.145190	−	0.446850i	−0.851845	−	0.523794i	$-0.824516\pi$
$719$	3.89316	−	11.9819i	0.145190	−	0.446850i	0.997035	+	0.0769437i	$0.0245162\pi$
$720$		0			0
$721$	0.0222047	+	0.0161327i	0.000826946	+	0.000600811i
$722$	−3.02092	+	9.29743i	−0.112427	+	0.346015i
$723$	−7.85381	−	24.1716i	−0.292086	−	0.898950i
$724$	−19.4393	+	14.1235i	−0.722456	+	0.524895i
$725$		0			0
$726$	8.06382	+	3.06154i	0.299276	+	0.113625i
$727$	−15.2116			−0.564169			−0.282084	−	0.959390i	$-0.591026\pi$
$727$	−15.2116			−0.564169			−0.282084	+	0.959390i	$0.591026\pi$
$728$	−1.52075	+	1.10489i	−0.0563629	+	0.0409501i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	16.5867	+	12.0510i	0.613482	+	0.445721i
$732$	12.4586	+	9.05168i	0.460482	+	0.334560i
$733$	9.44222	−	29.0602i	0.348756	−	1.07336i	−0.610786	−	0.791796i	$-0.709146\pi$
$733$	9.44222	−	29.0602i	0.348756	−	1.07336i	0.959542	−	0.281566i	$-0.0908537\pi$
$734$	6.43996	+	19.8201i	0.237703	+	0.731575i
$735$		0			0
$736$	−44.9575			−1.65716
$737$	3.02846	+	22.6821i	0.111555	+	0.835505i
$738$	1.05881			0.0389755
$739$	−7.08598	+	5.14827i	−0.260662	+	0.189382i	−0.710439	−	0.703759i	$-0.751504\pi$
$739$	−7.08598	+	5.14827i	−0.260662	+	0.189382i	0.449777	+	0.893141i	$0.351504\pi$
$740$		0			0
$741$	−0.808675	+	2.48885i	−0.0297074	+	0.0914301i
$742$	7.72036	+	5.60917i	0.283423	+	0.205919i
$743$	−24.5193	−	17.8143i	−0.899526	−	0.653544i	0.0388185	−	0.999246i	$-0.487641\pi$
$743$	−24.5193	−	17.8143i	−0.899526	−	0.653544i	−0.938344	+	0.345703i	$0.887641\pi$
$744$	−3.24633	+	9.99119i	−0.119016	+	0.366295i
$745$		0			0
$746$	12.1737	−	8.84469i	0.445710	−	0.323827i
$747$	11.7808			0.431037
$748$	−5.37456	−	5.64286i	−0.196513	−	0.206323i
$749$	−22.3117			−0.815251
$750$		0			0
$751$	0.385194	+	1.18551i	0.0140559	+	0.0432597i	0.957838	−	0.287307i	$-0.0927601\pi$
$751$	0.385194	+	1.18551i	0.0140559	+	0.0432597i	−0.943783	+	0.330567i	$0.892760\pi$
$752$	0.544549	−	1.67595i	0.0198577	−	0.0611156i
$753$	−11.9719	−	8.69810i	−0.436281	−	0.316976i
$754$	0.787519	+	0.572166i	0.0286797	+	0.0208371i
$755$		0			0
$756$	0.649754	+	1.99974i	0.0236313	+	0.0727298i
$757$	11.2746	−	8.19150i	0.409784	−	0.297725i	−0.363731	−	0.931504i	$-0.618497\pi$
$757$	11.2746	−	8.19150i	0.409784	−	0.297725i	0.773514	+	0.633779i	$0.218497\pi$
$758$	2.38446			0.0866075
$759$	22.9894	−	11.0172i	0.834462	−	0.399897i
$760$		0			0
$761$	2.56066	−	1.86043i	0.0928238	−	0.0674404i	−0.540405	−	0.841405i	$-0.681729\pi$
$761$	2.56066	−	1.86043i	0.0928238	−	0.0674404i	0.633229	+	0.773964i	$0.281729\pi$
$762$	4.39404	+	13.5235i	0.159179	+	0.489904i
$763$	−2.49458	+	7.67752i	−0.0903098	+	0.277945i
$764$	−24.8631	−	18.0641i	−0.899514	−	0.653535i
$765$		0			0
$766$	2.10651	−	6.48317i	0.0761113	−	0.234246i
$767$	1.08822	+	3.34920i	0.0392933	+	0.120932i
$768$	−11.0164	+	8.00389i	−0.397521	+	0.288816i
$769$	1.39451			0.0502874			0.0251437	−	0.999684i	$-0.491996\pi$
$769$	1.39451			0.0502874			0.0251437	+	0.999684i	$0.491996\pi$
$770$		0			0
$771$	−8.16954			−0.294219
$772$	29.4666	−	21.4087i	1.06053	−	0.770517i
$773$	1.03114	+	3.17352i	0.0370875	+	0.114144i	0.967886	−	0.251388i	$-0.0808871\pi$
$773$	1.03114	+	3.17352i	0.0370875	+	0.114144i	−0.930799	+	0.365532i	$0.880887\pi$
$774$	−2.92867	+	9.01351i	−0.105269	+	0.323984i
$775$		0			0
$776$	30.4970	+	22.1574i	1.09478	+	0.795404i
$777$	1.43513	−	4.41686i	0.0514849	−	0.158454i
$778$	3.31768	+	10.2108i	0.118945	+	0.366074i
$779$	6.12798	−	4.45224i	0.219558	−	0.159518i
$780$		0			0
$781$	23.0081	−	42.5615i	0.823295	−	1.52297i
$782$	10.2239			0.365606
$783$	2.15283	−	1.56412i	0.0769358	−	0.0558971i
$784$	−0.999598	−	3.07645i	−0.0356999	−	0.109873i
$785$		0			0
$786$	5.50119	+	3.99685i	0.196221	+	0.142563i
$787$	−12.7415	−	9.25726i	−0.454186	−	0.329986i	0.337060	−	0.941483i	$-0.390567\pi$
$787$	−12.7415	−	9.25726i	−0.454186	−	0.329986i	−0.791246	+	0.611497i	$0.790567\pi$
$788$	−4.96373	+	15.2768i	−0.176825	+	0.544213i
$789$	2.98560	+	9.18874i	0.106290	+	0.327128i
$790$		0			0
$791$	−14.5378			−0.516904
$792$	4.18654	−	7.74446i	0.148762	−	0.275187i
$793$	−5.18657			−0.184181
$794$	−5.68554	+	4.13078i	−0.201772	+	0.146596i
$795$		0			0
$796$	−6.17254	+	18.9971i	−0.218780	+	0.673335i
$797$	−20.3087	−	14.7552i	−0.719372	−	0.522655i	0.166811	−	0.985989i	$-0.446653\pi$
$797$	−20.3087	−	14.7552i	−0.719372	−	0.522655i	−0.886184	+	0.463334i	$0.846653\pi$
$798$	−5.40193	−	3.92473i	−0.191226	−	0.138934i
$799$	−1.34090	+	4.12685i	−0.0474375	+	0.145998i
$800$		0			0
$801$	−1.19704	+	0.869701i	−0.0422953	+	0.0307294i
$802$	−5.79964			−0.204793
$803$	−7.39619	−	1.35678i	−0.261006	−	0.0478799i
$804$	9.55689			0.337045
$805$		0			0
$806$	−0.447383	−	1.37690i	−0.0157584	−	0.0484994i
$807$	−0.117388	+	0.361282i	−0.00413224	+	0.0127177i
$808$	5.63511	+	4.09415i	0.198243	+	0.144032i
$809$	−38.4421	−	27.9298i	−1.35155	−	0.981960i	−0.998933	−	0.0461934i	$-0.985291\pi$
$809$	−38.4421	−	27.9298i	−1.35155	−	0.981960i	−0.352620	−	0.935767i	$-0.614709\pi$
$810$		0			0
$811$	2.03052	+	6.24930i	0.0713013	+	0.219443i	0.980357	−	0.197232i	$-0.0631953\pi$
$811$	2.03052	+	6.24930i	0.0713013	+	0.219443i	−0.909056	+	0.416675i	$0.863195\pi$
$812$	4.52664	−	3.28880i	0.158854	−	0.115414i
$813$	8.96837			0.314535
$814$	−7.17508	+	3.43850i	−0.251487	+	0.120519i
$815$		0			0
$816$	−0.945384	+	0.686862i	−0.0330951	+	0.0240450i
$817$	20.9513	+	64.4813i	0.732992	+	2.25592i
$818$	6.76176	−	20.8106i	0.236420	−	0.727625i
$819$	−0.572920	−	0.416251i	−0.0200195	−	0.0145450i
$820$		0			0
$821$	−5.04009	+	15.5118i	−0.175900	+	0.541365i	−0.999673	−	0.0255541i	$-0.991865\pi$
$821$	−5.04009	+	15.5118i	−0.175900	+	0.541365i	0.823773	+	0.566920i	$0.191865\pi$
$822$	−0.378187	−	1.16394i	−0.0131908	−	0.0405971i
$823$	−24.0864	+	17.4998i	−0.839599	+	0.610004i	−0.922259	−	0.386574i	$-0.873658\pi$
$823$	−24.0864	+	17.4998i	−0.839599	+	0.610004i	0.0826599	+	0.996578i	$0.473658\pi$
$824$	−0.0479931			−0.00167192
$825$		0			0
$826$	−8.98532			−0.312639
$827$	13.8347	−	10.0515i	0.481078	−	0.349524i	−0.320665	−	0.947193i	$-0.603906\pi$
$827$	13.8347	−	10.0515i	0.481078	−	0.349524i	0.801743	+	0.597669i	$0.203906\pi$
$828$	−3.29002	−	10.1257i	−0.114336	−	0.351891i
$829$	11.8730	−	36.5413i	0.412366	−	1.26913i	−0.502219	−	0.864740i	$-0.667483\pi$
$829$	11.8730	−	36.5413i	0.412366	−	1.26913i	0.914585	−	0.404393i	$-0.132517\pi$
$830$		0			0
$831$	2.73375	+	1.98618i	0.0948326	+	0.0689000i
$832$	0.462550	−	1.42358i	0.0160360	−	0.0493538i
$833$	2.46140	+	7.57542i	0.0852826	+	0.262473i
$834$	9.06415	−	6.58549i	0.313866	−	0.228037i
$835$		0			0
$836$	−3.41051	−	25.5436i	−0.117955	−	0.883442i
$837$	−3.95772			−0.136799
$838$	−16.1301	+	11.7192i	−0.557204	+	0.404832i
$839$	12.2300	+	37.6401i	0.422227	+	1.29948i	0.905624	+	0.424081i	$0.139403\pi$
$839$	12.2300	+	37.6401i	0.422227	+	1.29948i	−0.483397	+	0.875401i	$0.660597\pi$
$840$		0			0
$841$	17.7327	+	12.8836i	0.611473	+	0.444261i
$842$	−2.12871	−	1.54660i	−0.0733603	−	0.0532994i
$843$	1.56842	−	4.82709i	0.0540191	−	0.166254i
$844$	1.39840	+	4.30384i	0.0481350	+	0.148144i
$845$		0			0
$846$	−2.00584			−0.0689623
$847$	−0.812776	+	16.6783i	−0.0279273	+	0.573072i
$848$	5.52287			0.189656
$849$	−18.0395	+	13.1065i	−0.619114	+	0.449813i
$850$		0			0
$851$	−7.26675	+	22.3648i	−0.249101	+	0.766654i
$852$	−16.3471	−	11.8769i	−0.560044	−	0.406896i
$853$	−35.1544	−	25.5412i	−1.20366	−	0.874513i	−0.209024	−	0.977911i	$-0.567029\pi$
$853$	−35.1544	−	25.5412i	−1.20366	−	0.874513i	−0.994640	+	0.103397i	$0.967029\pi$
$854$	4.08942	−	12.5860i	0.139937	−	0.430682i
$855$		0			0
$856$	31.5632	−	22.9320i	1.07881	−	0.783801i
$857$	−22.0266			−0.752415			−0.376207	−	0.926536i	$-0.622772\pi$
$857$	−22.0266			−0.752415			−0.376207	+	0.926536i	$0.622772\pi$
$858$	0.160565	+	1.20257i	0.00548158	+	0.0410551i
$859$	−42.4022			−1.44675			−0.723373	−	0.690458i	$-0.757409\pi$
$859$	−42.4022			−1.44675			−0.723373	+	0.690458i	$0.757409\pi$
$860$		0			0
$861$	0.633413	+	1.94944i	0.0215866	+	0.0664369i
$862$	−2.51436	+	7.73841i	−0.0856395	+	0.263571i
$863$	6.50571	+	4.72668i	0.221457	+	0.160898i	0.692982	−	0.720955i	$-0.256296\pi$
$863$	6.50571	+	4.72668i	0.221457	+	0.160898i	−0.471525	+	0.881853i	$0.656296\pi$
$864$	−4.73191	−	3.43793i	−0.160983	−	0.116961i
$865$		0			0
$866$	6.58276	+	20.2596i	0.223691	+	0.688451i
$867$	−11.4254	+	8.30102i	−0.388026	+	0.281918i
$868$	−8.32170			−0.282457
$869$	−27.8629	−	29.2538i	−0.945183	−	0.992366i
$870$		0			0
$871$	−2.60402	+	1.89193i	−0.0882338	+	0.0641056i
$872$	−4.36203	−	13.4250i	−0.147717	−	0.454626i
$873$	−4.38851	+	13.5064i	−0.148529	+	0.457124i
$874$	27.3526	+	19.8728i	0.925216	+	0.672209i
$875$		0			0
$876$	−0.970452	+	2.98674i	−0.0327885	+	0.100913i
$877$	−17.7536	−	54.6399i	−0.599496	−	1.84506i	−0.530939	−	0.847410i	$-0.678161\pi$
$877$	−17.7536	−	54.6399i	−0.599496	−	1.84506i	−0.0685570	−	0.997647i	$-0.521839\pi$
$878$	−19.3982	+	14.0936i	−0.654658	+	0.475637i
$879$	−16.2166			−0.546971
$880$		0			0
$881$	−49.5171			−1.66827			−0.834137	−	0.551557i	$-0.814034\pi$
$881$	−49.5171			−1.66827			−0.834137	+	0.551557i	$0.814034\pi$
$882$	−2.97881	+	2.16423i	−0.100302	+	0.0728735i
$883$	−8.06367	−	24.8174i	−0.271364	−	0.835173i	−0.990159	−	0.139950i	$-0.955306\pi$
$883$	−8.06367	−	24.8174i	−0.271364	−	0.835173i	0.718794	−	0.695223i	$-0.244694\pi$
$884$	0.338721	−	1.04248i	0.0113924	−	0.0350623i
$885$		0			0
$886$	−2.59137	−	1.88274i	−0.0870588	−	0.0632519i
$887$	−3.25459	+	10.0166i	−0.109278	+	0.336324i	−0.990711	−	0.135986i	$-0.956580\pi$
$887$	−3.25459	+	10.0166i	−0.109278	+	0.336324i	0.881432	+	0.472310i	$0.156580\pi$
$888$	2.50947	+	7.72335i	0.0842122	+	0.259179i
$889$	−22.2702	+	16.1803i	−0.746919	+	0.542668i
$890$		0			0
$891$	3.26219	+	0.598429i	0.109287	+	0.0200481i
$892$	25.1104			0.840757
$893$	−11.6090	+	8.43443i	−0.388480	+	0.282248i
$894$	−2.66897	−	8.21423i	−0.0892636	−	0.274725i
$895$		0			0
$896$	−11.2763	−	8.19272i	−0.376715	−	0.273700i
$897$	2.90098	+	2.10768i	0.0968608	+	0.0703735i
$898$	−4.91965	+	15.1411i	−0.164171	+	0.505266i
$899$	3.25447	+	10.0162i	0.108542	+	0.334059i
$900$		0			0
$901$	−13.5995			−0.453064
$902$	1.66997	−	3.08920i	0.0556040	−	0.102859i
$903$	−18.3473			−0.610560
$904$	20.5659	−	14.9420i	0.684011	−	0.496963i
$905$		0			0
$906$	−1.04727	+	3.22315i	−0.0347931	+	0.107082i
$907$	12.1086	+	8.79742i	0.402060	+	0.292114i	0.770379	−	0.637586i	$-0.220067\pi$
$907$	12.1086	+	8.79742i	0.402060	+	0.292114i	−0.368320	+	0.929699i	$0.620067\pi$
$908$	31.5430	+	22.9174i	1.04679	+	0.760539i
$909$	−0.810890	+	2.49566i	−0.0268955	+	0.0827760i
$910$		0			0
$911$	−1.62459	+	1.18034i	−0.0538252	+	0.0391063i	−0.614373	−	0.789016i	$-0.710591\pi$
$911$	−1.62459	+	1.18034i	−0.0538252	+	0.0391063i	0.560547	+	0.828122i	$0.310591\pi$
$912$	−3.86434			−0.127961
$913$	18.5808	−	34.3717i	0.614935	−	1.13754i
$914$	−20.2417			−0.669535
$915$		0			0
$916$	7.85925	+	24.1883i	0.259677	+	0.799203i
$917$	−4.06787	+	12.5196i	−0.134333	+	0.413434i
$918$	1.07609	+	0.781829i	0.0355164	+	0.0258042i
$919$	13.5903	+	9.87393i	0.448303	+	0.325711i	0.788925	−	0.614489i	$-0.210638\pi$
$919$	13.5903	+	9.87393i	0.448303	+	0.325711i	−0.340623	+	0.940200i	$0.610638\pi$
$920$		0			0
$921$	−9.25638	−	28.4882i	−0.305008	−	0.938719i
$922$	1.61146	−	1.17080i	0.0530707	−	0.0385581i
$923$	6.80541			0.224003
$924$	6.85924	+	1.25829i	0.225652	+	0.0413945i
$925$		0			0
$926$	1.82445	−	1.32554i	0.0599551	−	0.0435600i
$927$	−0.00558722	−	0.0171957i	−0.000183508	−	0.000564781i
$928$	−4.80964	+	14.8026i	−0.157884	+	0.485918i
$929$	−27.4390	−	19.9356i	−0.900246	−	0.654067i	0.0382835	−	0.999267i	$-0.487811\pi$
$929$	−27.4390	−	19.9356i	−0.900246	−	0.654067i	−0.938529	+	0.345200i	$0.887811\pi$
$930$		0			0
$931$	−8.13969	+	25.0514i	−0.266767	+	0.821026i
$932$	3.86902	+	11.9076i	0.126734	+	0.390047i
$933$	4.13425	−	3.00371i	0.135349	−	0.0983371i
$934$	17.9037			0.585828
$935$		0			0
$936$	1.23831			0.0404753
$937$	−16.6188	+	12.0742i	−0.542911	+	0.394448i	−0.825165	−	0.564892i	$-0.808918\pi$
$937$	−16.6188	+	12.0742i	−0.542911	+	0.394448i	0.282254	+	0.959340i	$0.408918\pi$
$938$	−2.53786	−	7.81074i	−0.0828641	−	0.255030i
$939$	7.75958	−	23.8815i	0.253224	−	0.779345i
$940$		0			0
$941$	−42.7681	−	31.0728i	−1.39420	−	1.01295i	−0.995390	−	0.0959115i	$-0.969423\pi$
$941$	−42.7681	−	31.0728i	−1.39420	−	1.01295i	−0.398810	−	0.917034i	$-0.630577\pi$
$942$	−0.225709	+	0.694662i	−0.00735401	+	0.0226333i
$943$	−3.20728	−	9.87099i	−0.104443	−	0.321444i
$944$	−4.20703	+	3.05659i	−0.136927	+	0.0994834i
$945$		0			0
$946$	21.6787	+	22.7609i	0.704835	+	0.740020i
$947$	28.1947			0.916206			0.458103	−	0.888899i	$-0.348529\pi$
$947$	28.1947			0.916206			0.458103	+	0.888899i	$0.348529\pi$
$948$	−13.6499	+	9.91727i	−0.443330	+	0.322098i
$949$	−0.326847	−	1.00593i	−0.0106099	−	0.0326539i
$950$		0			0
$951$	10.0471	+	7.29966i	0.325800	+	0.236708i
$952$	5.52969	+	4.01755i	0.179218	+	0.130210i
$953$	−3.40489	+	10.4792i	−0.110295	+	0.339453i	−0.990937	−	0.134330i	$-0.957112\pi$
$953$	−3.40489	+	10.4792i	−0.110295	+	0.339453i	0.880642	+	0.473783i	$0.157112\pi$
$954$	−1.94262	−	5.97878i	−0.0628948	−	0.193570i
$955$		0			0
$956$	16.5160			0.534167
$957$	−1.16802	−	8.74805i	−0.0377567	−	0.282784i
$958$	18.7458			0.605649
$959$	1.91676	−	1.39261i	0.0618953	−	0.0449696i
$960$		0			0
$961$	−4.73921	+	14.5858i	−0.152878	+	0.470510i
$962$	−0.905406	−	0.657816i	−0.0291915	−	0.0212088i
$963$	11.8909	+	8.63928i	0.383180	+	0.278397i
$964$	−10.8786	+	33.4809i	−0.350377	+	1.07835i
$965$		0			0
$966$	−7.40191	+	5.37780i	−0.238152	+	0.173028i
$967$	−49.0215			−1.57643			−0.788213	−	0.615403i	$-0.788993\pi$
$967$	−49.0215			−1.57643			−0.788213	+	0.615403i	$0.788993\pi$
$968$	−15.9922	−	24.4293i	−0.514009	−	0.785188i
$969$	9.51553			0.305683
$970$		0			0
$971$	0.315326	+	0.970472i	0.0101193	+	0.0311439i	0.955989	−	0.293404i	$-0.0947880\pi$
$971$	0.315326	+	0.970472i	0.0101193	+	0.0311439i	−0.945869	+	0.324548i	$0.894788\pi$
$972$	0.428031	−	1.31734i	0.0137291	−	0.0422539i
$973$	17.5474	+	12.7489i	0.562543	+	0.408711i
$974$	8.66087	+	6.29249i	0.277512	+	0.201624i
$975$		0			0
$976$	−2.36672	−	7.28401i	−0.0757568	−	0.233155i
$977$	39.1393	−	28.4364i	1.25218	−	0.909760i	0.253831	−	0.967249i	$-0.418309\pi$
$977$	39.1393	−	28.4364i	1.25218	−	0.909760i	0.998346	+	0.0574890i	$0.0183094\pi$
$978$	13.2976			0.425210
$979$	0.649455	+	4.86419i	0.0207567	+	0.155460i
$980$		0			0
$981$	4.30228	−	3.12579i	0.137361	−	0.0997988i
$982$	−10.4490	−	32.1587i	−0.333440	−	1.02622i
$983$	19.0098	−	58.5062i	0.606319	−	1.86606i	0.118859	−	0.992911i	$-0.462076\pi$
$983$	19.0098	−	58.5062i	0.606319	−	1.86606i	0.487460	−	0.873146i	$-0.337924\pi$
$984$	−2.89970	−	2.10676i	−0.0924392	−	0.0671610i
$985$		0			0
$986$	1.09377	−	3.36628i	0.0348328	−	0.107204i
$987$	−1.19995	−	3.69308i	−0.0381949	−	0.117552i
$988$	2.93253	−	2.13061i	0.0932962	−	0.0677837i
$989$	92.9014			2.95409
$990$		0			0
$991$	31.0431			0.986117			0.493059	−	0.869996i	$-0.335879\pi$
$991$	31.0431			0.986117			0.493059	+	0.869996i	$0.335879\pi$
$992$	18.7276	−	13.6064i	0.594602	−	0.432003i
$993$	−2.58194	−	7.94640i	−0.0819355	−	0.252171i
$994$	−5.36581	+	16.5143i	−0.170193	+	0.523801i
$995$		0			0
$996$	−13.2016	−	9.59150i	−0.418308	−	0.303918i
$997$	−14.7103	+	45.2735i	−0.465879	+	1.43383i	0.391996	+	0.919967i	$0.371785\pi$
$997$	−14.7103	+	45.2735i	−0.465879	+	1.43383i	−0.857874	+	0.513860i	$0.828215\pi$
$998$	−2.89279	−	8.90310i	−0.0915697	−	0.281823i
$999$	−2.47509	+	1.79826i	−0.0783085	+	0.0568945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.o.751.5		24
5.2	odd	4		165.2.s.a.124.8	yes	48
5.3	odd	4		165.2.s.a.124.5	yes	48
5.4	even	2		825.2.n.p.751.2		24
11.2	odd	10		9075.2.a.dx.1.9		12
11.4	even	5	inner	825.2.n.o.301.5		24
11.9	even	5		9075.2.a.dz.1.4		12
15.2	even	4		495.2.ba.c.289.5		48
15.8	even	4		495.2.ba.c.289.8		48
55.2	even	20		1815.2.c.k.364.16		24
55.4	even	10		825.2.n.p.301.2		24
55.9	even	10		9075.2.a.dy.1.9		12
55.13	even	20		1815.2.c.k.364.9		24
55.24	odd	10		9075.2.a.ea.1.4		12
55.37	odd	20		165.2.s.a.4.5	✓	48
55.42	odd	20		1815.2.c.j.364.9		24
55.48	odd	20		165.2.s.a.4.8	yes	48
55.53	odd	20		1815.2.c.j.364.16		24
165.92	even	20		495.2.ba.c.334.8		48
165.158	even	20		495.2.ba.c.334.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.5	✓	48	55.37	odd	20
165.2.s.a.4.8	yes	48	55.48	odd	20
165.2.s.a.124.5	yes	48	5.3	odd	4
165.2.s.a.124.8	yes	48	5.2	odd	4
495.2.ba.c.289.5		48	15.2	even	4
495.2.ba.c.289.8		48	15.8	even	4
495.2.ba.c.334.5		48	165.158	even	20
495.2.ba.c.334.8		48	165.92	even	20
825.2.n.o.301.5		24	11.4	even	5	inner
825.2.n.o.751.5		24	1.1	even	1	trivial
825.2.n.p.301.2		24	55.4	even	10
825.2.n.p.751.2		24	5.4	even	2
1815.2.c.j.364.9		24	55.42	odd	20
1815.2.c.j.364.16		24	55.53	odd	20
1815.2.c.k.364.9		24	55.13	even	20
1815.2.c.k.364.16		24	55.2	even	20
9075.2.a.dx.1.9		12	11.2	odd	10
9075.2.a.dy.1.9		12	55.9	even	10
9075.2.a.dz.1.4		12	11.9	even	5
9075.2.a.ea.1.4		12	55.24	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.634375 - 0.460901i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.428031 + 1.31734i) q^{4} +(-0.634375 - 0.460901i) q^{6} +(0.469090 - 1.44371i) q^{7} +(0.820252 + 2.52448i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.634375 - 0.460901i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.428031 + 1.31734i) q^{4} +(-0.634375 - 0.460901i) q^{6} +(0.469090 - 1.44371i) q^{7} +(0.820252 + 2.52448i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.438933 + 3.28745i) q^{11} +1.38514 q^{12} +(-0.377416 + 0.274209i) q^{13} +(-0.367828 - 1.13206i) q^{14} +(-0.557320 - 0.404916i) q^{16} +(1.37234 + 0.997064i) q^{17} +(-0.242310 + 0.745753i) q^{18} +(1.73345 + 5.33501i) q^{19} -1.51801 q^{21} +(1.79364 + 1.88317i) q^{22} +7.68641 q^{23} +(2.14745 - 1.56021i) q^{24} +(-0.113040 + 0.347903i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.70108 + 1.23591i) q^{28} +(0.822307 - 2.53080i) q^{29} +(-3.20187 + 2.32629i) q^{31} -5.84896 q^{32} +(2.99091 - 1.43333i) q^{33} +1.33013 q^{34} +(-0.428031 - 1.31734i) q^{36} +(-0.945402 + 2.90965i) q^{37} +(3.55857 + 2.58545i) q^{38} +(0.377416 + 0.274209i) q^{39} +(-0.417266 - 1.28421i) q^{41} +(-0.962986 + 0.699650i) q^{42} +12.0864 q^{43} +(-4.51858 - 0.828906i) q^{44} +(4.87607 - 3.54267i) q^{46} +(0.790480 + 2.43285i) q^{47} +(-0.212877 + 0.655168i) q^{48} +(3.79887 + 2.76004i) q^{49} +(0.524187 - 1.61328i) q^{51} +(-0.199682 - 0.614557i) q^{52} +(-6.48598 + 4.71234i) q^{53} +0.784131 q^{54} +4.02938 q^{56} +(4.53823 - 3.29722i) q^{57} +(-0.644797 - 1.98448i) q^{58} +(2.33267 - 7.17923i) q^{59} +(8.99446 + 6.53486i) q^{61} +(-0.958996 + 2.95149i) q^{62} +(0.469090 + 1.44371i) q^{63} +(-2.59580 + 1.88596i) q^{64} +(1.23674 - 2.28778i) q^{66} +6.89959 q^{67} +(-1.90088 + 1.38107i) q^{68} +(-2.37523 - 7.31021i) q^{69} +(-11.8018 - 8.57452i) q^{71} +(-2.14745 - 1.56021i) q^{72} +(-0.700618 + 2.15628i) q^{73} +(0.741319 + 2.28155i) q^{74} -7.77002 q^{76} +(4.95202 + 0.908418i) q^{77} +0.365807 q^{78} +(-9.85457 + 7.15977i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.856598 - 0.622355i) q^{82} +(-9.53087 - 6.92458i) q^{83} +(0.649754 - 1.99974i) q^{84} +(7.66735 - 5.57065i) q^{86} -2.66104 q^{87} +(-7.93906 + 3.80462i) q^{88} +1.47962 q^{89} +(0.218836 + 0.673508i) q^{91} +(-3.29002 + 10.1257i) q^{92} +(3.20187 + 2.32629i) q^{93} +(1.62276 + 1.17901i) q^{94} +(1.80743 + 5.56269i) q^{96} +(11.4893 - 8.34744i) q^{97} +3.68201 q^{98} +(-2.28742 - 2.40161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

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